Fire Dynamics Tools (FDTs

) 

Quantitative Fire Hazard 

Analysis Methods for the 

U.S. Nuclear Regulatory 

Commission Fire Protection 

Inspection Program

Supplement 1

Office of Nuclear Regulatory Research

NUREG-1805

Supplement 1, Vol. 1
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Fire Dynamics Tools (FDTs

)

Quantitative Fire Hazard 

Analysis Methods for the U.S. 

Nuclear Regulatory Commission 

Fire Protection Inspection 

Program

Supplement 1

Manuscript Completed: June 2013

Date Published: July 2013

Prepared by: 

D. Stroup*, G. Taylor*, G. Hausman**

*Office of Nuclear Regulatory Research

**Region III

M. H. Salley, NRC Project Manager

Office of Nuclear Regulatory Research

NUREG-1805

Supplement 1, Vol. 1

iii 

ABSTRACT 

The U.S. Nuclear Regulatory Commission (NRC) has developed quantitative methods, known 

as “Fire Dynamics Tools” (FDTs

), for analyzing the impact of fire and fire protection systems in 

nuclear power plants (NPPs). These methods have been implemented in spreadsheets and 

taught at the NRC’s quarterly regional inspector workshops. The FDTs

 were developed using 

state-of-the-art fire dynamics equations and correlations that were preprogrammed and locked 

into Microsoft Excel® spreadsheets. These FDTs

 enable inspectors to perform quick, easy, firstorder calculations for potential fire scenarios using today’s state-of-the-art principles of fire 

dynamics. Each FDTs

 spreadsheet also contains a list of the physical and thermal properties of 

the materials commonly encountered in NPPs. 

This NUREG-series report documents a new spreadsheet that has been added to the FDTs

suite and describes updates, corrections, and improvements to the existing spreadsheets. The 

majority of the original FDTs

 were developed using principles and information from the Society 

of Fire Protection Engineers (SFPE) Handbook of Fire Protection Engineering, the National Fire 

Protection Association (NFPA) Fire Protection Handbook, and other fire science literature. The 

new spreadsheet predicts the behavior of power cables, instrument cables, and control cables 

during a fire. The thermally-induced electrical failure (THIEF) model was developed by the 

National Institute of Standards and Technology (NIST) as part of the Cable Response to Live 

Fire (CAROLFIRE) program sponsored by the NRC. The experiments for CAROLFIRE were 

conducted at Sandia National Laboratories, Albuquerque, New Mexico. THIEF model 

predictions have been compared to experimental measurements of instrumented cables in a 

variety of configurations, and the results indicate that the model is an appropriate analysis tool 

for NPP applications. The accuracy and simplicity of the THIEF model have been shown to be 

comparable to that of the activation algorithms for various fire protection devices (e.g., 

sprinklers, heat and smoke detectors). 

v 

CONTENTS 

ABSTRACT ................................................................................................................................. iii

CONTENTS .................................................................................................................................. v

FIGURES .................................................................................................................................... vii

TABLES ...................................................................................................................................... vii

EXECUTIVE SUMMARY ............................................................................................................. ix

ACKNOWLEDGMENTS .............................................................................................................. xi

ABBREVIATIONS ..................................................................................................................... xiii

NOMENCLATURE .................................................................................................................... xix

CHAPTER 1. INTRODUCTION ......................................................................................... 1-1

1.1 Purpose ........................................................................................... 1-1

1.2 Organization of this Report .............................................................. 1-1

CHAPTER 19. ESTIMATING THE THERMALLY-INDUCED ELECTRICAL FAILURE 

(THIEF) OF CABLES ................................................................................ 19-1

19.1 Objectives ...................................................................................... 19-1

19.2 Introduction .................................................................................... 19-1

19.3 Thermally-Induced Electrical Failure (THIEF) of Cables ............... 19-4

19.3.1 General ......................................................................... 19-4

19.3.2 Cable Properties and Selection Process ....................... 19-6

19.3.3 Exposure Gas Temperature .......................................... 19-8

19.4 Assumptions and Limitations ....................................................... 19-10

19.5 Required Input for Spreadsheet Calculations .............................. 19-10

19.6 Cautions ...................................................................................... 19-11

19.7 Summary ..................................................................................... 19-11

19.8 Decision Criteria .......................................................................... 19-11

19.9 References .................................................................................. 19-11

19.10 Additional Readings ..................................................................... 19-12

19.11 Problems ..................................................................................... 19-14

Example Problem 19.11-1 (SI Units) ........................................... 19-14

Example Problem 19.11-2 ........................................................... 19-19

Example Problem 19.11-3 ........................................................... 19-34

Example Problem 19.11-4 ........................................................... 19-48

Example Problem 19.11-5 (SI Units) ........................................... 19-78

Example Problem 19.11-6 (SI Units) ......................................... 19-108

APPENDIX A. REVISED SPREADSHEETS – EXAMPLE PROBLEMS (ENGLISH UNITS) .. A-1 

APPENDIX B. REVISED SPREADSHEETS – EXAMPLE PROBLEMS (SI UNITS) ............... B-1

 

vii 

FIGURES 

Figure 19-1. Different signal responses from a thermoset cable (top) and a thermoplastic 

cable (bottom) when exposed to a fire ............................................................. 19-3 

Figure 19-2. Drawing showing the four possible locations for a cable tray relative to the 

 fire .................................................................................................................... 19-9 

Figure 19-3. Schematic (left) and photograph (right) of the “penlight” test apparatus ........ 19-14 

Figure 19-4. Results comparing data (short dash line) for XLPE/CSPE, 7 conductor cable 

exposed to a shroud temperature (long dash line) of 475 °C and THIEF 

prediction (solid line) ...................................................................................... 19-15 

TABLES 

Table 1-1. List of Fire Dynamics Tools ................................................................................ 1-1 

Table 1-2. Summary of Technical Changes to Original NUREG-1805 Spreadsheets ......... 1-5 

Table 19-1. Common Thermoplastic and Thermoset Cable Insulation and Jacket 

 Materials ........................................................................................................... 19-8 

 

ix 

EXECUTIVE SUMMARY 

The U.S. Nuclear Regulatory Commission (NRC) has developed quantitative methods, known 

as “Fire Dynamics Tools” (FDTs

), for analyzing the impact of fire and fire protection systems in 

nuclear power plants (NPPs). These methods have been implemented in spreadsheets and 

taught at the NRC’s quarterly regional inspector workshops. The goal of the training is to assist 

inspectors in calculating the quantitative aspects of a postulated fire and its effects on safe NPP 

operation. The FDTs

 were developed using state-of-the-art fire dynamics equations and 

correlations that were preprogrammed and locked into Microsoft Excel® spreadsheets. These 

FDTs

 enable inspectors to perform quick, easy, first-order calculations for potential fire 

scenarios using today’s state-of-the-art principles of fire dynamics. Each FDTs

 spreadsheet 

also contains a list of the physical and thermal properties of the materials commonly 

encountered in NPPs. 

The FDTs

 are intended to assist fire protection inspectors in performing risk-informed 

evaluations of credible fires that may cause critical damage to essential safe-shutdown 

equipment, as required by the reactor oversight process (ROP) defined in the NRC’s inspection 

manual. In the ROP, the NRC is moving toward a more risk-informed, objective, predictable, 

understandable, and focused regulatory process. Key features of the program are a riskinformed regulatory framework, risk-informed inspections, a significance determination process 

(SDP) to evaluate inspection findings, performance indicators, a streamlined assessment 

process, and more clearly defined actions that the NRC will take for plants based on their 

performance. 

This NUREG-series report documents a new spreadsheet that has been added to the FDTs

suite and describes updates, corrections and improvements for the existing spreadsheets. The 

majority of the original FDTs

 were developed from the Society of Fire Protection Engineers 

(SFPE) Handbook of Fire Protection Engineering, the National Fire Protection Association 

(NFPA) Fire Protection Handbook, and other fire science literature. The new spreadsheet 

predicts the behavior of power cables, instrument cables, and control cables during a fire. The 

thermally-induced electrical failure (THIEF) model was developed by the National Institute of 

Standards and Technology (NIST) as part of the Cable Response to Live Fire (CAROLFIRE) 

program sponsored by the NRC. 

The primary objective of CAROLFIRE was to characterize the various modes of electrical failure 

(e.g. hot shorts, shorts to ground) within bundles of power, control and instrument cables. A 

secondary objective of the project was to develop a simple model to predict thermally-induced 

electrical failure (THIEF) when a given interior region of the cable reaches an empirically 

determined threshold temperature. The experiments for CAROLFIRE were conducted at 

Sandia National Laboratories. 

The THIEF model for cables has been shown to work effectively in realistic fire environments. 

The THIEF model is essentially a numerical solution of the one dimensional heat conduction 

equation within a homogenous cylinder with fixed, temperature independent properties. THIEF 

model predictions have been compared to experimental measurements of instrumented cables 

in a variety of configurations, and the results indicate that the model is an appropriate analysis 

tool for NPP applications. The model is of comparable accuracy and simplicity to the activation 

algorithms for various fire protection devices (e.g., sprinklers, heat and smoke detectors). 

xi 

ACKNOWLEDGMENTS 

Since the publication of NUREG-1805, Fire Dynamics Tools (FDTs

) Quantitative Fire Hazard 

Analysis Methods for the U.S. Nuclear Regulatory Commission Fire Protection Inspection 

Program, numerous comments and suggestions for additions, improvements, and a few 

corrections have been received from users throughout the world. This supplement addresses 

many of the issues identified by users and adds a new spreadsheet to the suite of FDTs

. The 

authors thank the internal and external stakeholders who have taken the time to provide 

comments and suggestions on the original report. We hope this supplement will receive similar 

attention and appreciate any feedback from users of the material in this supplement. 

The authors gratefully acknowledge the support and assistance provided by Naeem Iqbal and 

Mark Henry Salley of the U.S. Nuclear Regulatory Commission (NRC). They published the 

original NUREG-1805 in December 2004. The general concepts used in creating and 

developing the FDTs

 spreadsheets were similar to those taught by Dr. Frederick Mowrer whose 

fire modeling course they had attended during their postgraduate studies at the University of 

Maryland. 

We acknowledge and appreciate the contributions of Mollie Semmes, a fire protection 

engineering student at the University of Maryland. Mollie’s hard work and diligence during her 

summer internships at NRC ensured that this report was published in a timely fashion and with 

completely revised and tested spreadsheets. The authors also thank Nicolas Melly, David 

Gennardo, and Kendra Hill in the Fire Research Branch of the NRC Office of Nuclear 

Regulatory Research for their comments and testing of the spreadsheets. 

The new spreadsheet added to the FDTs

 implements a methodology for estimating the 

thermally-induced electrical failure of cables. This THIEF model was derived from an algorithm 

developed by Dr. Kevin McGrattan at the National Institute of Standards and Technology based 

on data obtained from cable tests conducted at Sandia National Laboratories by Mr. Steven 

Nowlen. 

Finally, the authors would like to thank H.W. ‘Roy’ Woods who provided invaluable support in 

publishing this report. In addition, we greatly appreciate the efforts of Guy Beltz, NRC printing 

specialist, and Tojuana Fortune-Grasty, NRC NUREG technical editor, whose expertise were 

critical to ensuring the quality of the published manuscript. 

xiii 

ABBREVIATIONS 

ABS Acrylonitrile Butadiene Styrene 

ACRS Advisory Committee on Reactor Safeguards (NRC) 

ADAMS Agencywide Documents Access and Management System (NRC) 

ADS Automatic Depressurization System 

AFFF Aqueous Film Forming Foam 

AFT Adiabatic Flame Temperature 

AFW Auxiliary Feedwater 

AGA American Gas Association 

AHJ Authority Having Jurisdiction 

AISI American Iron and Steel Institute 

AL Administrative Letter 

ALC Approximate Lethal Concentration 

ANS American Nuclear Society 

ANSI American National Standards Institute 

API American Petroleum Institute 

ASCE American Society of Civil Engineers 

ASCOS Analysis of Smoke Control Systems 

ASET Available Safe Egress Time 

ASHRAE American Society of Heating, Refrigeration, and Air Conditioning Engineers 

ASME American Society of Mechanical Engineers 

ASMET Atria Smoke Management Engineering Tools 

ASTM American Society for Testing and Materials 

AT Auxiliary Transformer 

ATF&E Alcohol, Tobacco, Firearms, and Explosives 

AWG American Wire Gauge 

BFC Bromochlorodifluoro-methane 

BFNP Browns Ferry Nuclear Power Plant 

BFRL Building and Fire Research Laboratory 

BL Bulletin 

BLEVE Boiling Liquid, Expanding Vapor Explosion 

BOCA Building Officials & Code Administration International 

BREAK1 Berkeley Algorithm for Breaking Window Glass in a Compartment Fire 

BS British Standard 

BTP Branch Technical Position 

BTU British Thermal Unit 

BWR Boiling-Water Reactor 

CAROLFIRE Cable Response to Live Fire 

CCW Component Cooling Water 

CFAST Consolidate Model of Fire Growth and Smoke Transport 

CFD Computational Fluid Dynamics 

CFI Certified Fire Inspector 

CFO Chief Financial Officer (NRC) 

CFR Code of Federal Regulations 

CHF Critical Heat Flux 

CIB Conseil Internationale du Batiment 

CIBSI Chartered Institution of Building Services Engineers 

CIO Chief Information Officer (NRC) 

CL.S.PE Chlorosulfonated Polyethylene 

xv 

FRXPE Fire-Retardant Crosslinked Polyethylene 

FSSD Post-Fire Safe-Shutdown 

FTA Federal Transit Authorization 

FTMS Federal Test Method Standard 

GDC General Design Criteria 

GL Generic Letter 

GSA General Service Administration 

GSI Generic Safety Issue 

H2O Water 

HBr Hydrogen Bromide 

HCI Hydrogen Chloride 

HCN Hydrogen Cyanide 

HEPA High-Efficiency Particulate Air Filter 

HF Hydrogen Fluoride 

HPCI High Pressure Cooling Injection 

HRR Heat Release Rate 

HTGR High-Temperature Gas-Cooled Reactor 

HVAC Heating, Ventilation, and Air Conditioning 

IAFSS International Association of Fire Safety Science 

IBC International Building Code 

ICBO International Conference of Building Officials 

ICS Integrated Control System 

ICSDTS International Committee for the Study and Development of Tubular Structures 

IE Initiative Events 

IEC International Electrotechnical Commission 

IEEE Institute of Electrical and Electronic Engineers 

IN Information Notice 

INEEL Idaho National Engineering and Environmental Laboratory 

IPEEE Individual Plant Examination of External Events 

ISO International Organization for Standardization 

LAVENT Link Actuation Vents 

LC Lethal Concentration LCL Lethal Concentration Low 

LD Lethal Dose 

LDL Lethal Dose Low 

LEL Lower Explosive Limit 

LER Licensee Event Report 

LFL Lower Flammability Limit 

LIFT Lateral Ignition and Flame Spread (ASTM E 1321 Standard Test Method) 

LLNL Lawrence Livermore National Laboratory 

LNG Liquified Natural Gas 

LOC Limiting Oxidant Concentration 

LOCA Loss-of-Coolant Accident 

LPG Liquid Propane Gas 

LWR Light-Water Reactor 

MCC Motor Control Center 

MCR Main Control Room 

MESG Maximum Experimental Safe Gap 

MOV Motor-Operated Valve 

MQH McCaffrey, Quintiere, and Harkleroad 

NBC National Building Code 

NBR Nitrile 
xvi 

NBS National Bureau of Standards 

NEA Nuclear Energy Agency 

NEI Nuclear Energy Institute 

NEMA National Electrical Manufacturers Association 

NFC National Fire Code 

NFPA National Fire Protection Association 

NIOSH National Institute of Occupational Safety and Health 

NIST National Institute of Standards and Technology 

NO2 Nitrogen Dioxide 

NOUN Notification of Unusual Event 

NPP Nuclear Power Plant 

NRC U.S. Nuclear Regulatory Commission 

NRR Office of Nuclear Reactor Regulation (NRC) 

NUREG NUclear REGulatory Guide 

OCIO Office of Chief Information Officer (NRC) 

OL Operating License 

ORNL Oak Ridge National Laboratory 

OSHA Occupational Safety and Health Administration 

OSU Ohio State University 

PASS Personal Alert Safety System 

PC Polycarbonate 

PDA Primary Disconnect Assembly 

PE Polyethylene 

PEF Polyethylene Fluoride 

PES Polyethersulphone 

PFA Perfluoroalkoxy Branched Polymers 

PMMA Polymethylmethacrylate 

PP Polypropylene 

PPE Polytetrafluoroethylene 

PRA Probabilistic Risk Assessment 

PS Polystyrene 

PTEF Polytetrafluoroethylene (Teflon®) 

PU Polyurethane 

PVC Polyvinylchloride 

PVF Polyvinylfluoride 

RCP Reactor Coolant Pump 

RES Office of Nuclear Regulatory Research (NRC) 

RG Regulatory Guide 

RHR Residual Heat Removal 

RIS Regulatory Issue Summary 

RMV Respiratory Minute Volume 

ROP Reactor Oversight Process 

RTECS Registry of the Toxic Effects of Chemical Substance 

RTI Response Time Index 

RWFD Red Wing Fire Department 

S/G Steam Generator 

SBC Standard Building Code 

SBCCI Southern Building Code Congress International 

SBDG Standby Diesel Generator 

SBR Styrene Butadiene Rubber 

SCBA Self-Contained Breathing Apparatus 
xvii 

SDP Significance Determination Process 

SER Significant Event Report 

SFPE Society of Fire Protection Engineers 

SI System International 

SNL Sandia National Laboratories 

SOLAS Safety of Lives at Sea 

SONGS San Onofre Nuclear Generating Station 

SPLB Plant Systems Branch (NRC) 

SRP Standard Review Plan (NUREG-0800) 

SSC Structure, System, and/or Component 

TASEF Temperature Analysis of Structure Exposed to Fire 

TCL Toxic Concentration Low 

TDL Toxic Dose Low 

TFE Tetrafluoroethylene (Teflon®) 

THIEF Thermally-Induced Electrical Failure 

TLC Toxic Concentration Low 

TLV Threshold Limit Value 

TNT Trinitrotoluene 

TP Thermoplastic 

TRP Thermal Response Parameter 

TS Thermoset 

TSC Technical Support Center 

TTC Time-Temperature Curve 

TVA Tennessee Valley Authority 

TVAN Tennessee Valley Authority Nuclear Program 

UBC Uniform Building Code 

UEL Upper Explosive Limit 

UFC Uniform Fire Code 

UFL Upper Flammability Limit 

UL Underwriters Laboratories 

UPS Uninterruptible Power Supply 

USFA United States Fire Administration 

UVCE Unconfined Vapor Cloud Explosion 

V&V Verification and Validation 

VRLA Valve-Regulated Lead Acid 

W/D Weight-to-Heated Perimeter Ratio 

XLPE Crosslinked Polyethylene 

XLPO Crosslinked Polyolefin 
xviii 
xix 

NOMENCLATURE 

Ac Compartment floor area 

Ae Surface of element 

Af Horizontal burning area of fuel 

AH Ampere hours 

As Cross sectional area 

AT Area of compartment enclosing surfaces (excluding vent areas) 

Av Area of ventilation openings 

B Flame spread parameter 

C Gas concentration by volume 

C Thermal capacity 

Ci Specific heat of insulation 

Cp Specific heat 

Cs Specific heat of steel 

Cv Specific heat at constant volume 

CHF Critical heat flux for ignition 

D Diameter 

D Heated parameter 

DSC Scaled distance 

E Emissive power 

E Explosive energy released 

F Configuration or shape factor 

F Fire resistance time 

FTP Flux time product 

Fc Float Current per 100 AH 

g Acceleration of gravity 

G Gas discharge rate 

H Thickness of insulation 

h Heat flux time product index 

hc Compartment height 

heff Effective heat transfer coefficient 

hig Heat transfer coefficient at ignition 

hk Convective heat transfer coefficient 

hv Height of ventilation opening 

H Thermal capacity of steel section at ambient 

H Height 

Hg Hydrogen gas generation 

hf Flame height 

hf(wall) Wall flame height 

hf(wall,line) Line fire flame height 

hf(corner) Corner fire flame height 

k Thermal conductivity 

ki Thermal conductivity of insulation 

kc Thermal inertia 

K Mixing efficiency factor 

K Proportionality constant 

Lc Compartment length 

L Length 

LFL Lower flammability limit 
xx 

m mass 

mf Mass of fuel vapor 

mf Mass of fuel burned 

mp Mass concentration of particulate 

m Mass flow rate 

me Mass entrainment rate 

mf Mass flow rate of fuel 

mo Mass flow rate out of enclosure 

mp Plume mass flow rate 

m” Mass loss rate per unit area 

Mp Mass of particulates produced 

N Number of cells (batteries) 

N Number of theoretical air changes 

P Pressure 

q” Heat flux 

q”crit Critical heat flux 

q”e External heat flux 

q”min Minimum heat flux required for ignition 

q”r Radiative heat flux 

Q Volume of air 

Qtotal Total energy release 

Q Heat release rate or energy release rate 

Qc Convective energy release rate 

QFO Energy release rate to cause flashover 

Qfs Full-scale energy release rate 

Qbs Bench-scale energy release rate 

R Radius 

R Radial distance 

R Fire Resistance 

RTI Response time index 

S Visibility 

T Time 

Tb Burning duration 

tD Detection time 

tig Ignition time 

tp Thermal penetration time 

tr Detector response time 

tt Smoke transit time 

tactivation Sprinkler activation time 

T Temperature 

Ta Ambient temperature 

Tf Fire temperature 

TFO(max) Post-flashover compartment temperature 

Tg Gas temperature 

Ts Steel temperature 

Tjet Ceiling jet temperature 

Tp(centerline) Plume centerline temperature 

Tactivation Activation temperature 

Ujet Ceiling jet velocity 

Uw Wind velocity 

Uo Gas velocity 
xxi 

u* Nondimensional wind velocity 

V Volume 

Vdef Volume of gas for deflagration 

W Fuel exposed width 

Wc Compartment width 

W Weight of steel column per linear foot 

WTNT Weight of TNT 

Yp Particulate yield 

Z Height of smoke layer interface above floor 

Zo Hypothetical virtual origin of fire source 

Zp Fireball flame height 

Hc Heat of Combustion 

Hc,eff Effective heat of combustion 

t Time step 

Tg Gas temperature above ambient 

Tig Ignition temperature above ambient 

  Heat transfer coefficient for steel l 

  Yield (fraction of available energy participating in blast wave generation) 

m  Specific extinction coefficient 

r  Fraction of total energy radiated 

  Thickness 

  Flame emissivity 

  Ventilation factor 

  Flame title or angle of deflection 

  Density 

a  Density of Ambient Air 

c  Density of combustion products 

c  Density of concrete 

F  Density of fuel vapor 

g  Density of gas 

i  Density of insulation 

  Stefan-Boltzmann constant 

o  Detector time constant 

  Regression rate 

Subscripts 

a Ambient 

bs Bench-scale 

c Compartment 

c Combustion 

c Concrete 

c Current 

D Detection 

def Deflagration 

e Convective 

e External 

eff Effective 

e Entrainment 
xxii 

f Fire 

f Flame 

f Fuel 

f(corner) Corner flame 

f(wall) Wall flame 

f(wall,line) Line fire flame 

FO Flashover 

fs Full-scale 

g Gas 

H Hours 

I Insulation 

ig Ignition 

jet Ceiling jet 

m Extinction 

min Minimum 

o Out 

p Specific 

p Particulate 

p Plume 

p Penetration 

r Radiative 

r Response 

SC Scale 

s Steel 

T Total 

Total Total 

t Transient 

TNT Trinitrotoluene 

v Vent 

v Volume 

w Wind 

Superscripts 

(			ሶ) Per unit time 

( )” Per unit area 

ሺ		ሶሻ” Per unit area, per unit time 

* Nondimensional 
1-1 

CHAPTER 1. 

INTRODUCTION 

1.1 Purpose 

This report supplements and updates NUREG 1805, Fire Dynamics Tools (FDTs

), Quantitative 

Fire Hazard Analysis Methods for the U.S. Nuclear Regulatory Commission Fire Protection 

Inspection Program. The dynamic nature of fire is a quantitative and mathematically complex 

subject. It combines physics, chemistry, mathematics, and engineering principles and can be 

difficult to comprehend for those who have a limited background in these areas. The Fire 

Dynamics Tools (FDTs

) were developed to assist fire protection inspectors and others in solving 

fire hazard problems in nuclear power plants (NPPs). NUREG-1805 and the related Fire 

Dynamics Tools (FDTs) provide first-order quantitative methods (i.e., traditional approaches, 

correlations, computations, closed form approximations or exact solutions, and hazard models) 

to assess the potential fire hazard development in commercial NPPs. 

1.2 Organization of this Report 

Since the publication of NUREG-1805 in December 2004, numerous comments and 

suggestions have been received from users of the spreadsheets. In response to these 

comments, all of the existing NUREG-1805 spreadsheets were updated to improve layout and 

printing. In addition, some spreadsheets have been revised to correct calculation errors and a 

new model has been added to the FDTs

 suite. Table 1 lists the Fire Dynamics Tools and the 

associated chapter and related calculation methods. Table 2 identifies the spreadsheets that 

have been modified to correct calculation errors in addition to layout improvements. 

Table 1-1. List of Fire Dynamics Tools 

FDTs

* Chapter and Related Calculation Method(s) 

*indicated revised spreadsheet 

Chapter 2. Predicting Hot Gas Layer Temperature and 

Smoke Layer Height in a Room Fire with Natural 

and Forced Ventilation

02.1_Temperature_NV_Sup1.xls

Method of McCaffrey, Quintiere, and Harkleroad (MQH) 

• Natural Ventilation 

02.2_Temperature_FV_Sup1.xls*

Method of Foote, Pagni, and Alvares (FPA) 

• Forced Ventilation 

Method of Deal and Beyler 

• Forced Ventilation 

02.3_Temperature_CC._Sup1.xls*

Method of Beyler 

• Fire in a Compartment with a Door Closed but with 

Sufficient Leaks to Prevent Pressure Buildup; 

Leakage is Ignored 
1-2 

FDTs* Chapter and Related Calculation Method(s) 

*indicated revised spreadsheet 

03_HRR_Flame_Height_Burning_ 

Duration_Calculation_Sup1.xls*

Chapter 3. Estimating Burning Characteristics of Liquid Pool 

Fire, Heat Release Rate, Burning Duration and 

Flame Height

04_Flame_Height_Calculations_Sup1.xls

Chapter 4. Estimating Wall Fire Flame Height, Line Fire 

Flame Height Against the Wall, and Corner Fire 

Flame Height

Chapter 5. Estimating Radiant Heat Flux from Fire to a 

Target Fuel

05.1_Heat_Flux_Calculations_Wind_ 

Free_Sup1.xls

Wind-Free Condition 

• Point Source Radiation Model (Target at Ground 

Level) 

• Solid Flame Radiation Model (Target at Ground 

Level) 

• Solid Flame Radiation Model 

(Target Above Ground Level)

05.2_Heat_Flux_Calculations_ 

Wind_Sup1.xls*

Presence of Wind 

• Solid Flame Radiation Model (Target at Ground 

Level) 

• Solid Flame Radiation Model (Target Above Ground 

Level)

05.3_Thermal_Radiation_From_ 

Hydrocarbon_Fireballs_Sup1.xls Estimating Thermal Radiation from Hydrocarbon Fireballs

06_Ignition_Time_Calculations_Sup1.xls

Chapter 6. Estimating the Ignition Time of a Target Fuel 

Exposed to a Constant Radiative Heat Flux 

• Method of Estimating Piloted Ignition Time of Solid 

Materials Under Radiant Exposures 

Method of (1) Mikkola and Wichman, (2) Quintiere 

and Harkleroad, and (3) Janssens 

• Method of Estimating Piloted Ignition Time of Solid 

Materials Under Radiant Exposures 

Method of Toal, Silcock and Shields 

• Method of Estimating Piloted Ignition Time of Solid 

Materials Under Radiant Exposures 

Method of Tewarson

07_Cable_HRR_Calculations_Sup1.xls Chapter 7. Estimating Full-Scale Heat Release Rate of a 

Cable Tray Fire

08_Burning_Duration_Soild_Sup1.xls Chapter 8. Estimating Burning Duration of Solid 

Combustibles
1-3 

FDTs* Chapter and Related Calculation Method(s) 

*indicated revised spreadsheet 

09_Plume_Temperature_ 

Calculations_Sup1.xls

Chapter 9. Estimating Centerline Temperature of a Buoyant 

Fire Plume

10_Detector_Activation_Time_Sup1.xls*

Estimating Detector Response Time 

Chapter 10. Estimating Sprinkler Response Time 

Chapter 11. Estimating Smoke Detector Response Time 

Chapter 12. Estimating Heat Detector Response Time

13_Compartment_ Flashover_ 

Calculations_Sup1.xls

Chapter 13. Predicting Compartment Flashover 

• Compartment Post-Flashover Temperature: 

Method of Law 

• Minimum Heat Release Rate Required to 

Compartment Flashover: 

Method of (1) McCaffrey, Quintiere, and Harkleroad 

(MQH); (2) Babrauskas; and (3) Thomas

14_Compartment_Over_Pressure_ 

Calculations_Sup1.xls

Chapter 14. Estimating Pressure Rise Attributable to a Fire 

in a Closed Compartment

15_Explosion_Claculations_Sup1.xls

Chapter 15. Estimating the Pressure Increase and 

Explosive Energy Release Associated with 

Explosions

16_Battery_Room_Flammable_Gas_ 

Conc_Sup1.xls*

Chapter 16. Calculating the Rate of Hydrogen Gas 

Generation in Battery Rooms 

• Method of Estimating Hydrogen Gas Generation 

Rate in Battery Rooms 

• Method of Estimating Flammable Gas and Vapor 

Concentration Buildup in Enclosed Spaces 

• Method of Estimating Flammable Gas and Vapor 

Concentration Buildup Time in Enclosed Spaces
1-4 

FDTs* Chapter and Related Calculation Method(s) 

*indicated revised spreadsheet 

Chapter 17. Calculating the Fire Resistance of Structural 

Steel Members

17.1_FR_Beams_Columns_ 

Substitution_Correlation_Sup1.xls* • Empirical Correlations

17.2_FR_Beams_Columns_Quasi_ 

Steady_State_Spray_Insulated_Sup1.xls*

• Beam Substitution Correlation (Spray-Applied 

Materials) 

• Column Substitution Correlation (Spray-Applied 

Materials) 

• Heat Transfer Analysis using Numerical Methods 

Protected Steel Beams and Columns (SprayApplied)

17.3_FR_Beams_Columns_Quasi_ 

Steady_State_Board_Insulated_Sup1.xls*

• Heat Transfer Analysis using Numerical Methods 

Protected Steel Beams and Columns (Board 

Materials)

17.4_FR_Beams_Columns_Quasi_ 

Steady_State_Uninsulated_Sup1.xls*

• Heat Transfer Analysis using Numerical Methods 

Unprotected Steel Beams and Columns

18_Visibility_Through_Smoke_Sup1.xls Chapter 18. Estimating Visibility Through Smoke

19_THIEF_of_Cables_Calculations_ 

Sup1.xls 

Chapter 19. Estimating the Thermally-Induced Electrical 

Failure (THIEF) of Cables

 
1-5 

Table 1-2. Summary of Technical Changes to Original NUREG-1805 Spreadsheets 

CHAPTER TITLE 

Spreadsheet Title Description of Revision 

CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE IN A ROOM FIRE WITH FORCED 

VENTILATION 

02.2_Temperature_FV_Sup.xls

Deleted extraneous variable in Cell C94. Under Deal & Beyler 

Method, added tp calculation in Cells starting B148, added hk

formula for t > tp in Cell E158 and changed equation for results 

table for hk in Cells starting D184. 

02.3_Temperature_CC_Sup1.xls Corrected calculation for Parameter K1. Added area of 

compartment enclosing surface boundaries (AT) in Parameter K1. 

CHAPTER 3. ESTIMATING BURNING CHARACTERISTICS OF LIQUID POOL FIRE, HEAT RELEASE 

RATE, BURNING DURATION, AND FLAME HEIGHT 

03_HRR_Flame_Height_Burning_ 

Duration_Calculations_Sup1.xls Corrected diameter reference in Q calculation column in table. 

CHAPTER 5. ESTIMATING RADIANT HEAT FLUX FROM FIRE TO A TARGET FUEL AT GROUND 

LEVEL IN PRESENCE OF WIND (TILTED FLAME) SOLID FLAME RADIATION MODEL 

05.2_Heat_Flux_Calculations_ 

Wind_Sup1.xls

Corrected typo in Cell C85. Corrected programming errors in 

Cells G156 and M158. 

CHAPTER 10. ESTIMATING SPRINKLER RESPONSE TIME 

10_Detector_Activation_ 

Time_Sup1.xls (Sprinkler)

Changed references from Qc to Q and 0.15 to 0.18 in cells B58, 

B59, B76, C62, C78, D74, D76, E58, and E59, as appropriate 

and changed calculations in cells C76, C79 and E76. 

CHAPTER 11. ESTIMATING SMOKE DETECTOR RESPONSE TIME 

10_Detector_Activation_ 

Time_Sup1.xls (Smoke_Detector)

Changed references from Qc to Q and 0.15 to 0.18 in cells B37, 

B38, B55, C41, C57, D53, D55, E37, and E38, as appropriate 

and changed calculations in cells C55, C58 and E55. 

CHAPTER 12. ESTIMATING HEAT DETECTOR RESPONSE TIME 

10_Detector_Activation_ 

Time_Sup1.xls (FTHDetector)

Changed references from Qc to Q and 0.15 to 0.18 in cells B98, 

B99, B116, C102, C118, D114, D116, E98, and E99, as 

appropriate and changed calculations in cells C116, C119 and 

E116. 

CHAPTER 16. CALCULATING THE RATE OF HYDROGEN GAS GENERATION IN BATTERY ROOMS 

16_Battery_Room_Flammable_Gas_ 

Conc_Sup1.xls

Corrected Filed D61 air flow rate (fresh air) in enclosure 

calculation. 
1-6 

CHAPTER TITLE 

Spreadsheet Title Description of Revision 

CHAPTER 17. ESTIMATING FIRE RESISTANCE TIME OF STEEL BEAMS PROTECTED BY FIRE 

PROTECTION INSULATION (QUASI-STEADY-STATE APPROACH) 

17.3_FR_Beams_Columns_Quasi_ 

Steady_State_Board_Insulated_Sup1.xls

Change reference from $I$16 to $I$15, add variable ambient 

temperature, and corrected ambient temperature reference in 

Results calculations.

17.3_FR_Beams_Columns_Quasi_ 

Steady_State_Board_Insulated_Sup1.xls

Change reference from $I$16 to $I$15, add variable ambient 

temperature, and corrected ambient temperature reference in 

Results calculations. 

17.4_FR_Beams_Columns_Quasi_ 

Steady_State_Board_Insulated_Sup1.xls

Corrected Typo in Equation Tf = C1 LOG (0.133 t + 1) + Ta to 

Calculate Fire Exposure Temperature. Corrected Conversion 

from Kelvin to Fahrenheit in Result Field. 

17.4_FR_Beams_Columns_Quasi_ 

Steady_State_Board_Insulated_Sup1.xls

Corrected Typo in Equation Tf = C1 LOG (0.133 t + 1) + Ta to 

Calculate Fire Exposure Temperature. Corrected Conversion 

from Kelvin to Fahrenheit in Result Field. 

Chapters 1 through 18 from NUREG-1805 are not duplicated in this report. However, example 

problems that have been solved using the revised NUREG-1805 spreadsheets are included in 

Appendix A (English Units) and Appendix B (S.I. Units) of this report. The reader is referred to 

the original NUREG-1805 report for technical documentation of those spreadsheets. The 

chapter describing the new model is labeled as Chapter 19 continuing in the FDTs

 series of 

chapters. The CD-ROM accompanying this report contains the new and updated 

spreadsheets. Spreadsheets which use English units for the majority of the input data are 

located in the folder labeled “English Units.” The folder labeled “SI Units” contains the same 

FDTs

 spreadsheets but requires user inputs to be in SI units. 

 
19-1 

CHAPTER 19. 

ESTIMATING THE THERMALLY-INDUCED ELECTRICAL 

FAILURE (THIEF) OF CABLES 

19.1 Objectives 

This chapter has the following objectives: 

 Describe the three primary functions performed by electrical cables in nuclear power plants 

(NPPs): control, instrumentation, and power. 

 Identify the two major types of insulation used for cables: thermoset (TS) and thermoplastic 

(TP). 

 Explain the factors that determine how a cable will respond to fire exposure. 

 Explain the processes that electrical failures can initiate in a cable tray. 

19.2 Introduction 

Electrical cables perform numerous functions in NPPs. For example, power cables supply 

electricity to motors, transformers, heaters, and light fixtures. Control cables connect plant 

equipment such as motor-operated valves (MOVs) and motor starters to remote initiating 

devices (e.g., switches, relays, and contacts). Instrumentation cables transmit low-voltage 

signals between input devices and readout display panels. 

NPPs typically contain hundreds of miles of electrical cables. A typical boiling-water reactor 

(BWR) requires about 97 km (60 miles) of power cable, 80.5 km (50 miles) of control cable, and 

402 km (250 miles) of instrument cable. A pressurized-water reactor (PWR) may require even 

more cables. The containment building of Waterford Steam Electric Generating Station, Unit 3 

requires nearly 1,609 km (1,000 miles) of cable (NUREG/CR-6384). 

Electrical cables have been responsible for a number of fires in NPPs over the years. A 1966 

National Fire Protection Association study (Hedland, 1966) identified 24 fires with the most 

serious at that time occurring at the Peach Bottom Atomic Power Station operated by 

Philadelphia Electric Company. In 1975, a fire involving electrical cables occurred at the 

Browns Ferry Nuclear Power Plant operated by the Tennessee Valley Authority (NUREG-0050). 

The fire caused damage to more than 1,600 cables resulting in significant loss of emergency 

core cooling system equipment. In addition to loss of power to motors, valves, and other 

equipment, fire-induced short circuits caused many instrument, alarm, and indicating circuits to 

produce false and conflicting indications of equipment operation. 

The behavior of cables in a fire depends on a number of factors including their constituent 

materials and construction as well as their location and installation geometry. Burning cables 

can propagate flames from one area to another or they can add to the amount of fuel available 

for combustion and can liberate smoke containing toxic and corrosive gases. Fire exposure of 

an electrical cable can cause a loss of insulation resistance, loss of insulation physical integrity 

(i.e., melting of the insulation), and electrical breakdown or short-circuiting. The lower the heat 
19-2 

flux required to ignite the electrical cables, the greater the fire hazard in terms of ignition and 

flame spread. 

Fire-induced damage to a cable can result in one of the following failure modes (LaChance et 

al., 2000): 

 Open Circuit: loss of electrical continuity of an individual conductor (i.e., the conductor is 

broken and the signal or power does not reach its destination). 

 Short to Ground: an individual conductor comes into electrical contact with a grounded 

conducting medium (such as a cable tray, conduit, or a grounded conductor) resulting in a 

low-resistance path that diverts current from a circuit. The fault may be accompanied by a 

surge of excess current to ground (particularly in higher voltage circuits) that is often 

damaging to the conductor. 

 Hot Short: electrical faults that involve an energized conductor contacting another conductor 

of either the same cable (a conductor-to-conductor hot short) or an adjacent cable (a cableto-cable hot short). A hot short has the potential to energize the affected conductor or to 

complete an undesirable circuit path. 

In addition to these failure modes, the wide variations in the composition of polymer materials 

used in electrical cable insulation has resulted in notable failure characteristics among the two 

broad classes of polymer materials—thermoset (TS) and thermoplastic (TP). Thermoplastic 

cables are characterized by softening, melting, and dripping when exposed to a damaging 

thermal environment. Thermoset insulated cables don’t have a distinct melting point. As a 

result of their molecular bonding, TS cable degradation is characterized by voiding, off gassing, 

and swelling. 

TS and TP cables not only fail differently, but their use in different types of circuits can cause 

unique circuit response. For instance, instrumentation circuits typically operate using a 4-20 mA 

signal, where 4 mA equals 0 percent of the parameter being measured (e.g., pressure, flow, 

volume, etc.) and 20 mA equals 100 percent. Testing has shown that a TP instrument cable will 

fail abruptly while a TS cable will fail gradually. This behavior in an instrument circuit could 

provide an operator with misleading information (e.g., loss of pressure or level). The operator 

would not be able to readily determine if the readout was an accurate indication of plant status 

or if it was the result of fire damage to a cable. A prolonged transition from “good signal” to 

obviously “faulty signal” proved to be typical of the TS cables. Figure 19-1 illustrates the 

different response characteristics of TS and TP cables when exposed to a fire environment. 
19-3 

Figure 19-1. Different signal responses from a thermoset cable (top) and a 

thermoplastic cable (bottom) when exposed to a fire. 

A key NPP application is the Fire Probabilistic Risk Assessment (FPRA), which often relies on 

fire models to predict cable failure times for a predefined set of fire conditions (NUREG/CR 

6850, Vol. 1). To assess the conditional probability of cable damage given a fire, these failure 

times are weighed against the likelihood that fire suppression succeeds within the available 

time. The ability of current compartment fire models to predict cable damage is limited. For 

example, in the NIST Consolidated Model of Fire and Smoke Transport (CFAST) (Jones, et al., 

2005), a general thermal target response submodel is available, but this model was not 

specifically developed for, nor has it been calibrated for, cables as the thermal target. Hence, 

one primary need with respect to fire model improvement is the development, calibration, and 

validation of predictive thermal/damage target response models specific to cables as the target. 
19-4 

In late 2006, a series of cable fire tests were performed by Sandia National Laboratories (SNL) 

under the sponsorship of the U.S. Nuclear Regulatory Commission (NRC) Office of Nuclear 

Regulatory Research (RES). This program, known as the CAble Response tO Live FIRE 

(CAROLFIRE) project, was designed to address two specific need areas: 

1. Provide an experimental basis for resolving five of the six items identified as “Bin 2” circuit 

configurations in Risk-informed Approach for Post-Fire Safe-Shutdown Circuit Inspections, 

Regulatory Issue Summary (RIS) 2004-03, Rev. 1, 12/29/04. 

2. Improve fire modeling tools for the prediction of cable damage under fire conditions. 

The project was conducted as a collaborative effort involving representatives of RES, SNL, the 

NRC Office of Nuclear Reactor Regulation (NRR), the National Institute of Standards and 

Technology (NIST), and the University of Maryland (UMd). 

The CAROLFIRE project included a series of 78 small-scale radiant heating tests and 18 

intermediate-scale open burn tests. The small-scale tests were performed in an SNL facility 

called Penlight and involved exposure of two to seven lengths of cable to grey-body radiant 

heating. These tests were aimed in large part at the fire model improvement need area, but 

they also provided data pertinent to the resolution of two of the five Bin 2 items. The 

intermediate-scale tests involved exposure of cables, generally in bundles of 6 to 12 cables, 

under various routing configurations and at various locations within a relatively open test 

structure. The fires were initiated by a propene (also known as propylene) gas diffusion burner. 

The fire typically ignited, at a minimum, those cables located directly above the fire source. The 

tested cables were representative of those currently in use at U.S. commercial NPPs. Testing 

included a broad range of both TS and TP insulated cables as well as one mixed TS-insulated 

and TP-jacketed cable. The three-volume test report includes two volumes documenting the 

test results (NUREG/CR-6931 Vol. 1, NUREG/CR-6931 Vol. 2) and a volume describing the 

development of the THIEF model (NUREG/CR-6931 Vol. 3). 

19.3 Thermally-Induced Electrical Failure (THIEF) of Cables 

19.3.1 General 

The development of a predictive model of cable failure has been elusive for a number of 

reasons. First, cables are a fairly complex combination of insulating plastics, metal conductors, 

protective armors, and a variety of filler materials. The availability of comprehensive thermophysical properties of these materials is limited. Even when the material properties for a 

particular cable are available, it is still a challenge to calculate the heat penetration through a 

bundle of the cables lying in a tray or run through a conduit. Rather than try to develop detailed 

models, a simpler approach is to develop an empirical relationship between the time to electrical 

failure and the “exposing” temperature (i.e., the temperature of the hot gases in the vicinity of 

the cable). 

In Appendix A of NUREG-1805, a set of engineering calculation methods specifically designed 

for nuclear power plant applications suggests that the time to electrical failure is inversely 

proportional to the exposing temperature. For the two major classes of cables, TS and TP, it 

provides an estimated failure time for a given exposing temperature. Although these equations 

are useful screening methods, they have some significant limitations. First, the equations are 
19-5 

based on constant temperature exposures, which is unrealistic in a fire scenario. Second, they 

do not account for different cable installations or configurations. The formulae only distinguish 

between a TS and TP cable based on the latter having been shown to fail at lower temperatures 

than the former. The formulae do not take into account size, mass, protective barriers, or sitespecific conditions. A more flexible predictive model should have some consideration for the 

thermal mass of the cable, and it must infer electrical failure from the attainment of a given 

“failure” temperature somewhere within the cable. 

Petra Andersson and Patrick Van Hees at the Swedish National Testing and Research Institute 

(SP) proposed that a cable’s thermally-induced electrical failure (THIEF) can be predicted via a 

simple one-dimensional heat-transfer calculation under the assumption that the cable can be 

treated as a homogenous cylinder (Andersson and Van Hees, 2005). Their results for PVC 

cables were encouraging and suggested that the simplified analysis could be used for other 

types of cables. Using the data from the CAROLFIRE project, researchers at NIST examined 

the feasibility of extending the THIEF model to other cable types (NUREG/CR-6931 Vol. 3). 

The governing equation for the cable temperature T(r,t) is given by: 

where ρ, c, and k are the effective density, specific heat, and thermal conductivity of the solid, 

respectively. The boundary condition at the exterior boundary, r = R is given by: 

where ݍሶ” is the assumed axially symmetric heat flux to the exterior of the cable. The heat flux is 

provided by the fire model or fire analysis that is being used to assess the overall thermal 

environment of the compartment where the cable is located. In most realistic fire scenarios, the 

heat flux to the cable is not axially symmetric. For the purpose of modeling the cable failure, it is 

recommended that the maximum value be used. 

While Andersson and Van Hees developed an analytical solution for their THIEF model, the 

NIST researchers proposed a numerical solution as simpler and easier to implement in fire 

models. To solve Eq. (19-1) numerically, the radius, R, of the cable is divided into N uniformly 

spaced increments of length, r = R/N. An appropriate value for r is about 0.1 mm for cables 

similar to those tested in CAROLFIRE. Next, a time step is defined that is related to the spatial 

increment. This is known as the time step constraint, which is necessary for accuracy and 

sometimes numerical stability: 

The temperature of the i-th radial increment (or cell) at the n-th time step (ݐ =௡nt) is denoted, 

ܶ௜

௡. The value of the radius at the forward edge of the i-th cell is denoted, ri = ir. Thus, r0 = 0 

and rN = R.

r

T rk

t r r

T

c







   1

 (19-1) 

  qtR

r

T k    ,  (19-2) 

k

rc

t

2

2    (19-3) 
19-6 

A finite difference approximation to equation 19-1 is given by: 

where  is the thermal diffusivity of the cable material (m2/s). 

The THIEF model predicts the temperature profile within the cable as a function of time, given a 

time-dependent exposing temperature or heat flux. The CAROLFIRE experimental program 

included bench-scale, single-cable experiments in which temperature measurements were 

made on the surface of, and at various points within, cables subjected to a uniform heat flux. 

These experiments provide the link between internal cable temperature and electrical failure. 

The model infers electrical failure when a given “failure” temperature is reached based on the 

calculated interior temperature. The temperature of the centermost point in the cable is not 

necessarily the indicator of electrical failure. This analysis method uses the temperature just 

inside the cable jacket rather than the centermost temperature because that is where electrical 

shorts in a multi-conductor cable are most likely to occur first. 

The THIEF model uses the general cable construction and bulk properties but does not require 

more detailed thermo-physical properties. For example, the mass per unit length and diameter 

are needed, but the thermal conductivity, specific heat, and emissivity are assumed based on 

the current generation of cables in existing plants. This latter detailed information is not always 

readily available for the wide variety of often proprietary cable materials, and bench-scale 

experiments to measure the properties can be expensive and difficult to perform for all existing 

and future cable materials. 

19.3.2 Cable Properties and Selection Process 

To determine the time of cable failure during thermal insult, the THIEF model requires three 

cable properties: 

 Cable outside diameter (OD). 

 Mass per unit length. 

 Jacket thickness. 

The THIEF spreadsheet allows the user to enter these parameters in two different ways. If the 

three cable parameters are known, the user can enter them directly into the THIEF spreadsheet. 

When the cable parameters are not known, the user can use the automated cable selection 

process built into the spreadsheet. 

To support the identification of cable properties, an extensive data-gathering effort was 

conducted to identify these properties for the most common cable types used in an NPP (i.e., 

power, control, and instrumentation cables). Over 3,000 cables from nine different major cable 

manufactures were identified. Cables are manufactured in various sizes, conductor counts, and 

material types to provide the appropriate circuit function for the particular application. These 

variations result in thousands of different cable designs being manufactured to support specific 

needs. As a result, it is nearly impossible to capture every single cable type that exists. 

   





 



     



 

r

TT

r

r

TT

r

rr

t TT

n

i

n

i

i

n

i

n

i

i

avg

n

i

n

i  

 1

1

1 1 (19-4) 
19-7 

The cable parameters gathered for this project are largely based on cable constructions typically 

found in an NPP, and the information is as accurate as what is presented on the manufacturer’s 

website. The following manufacturer’s cable specifications are included in the spreadsheet: 

 American Insulated Wire. 

 Cable USA. 

 Continental. 

 Dekoron. 

 Draka. 

 First Capital. 

 General Cable. 

 Okonite. 

 Rockbestos-Surprenant. 

The THIEF spreadsheet has been automated to sort the complete list of over 3,000 cables by 

characteristics that the user specifies. To perform this sorting function, the user first clicks on 

the “Select Cable” button located in the input parameters section of the spreadsheet. When a 

new window opens, click on the “Select Cable From List” choice. The next screen allows the 

user to select the general characteristics of the cable (i.e., cable type [control, instrument, or 

power], wire gauge [AWG], and the number of conductors). The THIEF model uses these three 

input parameters to sort the complete cable list and narrow it down to the cables that meet the 

user’s input parameters. The condensed list is displayed and sorted by manufacturer, cable 

model, insulation, and jacket material. The user then selects the cable to be analyzed from the 

list. 

The list is not intended to be inclusive of all cables, and there will be instances were a specific 

cable of concern is not listed. In cases where the cable of interest is not listed, the user may (1) 

look up the information from the cable manufacturer’s Web site, (2) get the information from the 

license documentation and enter the values directly into the spreadsheet, or (3) choose a 

“generic” cable from the list with similar construction and insulation materials. Based on an 

analysis of manufacturer data, “generic” cables have been identified for each insulation type, 

cable function, number of conductors, and wire gauge. 

When choosing a cable from the list, it is important to choose cable parameters that are 

representative of the cables found in the plant. For example, if a cable located in the plant has 

the identification, “GENERAL CABLE® EHTC 7/C 12 AWG EPR/HYP UL TYPE TC 90°C,” it is 

important to choose a cable that has the same general characteristics. That is, choose a cable 

with seven conductors (7/C) with each conductor size 12 AWG and with the same insulation and 

jacket materials. Choosing the exact manufacture is less important than physical properties; 

however, if the exact cable is found in the list, this is the most appropriate choice. Some types 

of instrumentation cables may be identified in terms of numbers of pairs or numbers of triads. In 

these cases, the actual number of conductors should be used as input for the spreadsheet. For 

example, a two-pair cable would be analyzed as a four-conductor cable. A three-triad cable 

would have nine conductors. In cases where the specific cable to be analyzed is not listed in 

the condensed cable list, the user may select a cable with identical cable materials (PVC, XLPE, 

SR, etc.) or an insulation material of the same type (TP or TS). Table 19-1 presents a grouping 

of various cable insulation materials into the two classes. 
19-8 

Table 19-1. Common Thermoplastic and Thermoset Cable Insulation and Jacket 

Materials 

Thermoplastic (TP) Thermoset (TS) 

ETFE (Tefzel) SR (Silicon Rubber) 

FEP (Teflon) EPR (Ethylene Propylene Rubber) 

CPE (Chlorinated Polyethylene) EPDM (Ethylene Propylene diene 

monomer rubber) 

PE (Polyethylene) CP (Neoprene) 

PVC (Polyvinyl Chloride) CSPE (Chlorosulphonated polyethylene) 

XLPE (Cross-linked Polyethylene) 

XLPO (Cross-linked Polyolofin) 

The last input parameter needed from the user is information related to where the cable is 

located (air drop, cable tray, or conduit). When a cable is suspended in air (air drop) or in a 

cable tray, a majority of the cable will be exposed to the fire environment. A cable in conduit or 

armored cable will be “shielded” to some extent from direct exposure to the fire environment. 

Once the cable location is selected, the cable parameters are automatically entered into the 

THIEF spreadsheet, including the failure temperature, based on the cables insulation type (TP 

or TS). 

19.3.3 Exposure Gas Temperature 

The exposure gas temperature can be obtained in several ways. First, the user can manually 

enter a set of data points obtained from the results of a fire model such as CFAST, MAGIC, or 

FDS. Alternatively, the data points could be obtained from measurements recorded during a fire 

test representative of the scenario. Finally, the THIEF model spreadsheet has been integrated 

with several spreadsheets previously issued in NUREG 1805. These spreadsheets are 

appropriate for determining hot gas layer temperature (Chapter 2.6) or plume centerline 

temperature (Chapter 9). Specifically, the following methods are included: 

 McCaffrey, Quintiere, and Harkleroad (MQH) for natural ventilation (2.6.1). 

 Beyler for natural ventilation in a closed compartment (2.6.2). 

 Foote, Pagni, and Alvares (FPA) for forced ventilation (2.6.3). 

 Deal and Beyler for forced ventilation (2.6.4). 

 Centerline temperature of a buoyant plume (9). 

 

These spreadsheets can be used to calculate the exposure gas temperature profile, and the 

results will be automatically incorporated into the THIEF model calculation. 

Typically, a cable will be in one of four locations relative to the fire at any given time. Figure 

19-2 illustrates the four possible orientations for the cable and fire. The cable can be (a) in the 

flames, (b) in the smoke plume, (c) in the hot gas layer, or (d) in the “ambient” lower layer. The 

dashed lines in Figure 19-2 represent the radiant energy from the fire. Typically, a small 

amount of the radiant flux reaching the hot gas layer will be absorbed (smaller arrows in Figure 

19-2) while the remainder is “reflected” back to the items in the lower layer. The object labeled 

“cable tray” in Figure 19-2 could represent a cable tray, an air drop, or a conduit. The exposure 

gas temperature will depend on the assumed location of the cables relative to the fire at the time 
19-9 

of interest. As the fire develops, the location of the cables relative to the fire may change. So, 

multiple calculations may be necessary to evaluate the potential for cable failure. 

(a) Cable within flames from fire. (b) Cable within smoke plume from fire. 

(c) Cable in hot gas layer. (d) Cable in “ambient” lower layer. 

Figure 19-2. Drawing showing the four possible locations for a cable tray relative to the 

fire. 

When the cable is within the flames from the fire (Figure 19-2[a]), the cable is assumed to fail 

upon flame contact. If it needs to function, it does not; if it could have "Hot Shorted" and made 

bad things happen, it did. The cable is on fire or shortly will be on fire. When the cable is within 

the smoke plume directly above the fire (Figure 19-2[b]), the temperature exposure is not as 

severe as when it is within the flames. The temperature at any location within the fire plume can 

be calculated using the spreadsheet described in Chapter 9 of NUREG-1805. When the cable 

is in the hot gas layer (Figure 19-2[c]), the fire is located in another part of the room not directly 

under the cable. The fire will “pump” hot gas into the upper part of the room. This gas will be 

contained in the room until the interface (the separation between the hot gas layer and the 

“ambient” lower layer) drops below the top level of some opening, such as an open door or 

window. When the cable is located with the hot gas layer, the exposure gas temperature will be 

equal to the hot gas layer temperature. Chapter 2 of NUREG 1805 describes several 

spreadsheets that calculate hot gas layer temperature depending on room openings and 

ventilation conditions. In the final scenario (Figure 19-2[d]), the hot gas layer never reaches the 

cables of interest. The cables remain in the lower “ambient” temperature layer. In this case, the 

cable will be heated solely by the radiant energy from the fire. The THIEF model is not directly 

applicable to this scenario because there is no surrounding hot gas layer. However, the cable 
19-10 

could still fail from the radiant energy exposure. NUREG 1805 includes spreadsheets in 

Chapter 5 for calculating the radiant exposure to the cables and guidance on selecting radiant 

exposure levels that could lead to cable failure. 

19.4 Assumptions and Limitations 

The method discussed in this chapter is subject to several assumptions and limitations 

(NUREG/CR-6931 Vol. 3): 

(1) The heat penetration into a cable of circular cross section is largely in the radial direction. 

This greatly simplifies the analysis, and it is also conservative because it is assumed that 

the cable is completely surrounded by the heat source. 

(2) The cable is homogenous in composition. In reality, a cable is constructed of several 

different types of polymeric materials, cellulose fillers, and a conducting metal, most often 

copper. 

(3) The thermal properties—conductivity, specific heat, and density—of the assumed 

homogenous cable are independent of temperature. In reality, both the thermal 

conductivity and specific heat of polymers are temperature-dependent, but this information 

is very difficult to obtain from the manufacturers. 

(4) It is assumed that no decomposition reactions occur within the cable during its heating, 

and ignition and burning are not considered in the model. 

(5) Electrical failure occurs when the temperature just inside the cable jacket reaches an 

experimentally determined value. 

(6) The temperature in the upper layer is uniform throughout the layer regardless of location 

within the layer or distance from the fire. 

19.5 Required Input for Spreadsheet Calculations 

The user must obtain the following information before using the spreadsheet: 

(1) Gas temperature around the cable as a function time (from fire models, fire tests, or 

integrated spreadsheets). 

(2) Type of cable (thermoplastic, thermoset).* 

(3) Cable diameter.* 

(4) Cable mass per unit length.* 

(5) Cable jacket thickness.* 

(6) Conduit thickness, if any. 

(7) Conduit outer diameter, if any. 
19-11 

* Can be obtained from list of cable properties integrated into THIEF spreadsheet when cable 

function (power, control, or instrumentation), wire size (AWG), and number of conductors are 

known. 

19.6 Cautions 

(1) Use the (19_THIEF_Thermally_Induced_Electrical_Failure_of_Cables.xls) spreadsheet on 

the CD-ROM. 

(2) Make sure to enter the input parameters in the correct units. 

(3) The failure temperature is an estimate based on data from a number of different cable 

tests. Although a single value is used to estimate failure, the graph shows the 

temperature range over which failure may occur for the selected cable type (TP or TS). 

19.7 Summary 

Determining the failure time of cables exposed to a hot gas layer involves the following steps: 

(1) Determine the exposure gas temperature using test data, fire model results, or 

incorporated spreadsheets. 

(2) Select cable of interest from one of the lists or enter user determined cable properties. 

(3) Calculate temperature profile through cable as a function of time and hot gas exposure. 

(4) Determine when failure temperature is reached. 

19.8 Decision Criteria 

The failure temperature range is estimated from temperature measurements obtained just below 

the cable jacket during the CAROLFIRE tests. For TP cables, the temperatures reached 

somewhere between 200 °C (390 °F) and 250 °C (480 °F). For TS cables, the range was about 

400 °C (750 °F) to 450 °C (840 °F). 

19.9 References 

Andersson, P. and P. Van Hees, “Performance of Cables Subjected to Elevated Temperatures,” 

Fire Safety Science – Proceedings of the Eighth International Symposium, International 

Association for Fire Safety Science, 2005. 

Hedlund, C.F., “Grouped Combustible Wire and Cables,” Fire Journal, Volume 60, pp. 5–8, 

March 1966. 

Jones, W. W., R.D. Peacock, G.P. Forney, and P.A. Reneke, “Consolidated Model of Fire 

Growth and Smoke Transport (Version 6): Technical Reference Guide,” NIST SP 1026, National 

Institute of Standards and Technology, Gaithersburg, MD, 2005. 
19-12 

LaChance, J., S.P. Nowlen, F. Wyant, and V. Dandini, “Circuit Analysis-Failure Mode and 

Likelihood Analysis,” A Letter Report to USNRC, Sandia National Laboratory, Albuquerque, 

New Mexico, May 8, 2000. 

NUREG-0050, “Recommendations Related to Browns Ferry Fire,” U.S. Nuclear Regulatory 

Commission, Washington, DC, February 1976. 

NUREG-1805, Fire Dynamics Tools (FDTs

) – Quantitative Fire Hazard Analysis Methods for the 

U.S. Nuclear Regulatory Commission Fire Protection Inspection Program, U.S. Nuclear 

Regulatory Commission, Washington, D.C., 2004. 

NUREG/CR-6384 Vol. 1, “Literature Review of Environmental Qualification of Safety-Related 

Electric Cables,” U.S. Nuclear Regulatory Commission, Washington, DC, April 1996. 

NUREG/CR-6850 Vol. 1, “EPRI/NRC-RES Fire PRA Methodology for Nuclear Power Facilities 

Volume 1: Summary & Overview,” U.S. Nuclear Regulatory Commission, Washington, DC, 

September 2005. 

NUREG/CR-6931 Vol. 1, “Cable Response to Live Fire (CAROLFIRE) Volume 1: General Test 

Descriptions and the Analysis of Circuit Response Data,” U.S. Nuclear Regulatory Commission, 

Washington, DC, 2007. 

NUREG/CR-6931 Vol. 2, “Cable Response to Live Fire (CAROLFIRE) Volume 2: Cable Fire 

Response Data for Fire Model Improvement,” U.S. Nuclear Regulatory Commission, 

Washington, DC, 2007. 

NUREG/CR-6931 Vol. 3, “Cable Response to Live Fire (CAROLFIRE) Volume 3: ThermallyInduced Electrical Failure (THIEF) Model,” U.S. Nuclear Regulatory Commission, Washington, 

DC, 2008. 

Risk-informed Approach for Post-Fire Safe-Shutdown Circuit Inspections,” Regulatory Issue 

Summary (RIS) 2004-03, Rev. 1, U.S. Nuclear Regulatory Commission, Washington, DC, 

December 2004. 

19.10 Additional Readings 

Chavez, J.M., and Klamerus, L.J., “Cable Tray Fire Experimentation,” LA-9911-C-Vol. 1; LA9911-C-Vol. 2; CSNI No. 83; CSNI Specialist Meeting on Interaction of Fire and Explosion With 

Ventilation Systems in Nuclear Facilities, April 25-28, 1983, Los Alamos, New Mexico, pp. 375-

390, 1983. 

Dey, M.K., “Evaluation of Fire Models for Nuclear Power Plant Applications: Cable Tray Fires,” 

NISTIR 6872, National Institute of Standards and Technology, Gaithersburg, Maryland, June 

2002. 

Klamerus, L.J., “Cable Tray Fire Tests,” IEEE Power Generation Committee of the IEEE Power 

Engineering Society, IEEE Winter Meeting, February 4-9, 1979, New York, New York, pp. 1-12, 

1979. 
19-13 

Lee, B.T., “Heat Release Rate Characteristics of Some Combustible Fuel Sources in Nuclear 

Power Plants,” NBSIR 85-3195, National Bureau of Standards, Gaithersburg, Maryland, July 

1985. 

Nicolette, V.F., and Yang, K.T., “Modeling of HDR Oil and Cable Fire Tests,” Structural 

Mechanics in Reactor Technology, 12th International Conference, Post Conference Seminar #6: 

Fire Safety of Nuclear Power Plants, August 23-24, 1993, Heidelberg, Germany, pp. 1-18, 1993. 

NUREG/BR-0361, “The Browns Ferry Nuclear Plant Fire of 1975 and the History of NRC Fire 

Regulations,” U.S. Nuclear Regulatory Commission, Washington, DC, February 2009. 

NUREG/CR-2431, “Burn Mode Analysis of Horizontal Cable Tray Fires,” U.S. Nuclear 

Regulatory Commission, Washington, DC, February 1982. 

NUREG/CR-2927, “Nuclear Power Plant Electrical Cable Damageability Experiments,” U.S. 

Nuclear Regulatory Commission, Washington, DC, October 1982. 

NUREG/CR-4527 Vol. 2, “Experimental Investigation of Internally Ignited Fires in Nuclear Power 

Plant Control Cabinets, Part 2, Room Effects Tests,” U.S. Nuclear Regulatory Commission, 

Washington, DC, November 1988. 

NUREG/CR-4679, “Quantitative Data on the Fire Behavior of Combustible Materials Found in 

Nuclear Power Plants: A Literature Review,” U.S. Nuclear Regulatory Commission, Washington, 

DC, February 1987. 

NUREG/CR-6776, “Cable Insulation Resistance Measurements Made During Cable Fire Tests,” 

U.S. Nuclear Regulatory Commission, Washington, DC, June 2002. 

Pryor, A.J., “Browns Ferry Revisited,” Fire Journal, Vol. 71, No. 3, pp. 85-86, 88-89, 120-121, 

May 1977. 

Sawyer, R.G.; and Elsner, J.A., “Cable Fire at Browns Ferry Nuclear Power Plant,” Fire Journal, 

Vol. 70, No. 4, pp. 5-10, July 1976. 

Shen, T.S., “Will the Second Cable Tray Be Ignited In a Nuclear Power Plant?,” Journal of Fire 

Sciences, Vol. 24, No. 4, 265-274, July 2006. 

 
19-14 

19.11 Problems 

Example Problem 19.11-1 (SI Units) 

(User Input - Cable Properties and Exposure Gas Temperature) 

Problem Statement 

As part of the development of the THIEF model, a number of experiments were conducted in 

the “Penlight” apparatus by Sandia National Laboratories. Figure 19-3 shows a schematic and 

photograph of the penlight apparatus. The penlight apparatus is a cylinder, usually oriented 

horizontally, formed by heating elements 0.6 m (2 ft) long and 0.45 m (1.5 ft) in diameter. In the 

experiments, the temperature of the cylindrical “shroud” was controlled according to a specified 

function of time while pairs of cables were monitored, one for thermal and the other for electrical 

response. 

Figure 19-3. Schematic (left) and photograph (right) of the “penlight” test apparatus. 

Figure 19-4 shows the results for a 7 conductor cable with XLPE insulation and a CSPE jacket. 

The penlight apparatus was set to provide an approximate shroud temperature of 475 °C. This 

cable has jacket thickness of 1.5 mm, an overall diameter of 15 mm, a mass per unit length of 

0.410 kg/m, and is a thermoset. 
19-15 

Figure 19-4. Results comparing data (short dash line) for XLPE/CSPE, 7 conductor 

cable exposed to a shroud temperature (long dash line) of 475 °C and 

THIEF prediction (solid line). 

Solution 

Purpose: 

(1) Determine the time to failure for the cable exposed in the penlight 

apparatus. 

Assumptions: 

(1) The penlight apparatus exposure is uniform. 

(2) The cable properties do not change with temperature increase. 

(3) Failure is indicated when the temperature inside the cable jacket 

exceeds 400 °C. 

 

0

100

200

300

400

500

600

700

0 200 400 600 800 1000 1200 1400

Tempearture (oC)

Time (s)

Shroud Temperature

Penlight Test 12

THIEF

Prediction
19-16 

Spreadsheet (FDTs

) Information: 

 

Use the following FDTs

: 

(a) 19_THIEF_Thermally_Induced_Electrical_Failure_of_Cables_ 

Sup1_SI.xls (click on THIEF) 

FDTs

 Input Parameters: 

-Gas temperature around the cable as a function time (4 points): 

Time (s) Temperature (°C) 

0 28 

100 475 

1300 475 

1700 300 

-Type of cable (thermoplastic, thermoset) = Thermoset 

-Cable diameter = 15 mm 

-Cable mass per unit length = 0.410 kg/m 

-Cable jacket thickness =1.5 mm 

-Air Drop 

Results* 

Time to Cable Failure (minutes) 9.1 

*see spreadsheet 
CHAPTER 19. ESTIMATING THE THERMALLY-INDUCED

ELECTRICAL FAILURE (THIEF)

OF CABLES

Version 1805.1

(SI Units)

mm 0.0075 m

kg/m Do Not Enter Any 0.41000 kg/m

mm Values in the 0.0015 m o

C Green Boxes! 294.00 K

o

C 673.00 K

s They are entered

mm automatically 0 m

mm based on the 0 m

kg/m3 cable selection.

Failure Temperature

Maximum Time

Conduit Thickness

Conduit Outside Diameter

Project / Inspection 

Title: NUREG-1805 Supplement 1 Example 19.11-1

Cable Mass per Unit Length

400

4000

0.00

0.00

All subsequent output values are calculated by the spreadsheet and based on values specified in the input parameters. This spreadsheet is protected 

and secure to avoid errors due to a wrong entry in a cell(s). The chapter in the NUREG should be read before an analysis is made.

Click to Select Source for Exposure Gas Temperature Profile:

INPUT PARAMETERS

Cable Density

Cable Insulation Type (Thermoplastic or Thermoset)

Cable Function (Control, Instrumentation or Power)

Cable Diameter

The following calculations estimate the time to failure of cables exposed to a specified hot gas layer.

Parameters in YELLOW CELLS are Entered by the User.

Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU or SELECT CABLE BUTTON.

Cable Jacket Thickness

Ambient Air Temperature

Number of Conductors

Cable Location

Wire Gauge (AWG)

Warning: You MUST Click the Calculate Button Below when Finished Entering or Changing Data!

2320.13

Thermoset

Instrumentation

14

15.00

0.41

1.500

21

7

Air Drop

Calculate

Select Cable

Natural Ventilation - Method of McCaffrey, Quintiere, Harkleroad (MQH)

Forced Ventilation - Method of Foote, Pagni, and Alvares (FPA)

Forced Ventilation - Method of Deal and Beyler

Room Fire with Closed Door

Within Fire Plume

User Defined

Selecting one of 

these items will 

automatically 

transfer you to the 

appropriate 

spreadsheet to 

calculate the 

exposure gas 

temperature profile

19-17
CHAPTER 19. ESTIMATING THE THERMALLY-INDUCED

ELECTRICAL FAILURE (THIEF)

OF CABLES

Version 1805.1

(SI Units)

Answer: Cable fails at 9.1 minutes

EXPOSURE GAS TEMPERATURE PROFILE

Time (s)

300.00

475.00

0

Gas Temperature (oC) Gas Temperature (oK)

1300

100

1700

28.00

475.00

301.15

748.15

748.15

573.15

Failure Range

0

50

100

150

200

250

300

350

400

450

500

0 100 200 300 400 500 600

Temperature (°C)

Time (s)

RESULTS

Exposing Temp Cable Temp Conduit Temp

For User Defined 

Exposure Gas 

Temperature Profile: 

Enter Time and 

Temperature Pairs in 

Table

 (Temperatures are 

automatically converted 

to Kelvin.)

19-18
19-19 

Example Problem 19.11-2 

(Ventilation Differences – Natural vs. Forced) 

Problem Statement 

Consider a concrete compartment that is 16.40 ft (5.00 m) wide x 16.40 ft (5.00 m) long x 

11.48 ft (3.50 m) high (wc x Ic x hc), with a simple vent that is 3.28 ft (1.00 m) wide x 6.90 ft 

(2.10 m) high (wv x hv) (open door). Assume the vent is flush with the floor. There is an HVAC 

system that can be used for smoke exhaust during a fire. The fire is constant with a HRR of 500 

kW. A cable tray containing control cables passes through the compartment. The cables are 7 

conductor, 10 gauge, power and control cables manufactured by Draka with PVC insulation. 

Compute the time to cable failure under two scenarios: (a) the HVAC system is off and the room 

door is open and (b) the door is closed and the HVAC is operating at a rate of 4,000 cfm. The 

same cable is to be analyzed in both scenarios. 

Example 19.11-2. Concrete Compartment with a Door and Forced Ventilation. 

Solution 

Purpose: 

(1) Determine the time to failure for the two scenarios and compare the results 

for natural and forced ventilation. 

Assumptions: 

(1) The cables are surrounded by a uniform temperature hot gas layer. 

4000 cfm 
19-20 

(2) The cable properties do not change with temperature increase. 

(3) Failure is indicated when the temperature inside the cable jacket exceeds 

390 °F (200 °C). 

Spreadsheet (FDTs

) Information: 

 

Use the following FDTs

: 

(a) 02.1_Temperature_NV_Sup1.xls (click on Temperature_NV) 

(b) 02.2_Temperature_FV_Sup1.xls (click on Temperature_FV) 

(c) 19_THIEF_Thermally_Induced_Electrical_Failure_of_Cables_ 

Sup1.xls (click on THIEF) 

FDTs

 Input Parameters: 

-Gas temperature around the cable as a function time: 

(a) Use 02.1_Temperature_NV_Sup1.xls and the parameters presented 

above to determine the gas temperature for natural ventilation 

On the THIEF spreadsheet, select: Natural Ventilation– Method of 

McCaffrey, Quintiere, Harkleroad (MQH) 

(b) Use 02.2_Temperature_FV_Sup1.xls and the parameters presented 

above to determine the gas temperature for forced ventilation 

On the THIEF spreadsheet, select: Forced Ventilation – Method of 

Foote, Pagni, and Alvares (FPA) 

-Press “Select Cable” Button 

-Choose appropriate cable from list. 

-Press “Calculate” Button 

Results* 

 Ventilation 

Natural Forced 

Time to Cable Failure (minutes) 46.2 No Failure 

*see spreadsheets 
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

AND SMOKE LAYER HEIGHT IN A ROOM FIRE

WITH NATURAL VENTILATION

Version 1805.1

(English Units)

16.40 4.99872 m

16.40 4.99872 m

11.48 3.499104 m

3.28 1.000 m

6.90 2.103 m

6.90 ft 2.103 m

12.00 0.3048 m

70.00 21.11 °C

294.11 °K

1.00

1.20

2.9

0.0016

0.75

2400

Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU for the Material Selected.

ft

ft

Compartment Height (hc)

Vent Width (wv)

Vent Height (hv)

Top of Vent from Floor (VT)

INPUT PARAMETERS

COMPARTMENT INFORMATION

Parameters in YELLOW CELLS are Entered by the User.

Ambient Air Density (a)

Ambient Air Temperature (Ta)

Specific Heat of Air (cp)

ft

ft

COMPARTMENT WITH THERMALLY THICK/THIN BOUNDARIES 

All subsequent output values are calculated by the spreadsheet and based on values specified in the input parameters. This spreadsheet is protected 

and secure to avoid errors due to a wrong entry in a cell(s). The chapter in the NUREG should be read before an analysis is made.

The following calculations estimate the hot gas layer temperature and smoke layer height in enclosure fire.

°F

AMBIENT CONDITIONS

Interior Lining Thickness ()

Compartment Width (wc)

Compartment Length (lc)

ft

in

Project / Inspection 

Title: NUREG-1805 Supplement 1 Example 19.11-2a

Interior Lining Thermal Conductivity (k) kW/m-K

kJ/kg-K

kg/m3

THERMAL PROPERTIES OF COMPARTMENT ENCLOSING SURFACES FOR

Interior Lining Thermal Inertia (kc)

kJ/kg-K

kg/m3

(kW/m2-K)2-sec

Note: Ambient Air Density (a) will automatically correct with Ambient Air Temperature (Ta) Input

Interior Lining Specific Heat (c)

Interior Lining Density ()

19-21
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

AND SMOKE LAYER HEIGHT IN A ROOM FIRE

WITH NATURAL VENTILATION

Version 1805.1

(English Units)

kc k c 

(kW/m2

-K)2-sec (kW/m-K) (kJ/kg-K) (kg/m3)

500 0.206 0.895 2710

197 0.054 0.465 7850

2.9 0.0016 0.75 2400

1.7 0.0008 0.8 2600

1.6 0.00076 0.8 2710

1.2 0.00073 0.84 1900

0.18 0.00017 1.1 960

0.16 0.00012 2.5 540

0.16 0.00053 1.25 240

0.15 0.00015 1.25 800

0.12 0.00026 0.96 500

0.12 0.00016 0.84 950

0.098 0.00013 1.12 700

0.036 0.00014 1 260

0.0018 0.000037 0.8 60

0.001 0.000034 1.5 20

Enter Value Enter Value Enter Value Enter Value

500.00

Aerated Concrete

Plasterboard

User Specified Value

Calcium Silicate Board 

Alumina Silicate Block

Glass Fiber Insulation

Expanded Polystyrene

Glass, Plate

Brick/Concrete Block

Fiber Insulation Board

Chipboard

Gypsum Board

Plywood

Aluminum (pure)

Steel (0.5% Carbon)

Concrete

Brick

Select Material

Material

THERMAL PROPERTIES FOR COMMON INTERIOR LINING MATERIALS

FIRE SPECIFICATIONS

Fire Heat Release Rate (Q) kW

Scroll to desired material

Click the selection

Reference: Klote, J., J. Milke, Principles of Smoke Management, 2002, Page 270.

Click Here to Calculate this Sheet 

and Return to THIEF

Concrete

19-22
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

AND SMOKE LAYER HEIGHT IN A ROOM FIRE

WITH NATURAL VENTILATION

Version 1805.1

(English Units)

hk Tg Tg Tg Tg

(min) (sec) (kW/m2

-K) (°K) (°K) (°C) (°F)

0 0.00 - - 294.11 21.11 70.00

1 60 0.22 100.57 394.68 121.68 251.03

2 120 0.16 112.89 407.00 134.00 273.20

3 180 0.13 120.78 414.89 141.89 287.40

4 240 0.11 126.71 420.82 147.82 298.08

5 300 0.10 131.51 425.62 152.62 306.72

10 600 0.07 147.62 441.73 168.73 335.71

15 900 0.06 157.94 452.05 179.05 354.29

20 1200 0.05 165.70 459.81 186.81 368.25

25 1500 0.04 171.97 466.09 193.09 379.55

30 1800 0.04 177.28 471.39 198.39 389.11

35 2100 0.04 181.89 476.01 203.01 397.41

40 2400 0.03 185.99 480.10 207.10 404.78

45 2700 0.03 189.68 483.79 210.79 411.42

50 3000 0.03 193.04 487.15 214.15 417.46

55 3300 0.03 196.13 490.24 217.24 423.03

60 3600 0.03 198.99 493.10 220.10 428.18

Results Time After Ignition (t)

0

50

100

150

200

250

300

350

400

450

0 10 20 30 40 50 60

Temperature (°F)

Time (min)

Hot Gas Layer Temperature

Natural Ventilation (MQH Method)

19-23
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

AND SMOKE LAYER HEIGHT IN A ROOM FIRE

WITH NATURAL VENTILATION

Version 1805.1

(English Units)

Results

Time g Constant (k)

Smoke Layer 

Height

Smoke Layer 

Height

(min) (kg/m3

) (kW/m-K) z (m) z (ft)

0 1.20 0.063 3.50 11.48

1 0.89 0.085 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

2 0.87 0.088 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

3 0.85 0.089 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

4 0.84 0.091 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

5 0.83 0.092 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

10 0.80 0.095 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

15 0.78 0.097 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

20 0.77 0.099 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

25 0.76 0.100 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

30 0.75 0.101 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

35 0.74 0.102 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

40 0.74 0.103 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

45 0.73 0.104 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

50 0.72 0.105 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

55 0.72 0.106 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

60 0.72 0.106 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

Caution! The smoke layer height is a conservative estimate and is only intended to provide an indication where 

the hot gas layer is located. Calculated smoke layer height below the vent height are not creditable since the 

calculation is not accounting for the smoke exiting the vent.

The above calculations are based on principles developed in the SFPE Handbook of Fire Protection Engineering, 3rd Edition, 2002. Calculations are based on 

certain assumptions and have inherent limitations. The results of such calculations may or may not have reasonable predictive capabilities for a given situation 

and should only be interpreted by an informed user. Although each calculation in the spreadsheet has been verified with the results of hand calculation, there is 

no absolute guarantee of the accuracy of these calculations. Any questions, comments, concerns, and suggestions, or to report an error(s) in the spreadsheet, 

please send an email to David.Stroup@nrc.gov and Naeem.Iqbal@nrc.gov or MarkHenry.Salley@nrc.gov.

NOTE:

0

2

4

6

8

10

12

14

0 10 20 30 40 50 60

Height from Floor (ft)

Time (min)

Smoke Layer Height

Natural Ventilation (Method of Yamana and Tanaka)

19-24
CHAPTER 19. ESTIMATING THE THERMALLY-INDUCED

ELECTRICAL FAILURE (THIEF)

OF CABLES

Version 1805.1

(English Units)

in 0.00825498 m

lb/ft Do Not Enter Any 0.53872 kg/m

in Values in the 0.001524 m o

F Green Boxes! 294.26 K

o

F 473.15 K

s They are entered

in automatically 0 m

in based on the 0 m

kg/m3 cable selection.

All subsequent output values are calculated by the spreadsheet and based on values specified in the input parameters. This spreadsheet is protected 

and secure to avoid errors due to a wrong entry in a cell(s). The chapter in the NUREG should be read before an analysis is made.

Failure Temperature

Maximum Time

Conduit Thickness

Conduit Outside Diameter

Project / Inspection 

Title:

Warning: You MUST Click the Calculate Button Below when Finished Entering or Changing Data!

Cable Function (Control, Instrumentation or Power)

Cable Diameter

Cable Mass per Unit Length

392

NUREG-1805 Supplement 1 Example 19.11-2a

INPUT PARAMETERS

Cable Density

Cable Insulation Type (Thermoplastic or Thermoset)

Cable Jacket Thickness

The following calculations estimate the time to failure of cables exposed to a specified hot gas layer.

Parameters in YELLOW CELLS are Entered by the User.

Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU or SELECT CABLE BUTTON.

Ambient Air Temperature

Number of Conductors

Cable Location

Wire Gauge (AWG)

4000

0.00

0.00

Thermoplastic

Control

10

0.65

0.36

0.060

70

7

Cable Tray

Click to Select Source for Exposure Gas Temperature Profile:

2516.39

Calculate

Select Cable

Natural Ventilation - Method of McCaffrey, Quintiere, Harkleroad (MQH)

Forced Ventilation - Method of Foote, Pagni, and Alvares (FPA)

Forced Ventilation - Method of Deal and Beyler

Room Fire with Closed Door

Within Fire Plume

User Defined

Selecting one of 

these items will 

automatically 

transfer you to the 

appropriate 

spreadsheet to 

calculate the 

exposure gas 

temperature profile

19-25
CHAPTER 19. ESTIMATING THE THERMALLY-INDUCED

ELECTRICAL FAILURE (THIEF)

OF CABLES

Version 1805.1

(English Units)

EXPOSURE GAS TEMPERATURE PROFILE

Time (s)

287.40

298.08

Answer: Cable fails at 46.2 minutes

240

354.29

180

306.72

335.71 441.88

368.25

1800

60

273.20

0

120

Gas Temperature (oF)

251.03

Gas Temperature (oK)

70.00

389.11

2100

2400

379.55

300

600

900

1500

1200

397.41

404.78

423.03

428.18

2700

3000

411.42

417.46

452.20

459.96

466.24

3300

3600

471.54

476.16

294.26

394.83

407.15

415.04

420.97

425.77

480.25

483.94

487.30

490.39

493.25

Failure Range

0

50

100

150

200

250

300

350

400

450

500

0 500 1000 1500 2000 2500 3000

Temperature (°F)

Time (s)

RESULTS

Exposing Temp Cable Temp Conduit Temp

19-26
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(English Units)

16.40 ft 5.00 m

16.40 ft 5.00 m

11.48 ft 3.50 m

12.00 in 0.3048 m

70.00 21.11 °C

294.11 K

1.00 kJ/kg-K

1.20 kg/m3

2.9

0.0016

0.75

2400

Interior Lining Thermal Inertia (kc)

Interior Lining Thermal Conductivity (k)

Interior Lining Specific Heat (c)

Interior Lining Density ()

(kW/m2

-K)2-sec

kW/m-K

kJ/kg-K

kg/m3

COMPARTMENT INFORMATION

AMBIENT CONDITIONS

Compartment Width (wc)

Compartment Length (lc)

Compartment Height (hc)

All subsequent output values are calculated by the spreadsheet and based on values specified in the input parameters. This spreadsheet is protected 

Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU for the Material Selected.

COMPARTMENT WITH THERMALLY THICK/THIN BOUNDARIES 

The following calculations estimate the hot gas layer temperature and smoke layer height in enclosure fire.

Parameters in YELLOW CELLS are Entered by the User.

Project / Inspection 

Title: NUREG-1805 Supplement 1 Example 19-11.2b

Ambient Air Temperature (Ta)

Specific Heat of Air (cp)

Ambient Air Density (a)

Interior Lining Thickness ()

and secure to avoid errors due to a wrong entry in a cell(s). The chapter in the NUREG should be read before an analysis is made.

INPUT PARAMETERS

Note: Ambient Air Density (a) will automatically correct with Ambient Air Temperature (Ta) Input

°F

THERMAL PROPERTIES OF COMPARTMENT ENCLOSING SURFACES FOR

19-27
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(English Units)

kc k c 

(kW/m2

-K)2-sec (kW/m-K) (kJ/kg-K) (kg/m3)

500 0.206 0.895 2710

197 0.054 0.465 7850

2.9 0.0016 0.75 2400

1.7 0.0008 0.8 2600

1.6 0.00076 0.8 2710

1.2 0.00073 0.84 1900

0.18 0.00017 1.1 960

0.16 0.00012 2.5 540

0.16 0.00053 1.25 240

0.15 0.00015 1.25 800

0.12 0.00026 0.96 500

0.12 0.00016 0.84 950

0.098 0.00013 1.12 700

0.036 0.00014 1 260

0.0018 0.000037 0.8 60

0.001 0.000034 1.5 20

Enter Value Enter Value Enter Value Enter Value

4000.00 cfm 1.888 m3

/sec

2.266 kg/sec

500.00 kW

COMPARTMENT MASS VENTILATION FLOW RATE

Chipboard

Aerated Concrete

Plasterboard

Calcium Silicate Board 

Alumina Silicate Block

Glass Fiber Insulation

Reference: Klote, J., J. Milke, Principles of Smoke Management, 2002 Page 270.

Fire Heat Release Rate (Q)

FIRE SPECIFICATIONS

Aluminum (pure)

Steel (0.5% Carbon)

Concrete

Brick

Fiber Insulation Board

Forced Ventilation Flow Rate (m)

User Specified Value

Glass, Plate

Brick/Concrete Block

THERMAL PROPERTIES FOR COMMON INTERIOR LINING MATERIALS

Expanded Polystyrene

Material

Gypsum Board

Plywood

Scroll to desired material

Click on selection

Select Material

Click Here to Calculate this Sheet 

and Return to THIEF

Concrete

19-28
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(English Units)

Results Time After Ignition (t) hk Tg/Ta Tg Tg Tg Tg 

(min) (sec) (kW/m2

-K) (°K) (°K) (°C) (°F)

0 0 - - - 294.11 21.11 70.00

1 60 0.22 0.21 62.28 356.39 83.39 182.10

2 120 0.16 0.24 70.55 364.66 91.66 196.99

3 180 0.13 0.26 75.89 370.00 97.00 206.61

4 240 0.11 0.27 79.93 374.04 101.04 213.87

5 300 0.10 0.28 83.20 377.31 104.31 219.76

10 600 0.07 0.32 94.26 388.37 115.37 239.66

15 900 0.06 0.34 101.39 395.50 122.50 252.51

20 1200 0.05 0.36 106.78 400.89 127.89 262.21

25 1500 0.04 0.38 111.16 405.27 132.27 270.09

30 1800 0.04 0.39 114.87 408.98 135.98 276.76

35 2100 0.04 0.40 118.10 412.21 139.21 282.58

40 2400 0.03 0.41 120.97 415.08 142.08 287.75

45 2700 0.03 0.42 123.56 417.68 144.68 292.42

50 3000 0.03 0.43 125.93 420.04 147.04 296.67

55 3300 0.03 0.44 128.11 422.22 149.22 300.60

60 3600 0.03 0.44 130.13 424.24 151.24 304.24

Tg = Tg - Ta

Tg = Tg + Ta

Tg/Ta = 0.63(Q/mcpTa)

0.72(hkAT/mcp)-0.36

Compartment Hot Gas Layer Temperature With Forced Ventilation

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60

Temperature (°F)

Time (min)

Hot Gas Layer Temperature

Forced Ventilation - FPA Method

19-29
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(English Units)

Results hk Tg Tg Tg Tg 

(min) (sec) (kW/m2

-K) (°K) (°K) (°C) (°F)

0 0 - - 294.11 21.11 70.00

1 60 0.09 39.02 333.13 60.13 140.24

2 120 0.06 51.42 345.53 72.53 162.56

3 180 0.05 59.84 353.95 80.95 177.72

4 240 0.04 66.32 360.43 87.43 189.37

5 300 0.04 71.61 365.72 92.72 198.89

10 600 0.03 89.27 383.38 110.38 230.68

15 900 0.02 100.22 394.33 121.33 250.39

20 1200 0.02 108.13 402.24 129.24 264.63

25 1500 0.02 114.28 408.39 135.39 275.70

30 1800 0.02 119.29 413.40 140.40 284.72

35 2100 0.01 123.50 417.61 144.61 292.30

40 2400 0.01 127.11 421.23 148.23 298.81

45 2700 0.01 130.27 424.38 151.38 304.49

50 3000 0.01 133.07 427.18 154.18 309.53

55 3300 0.01 135.58 429.69 156.69 314.04

60 3600 0.01 137.84 431.95 158.95 318.11

Time After Ignition (t)

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60

Temperature (°F)

Time (min)

Hot Gas Layer Temperature

Forced Ventilation - Deal and Beyler Method

19-30
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(English Units)

Prepared by: Date:

Checked by: Date: Organization:

Additional Information:

NOTE:

Summary of Results

The above calculations are based on principles developed in the SFPE Handbook of Fire Protection Engineering, 2nd Edition, 1995. Calculations 

are based on certain assumptions and have inherent limitations. The results of such calculations may or may not have reasonable predictive 

capabilities for a given situation, and should only be interpreted by an informed user. Although each calculation in the spreadsheet has been 

verified with the results of hand calculation, there is no absolute guarantee of the accuracy of these calculations. Any questions, comments, 

concerns, and suggestions, or to report an error(s) in the spreadsheets, please send an email to David.Stroup@nrc.gov and Naeem.Iqbal@nrc.gov 

or MarkHenry.Salley@nrc.gov.

Organization:

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60

Temperature (°F)

Time (min)

Hot Gas Layer Temperature

Forced Ventilation

FPA Method

Deal and Beyler Method

19-31
CHAPTER 19. ESTIMATING THE THERMALLY-INDUCED

ELECTRICAL FAILURE (THIEF)

OF CABLES

Version 1805.1

(English Units)

in 0.00825498 m

lb/ft Do Not Enter Any 0.53872 kg/m

in Values in the 0.001524 m o

F Green Boxes! 294.26 K

o

F 473.15 K

s They are entered

in automatically 0 m

in based on the 0 m

kg/m3 cable selection.

All subsequent output values are calculated by the spreadsheet and based on values specified in the input parameters. This spreadsheet is protected 

and secure to avoid errors due to a wrong entry in a cell(s). The chapter in the NUREG should be read before an analysis is made.

Failure Temperature

Maximum Time

Conduit Thickness

Conduit Outside Diameter

Project / Inspection 

Title:

Warning: You MUST Click the Calculate Button Below when Finished Entering or Changing Data!

Cable Function (Control, Instrumentation or Power)

Cable Diameter

Cable Mass per Unit Length

392

NUREG-1805 Supplement 1 Example 19.11-2b

INPUT PARAMETERS

Cable Density

Cable Insulation Type (Thermoplastic or Thermoset)

Cable Jacket Thickness

The following calculations estimate the time to failure of cables exposed to a specified hot gas layer.

Parameters in YELLOW CELLS are Entered by the User.

Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU or SELECT CABLE BUTTON.

Ambient Air Temperature

Number of Conductors

Cable Location

Wire Gauge (AWG)

4000

0.00

0.00

Thermoplastic

Control

10

0.65

0.36

0.060

70

7

Cable Tray

Click to Select Source for Exposure Gas Temperature Profile:

2516.39

Calculate

Select Cable

Natural Ventilation - Method of McCaffrey, Quintiere, Harkleroad (MQH)

Forced Ventilation - Method of Foote, Pagni, and Alvares (FPA)

Forced Ventilation - Method of Deal and Beyler

Room Fire with Closed Door

Within Fire Plume

User Defined

Selecting one of 

these items will 

automatically 

transfer you to the 

appropriate 

spreadsheet to 

calculate the 

exposure gas 

temperature profile

19-32
CHAPTER 19. ESTIMATING THE THERMALLY-INDUCED

ELECTRICAL FAILURE (THIEF)

OF CABLES

Version 1805.1

(English Units)

EXPOSURE GAS TEMPERATURE PROFILE

Time (s)

206.61

213.87

Answer: Cable does not reach failure temperature in 4000.2 seconds

240

252.51

180

219.76

239.66 388.52

262.21

1800

60

196.99

0

120

Gas Temperature (oF)

182.10

Gas Temperature (oK)

70.00

276.76

2100

2400

270.09

300

600

900

1500

1200

282.58

287.75

300.60

304.24

2700

3000

292.42

296.67

395.65

401.04

405.42

3300

3600

409.13

412.36

294.26

356.54

364.81

370.15

374.19

377.46

415.23

417.83

420.19

422.37

424.39

Failure Range

0

50

100

150

200

250

300

350

400

450

500

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Temperature (°F)

Time (s)

RESULTS

Exposing Temp Cable Temp Conduit Temp

19-33
19-34 

Example Problem 19.11-3 

(Cable Location – Cable Tray vs. Conduit - Natural Ventilation)

Problem Statement 

Consider a concrete compartment that is 16.40 ft (5.00 m) wide x 32.81 ft (10.00 m) long x 

9.84 ft (3.00 m) high (wc x Ic x hc), with a simple vent that is 3.28 ft (1.00 m) wide x 6.90 ft 

(2.10 m) high (wv x hv) (open door). Assume the vent is flush with the floor. The fire is constant 

with a HRR of 575 kW and no HVAC is located in this room. Compute the time to cable failure 

under two scenarios: (a) the cable is located in a cable tray and (b) the cable is located in a 3-

inch (78 mm) rigid conduit. The same cable is to be analyzed in both scenarios, and the 

identification print located on the exterior of the cable jacket reads the following: 

GENERAL CABLE® 20/10 CONTROL CABLE 7/C 12AWG PE/PVC 75°C 600V 

Example 19.11-3. Concrete Compartment with Natural Ventilation. 

575 kW 
19-35 

Solution

Purpose: 

(1) Determine the time to failure and compare the results of an electrical 

cable located in a cable tray and one located in a rigid conduit. 

Assumptions: 

(1) The cables are surrounded by a uniform temperature hot gas layer. 

(2) The cable properties do not change with temperature increase. 

(3) Failure is indicated when the temperature inside the cable jacket exceeds 

392°F (200°C) (thermoplastic cable). 

Spreadsheet (FDTs

) Information: 

 Use the following FDTs

: 

(a) 02.1_Temperature_NV_Sup1.xls (click on Temperature_NV) 

(b) 19_THIEF_Thermally_Induced_Electrical_Failure_of_Cables_ 

Sup1.xls (click on THIEF) 

FDTs

 Input Parameters 

 -Gas temperature around the cable as a function time: 

o Use 02.1_Temperature_NV_Sup1.xls and the parameters presented above 

to determine the gas temperature (same for both scenarios) 

o On the THIEF spreadsheet, select: Natural Ventilation – Method of 

McCaffrey, Quintiere, Harkleroad (MQH) 

-Press “Select Cable” Button 

-Choose appropriate cable from list (i.e., Control – 12 AWG – 7 conductor – 

 General Cable – 20/10 – PE – PVC) 

- Choose appropriate “Cable Location” 

(a) “Cable Tray” 

(b) “Conduit – Rigid” & 3” for Conduit outside diameter 

-Press “Calculate” Button 

Results* 

Cable Tray – Time to Cable Failure (minutes) 54.6 

Cable Conduit – Time to Cable Failure (minutes) No failure 

*see spreadsheets 

This example illustrates the additional thermal protection provided by the conduit. The conduit 

has a mass that must first be heated before the cable can be exposed to elevated temperature. 

The conduit’s thermal inertia provides the additional time (protection) to cable failure. 
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

AND SMOKE LAYER HEIGHT IN A ROOM FIRE

WITH NATURAL VENTILATION

Version 1805.1

(English Units)

16.40 4.99872 m

32.81 10.000488 m

9.84 2.999232 m

3.28 1.000 m

6.90 2.103 m

6.90 ft 2.103 m

12.00 0.3048 m

70.00 21.11 °C

294.11 °K

1.00

1.20

2.9

0.0016

0.75

2400

Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU for the Material Selected.

ft

ft

Compartment Height (hc)

Vent Width (wv)

Vent Height (hv)

Top of Vent from Floor (VT)

INPUT PARAMETERS

COMPARTMENT INFORMATION

Parameters in YELLOW CELLS are Entered by the User.

Ambient Air Density (a)

Ambient Air Temperature (Ta)

Specific Heat of Air (cp)

ft

ft

COMPARTMENT WITH THERMALLY THICK/THIN BOUNDARIES 

All subsequent output values are calculated by the spreadsheet and based on values specified in the input parameters. This spreadsheet is protected 

and secure to avoid errors due to a wrong entry in a cell(s). The chapter in the NUREG should be read before an analysis is made.

The following calculations estimate the hot gas layer temperature and smoke layer height in enclosure fire.

°F

AMBIENT CONDITIONS

Interior Lining Thickness ()

Compartment Width (wc)

Compartment Length (lc)

ft

in

Project / Inspection 

Title: NUREG-1805 Supplement 1 Example 19-11.3a

Interior Lining Thermal Conductivity (k) kW/m-K

kJ/kg-K

kg/m3

THERMAL PROPERTIES OF COMPARTMENT ENCLOSING SURFACES FOR

Interior Lining Thermal Inertia (kc)

kJ/kg-K

kg/m3

(kW/m2-K)2-sec

Note: Ambient Air Density (a) will automatically correct with Ambient Air Temperature (Ta) Input

Interior Lining Specific Heat (c)

Interior Lining Density ()

19-36
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

AND SMOKE LAYER HEIGHT IN A ROOM FIRE

WITH NATURAL VENTILATION

Version 1805.1

(English Units)

kc k c 

(kW/m2

-K)2-sec (kW/m-K) (kJ/kg-K) (kg/m3)

500 0.206 0.895 2710

197 0.054 0.465 7850

2.9 0.0016 0.75 2400

1.7 0.0008 0.8 2600

1.6 0.00076 0.8 2710

1.2 0.00073 0.84 1900

0.18 0.00017 1.1 960

0.16 0.00012 2.5 540

0.16 0.00053 1.25 240

0.15 0.00015 1.25 800

0.12 0.00026 0.96 500

0.12 0.00016 0.84 950

0.098 0.00013 1.12 700

0.036 0.00014 1 260

0.0018 0.000037 0.8 60

0.001 0.000034 1.5 20

Enter Value Enter Value Enter Value Enter Value

575.00

Aerated Concrete

Plasterboard

User Specified Value

Calcium Silicate Board 

Alumina Silicate Block

Glass Fiber Insulation

Expanded Polystyrene

Glass, Plate

Brick/Concrete Block

Fiber Insulation Board

Chipboard

Gypsum Board

Plywood

Aluminum (pure)

Steel (0.5% Carbon)

Concrete

Brick

Select Material

Material

THERMAL PROPERTIES FOR COMMON INTERIOR LINING MATERIALS

FIRE SPECIFICATIONS

Fire Heat Release Rate (Q) kW

Scroll to desired material

Click the selection

Reference: Klote, J., J. Milke, Principles of Smoke Management, 2002, Page 270.

Click Here to Calculate this Sheet 

and Return to THIEF

Concrete

19-37
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

AND SMOKE LAYER HEIGHT IN A ROOM FIRE

WITH NATURAL VENTILATION

Version 1805.1

(English Units)

hk Tg Tg Tg Tg

(min) (sec) (kW/m2

-K) (°K) (°K) (°C) (°F)

0 0.00 - - 294.11 21.11 70.00

1 60 0.22 94.50 388.61 115.61 240.10

2 120 0.16 106.07 400.18 127.18 260.93

3 180 0.13 113.49 407.60 134.60 274.28

4 240 0.11 119.06 413.17 140.17 284.31

5 300 0.10 123.57 417.68 144.68 292.43

10 600 0.07 138.71 432.82 159.82 319.67

15 900 0.06 148.40 442.52 169.52 337.13

20 1200 0.05 155.69 449.80 176.80 350.25

25 1500 0.04 161.59 455.70 182.70 360.87

30 1800 0.04 166.58 460.69 187.69 369.84

35 2100 0.04 170.91 465.02 192.02 377.64

40 2400 0.03 174.76 468.87 195.87 384.57

45 2700 0.03 178.22 472.33 199.33 390.80

50 3000 0.03 181.38 475.49 202.49 396.49

55 3300 0.03 184.29 478.40 205.40 401.71

60 3600 0.03 186.98 481.09 208.09 406.56

Results Time After Ignition (t)

0

50

100

150

200

250

300

350

400

450

0 10 20 30 40 50 60

Temperature (°F)

Time (min)

Hot Gas Layer Temperature

Natural Ventilation (MQH Method)

19-38
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

AND SMOKE LAYER HEIGHT IN A ROOM FIRE

WITH NATURAL VENTILATION

Version 1805.1

(English Units)

Results

Time g Constant (k)

Smoke Layer 

Height

Smoke Layer 

Height

(min) (kg/m3

) (kW/m-K) z (m) z (ft)

0 1.20 0.063 3.00 9.84

1 0.91 0.084 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

2 0.88 0.086 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

3 0.87 0.088 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

4 0.85 0.089 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

5 0.85 0.090 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

10 0.82 0.093 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

15 0.80 0.095 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

20 0.78 0.097 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

25 0.77 0.098 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

30 0.77 0.099 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

35 0.76 0.100 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

40 0.75 0.101 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

45 0.75 0.102 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

50 0.74 0.102 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

55 0.74 0.103 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

60 0.73 0.104 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

Caution! The smoke layer height is a conservative estimate and is only intended to provide an indication where 

the hot gas layer is located. Calculated smoke layer height below the vent height are not creditable since the 

calculation is not accounting for the smoke exiting the vent.

The above calculations are based on principles developed in the SFPE Handbook of Fire Protection Engineering, 3rd Edition, 2002. Calculations are based on 

certain assumptions and have inherent limitations. The results of such calculations may or may not have reasonable predictive capabilities for a given situation 

and should only be interpreted by an informed user. Although each calculation in the spreadsheet has been verified with the results of hand calculation, there is 

no absolute guarantee of the accuracy of these calculations. Any questions, comments, concerns, and suggestions, or to report an error(s) in the spreadsheet, 

please send an email to David.Stroup@nrc.gov and Naeem.Iqbal@nrc.gov or MarkHenry.Salley@nrc.gov.

NOTE:

0

2

4

6

8

10

12

0 10 20 30 40 50 60

Height from Floor (ft)

Time (min)

Smoke Layer Height

Natural Ventilation (Method of Yamana and Tanaka)

19-39
CHAPTER 19. ESTIMATING THE THERMALLY-INDUCED

ELECTRICAL FAILURE (THIEF)

OF CABLES

Version 1805.1

(English Units)

in 0.00749299 m

lb/ft Do Not Enter Any 0.37948 kg/m

in Values in the 0.001143 m o

F Green Boxes! 294.26 K

o

F 473.15 K

s They are entered

in automatically 0 m

in based on the 0 m

kg/m3 cable selection.

All subsequent output values are calculated by the spreadsheet and based on values specified in the input parameters. This spreadsheet is protected 

and secure to avoid errors due to a wrong entry in a cell(s). The chapter in the NUREG should be read before an analysis is made.

Failure Temperature

Maximum Time

Conduit Thickness

Conduit Outside Diameter

Project / Inspection 

Title:

Warning: You MUST Click the Calculate Button Below when Finished Entering or Changing Data!

Cable Function (Control, Instrumentation or Power)

Cable Diameter

Cable Mass per Unit Length

392

NUREG-1805 Supplement 1 Example 19.11-3a

INPUT PARAMETERS

Cable Density

Cable Insulation Type (Thermoplastic or Thermoset)

Cable Jacket Thickness

The following calculations estimate the time to failure of cables exposed to a specified hot gas layer.

Parameters in YELLOW CELLS are Entered by the User.

Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU or SELECT CABLE BUTTON.

Ambient Air Temperature

Number of Conductors

Cable Location

Wire Gauge (AWG)

4000

0.00

0.00

Thermoplastic

Control

12

0.59

0.26

0.045

70

7

Cable Tray

Click to Select Source for Exposure Gas Temperature Profile:

2151.45

Calculate

Select Cable

Natural Ventilation - Method of McCaffrey, Quintiere, Harkleroad (MQH)

Forced Ventilation - Method of Foote, Pagni, and Alvares (FPA)

Forced Ventilation - Method of Deal and Beyler

Room Fire with Closed Door

Within Fire Plume

User Defined

Selecting one of 

these items will 

automatically 

transfer you to the 

appropriate 

spreadsheet to 

calculate the 

exposure gas 

temperature profile

19-40
CHAPTER 19. ESTIMATING THE THERMALLY-INDUCED

ELECTRICAL FAILURE (THIEF)

OF CABLES

Version 1805.1

(English Units)

EXPOSURE GAS TEMPERATURE PROFILE

Time (s)

274.28

284.31

Answer: Cable fails at 54.6 minutes

240

337.13

180

292.43

319.67 432.97

350.25

1800

60

260.93

0

120

Gas Temperature (oF)

240.10

Gas Temperature (oK)

70.00

369.84

2100

2400

360.87

300

600

900

1500

1200

377.64

384.57

401.71

406.56

2700

3000

390.80

396.49

442.67

449.95

455.85

3300

3600

460.84

465.17

294.26

388.76

400.33

407.75

413.32

417.83

469.02

472.48

475.64

478.55

481.24

Failure Range

0

50

100

150

200

250

300

350

400

450

500

0 500 1000 1500 2000 2500 3000 3500

Temperature (°F)

Time (s)

RESULTS

Exposing Temp Cable Temp Conduit Temp

19-41
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

AND SMOKE LAYER HEIGHT IN A ROOM FIRE

WITH NATURAL VENTILATION

Version 1805.1

(English Units)

16.40 4.99872 m

32.81 10.000488 m

9.84 2.999232 m

3.28 1.000 m

6.90 2.103 m

6.90 ft 2.103 m

12.00 0.3048 m

70.00 21.11 °C

294.11 °K

1.00

1.20

2.9

0.0016

0.75

2400

Interior Lining Specific Heat (c)

Interior Lining Density ()

THERMAL PROPERTIES OF COMPARTMENT ENCLOSING SURFACES FOR

Interior Lining Thermal Inertia (kc)

kJ/kg-K

kg/m3

(kW/m2-K)2-sec

Note: Ambient Air Density (a) will automatically correct with Ambient Air Temperature (Ta) Input

Interior Lining Thermal Conductivity (k) kW/m-K

kJ/kg-K

kg/m3

Project / Inspection 

Title: NUREG-1805 Supplement 1 Example 19-11.3b

°F

AMBIENT CONDITIONS

Interior Lining Thickness ()

Compartment Width (wc)

Compartment Length (lc)

ft

in

COMPARTMENT WITH THERMALLY THICK/THIN BOUNDARIES 

All subsequent output values are calculated by the spreadsheet and based on values specified in the input parameters. This spreadsheet is protected 

and secure to avoid errors due to a wrong entry in a cell(s). The chapter in the NUREG should be read before an analysis is made.

The following calculations estimate the hot gas layer temperature and smoke layer height in enclosure fire.

Parameters in YELLOW CELLS are Entered by the User.

Ambient Air Density (a)

Ambient Air Temperature (Ta)

Specific Heat of Air (cp)

ft

ft

Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU for the Material Selected.

ft

ft

Compartment Height (hc)

Vent Width (wv)

Vent Height (hv)

Top of Vent from Floor (VT)

INPUT PARAMETERS

COMPARTMENT INFORMATION

19-42
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

AND SMOKE LAYER HEIGHT IN A ROOM FIRE

WITH NATURAL VENTILATION

Version 1805.1

(English Units)

kc k c 

(kW/m2

-K)2-sec (kW/m-K) (kJ/kg-K) (kg/m3)

500 0.206 0.895 2710

197 0.054 0.465 7850

2.9 0.0016 0.75 2400

1.7 0.0008 0.8 2600

1.6 0.00076 0.8 2710

1.2 0.00073 0.84 1900

0.18 0.00017 1.1 960

0.16 0.00012 2.5 540

0.16 0.00053 1.25 240

0.15 0.00015 1.25 800

0.12 0.00026 0.96 500

0.12 0.00016 0.84 950

0.098 0.00013 1.12 700

0.036 0.00014 1 260

0.0018 0.000037 0.8 60

0.001 0.000034 1.5 20

Enter Value Enter Value Enter Value Enter Value

575.00

Scroll to desired material

Click the selection

Reference: Klote, J., J. Milke, Principles of Smoke Management, 2002, Page 270.

kW

THERMAL PROPERTIES FOR COMMON INTERIOR LINING MATERIALS

FIRE SPECIFICATIONS

Fire Heat Release Rate (Q)

Material

Select Material

Aluminum (pure)

Steel (0.5% Carbon)

Concrete

Brick

Glass, Plate

Brick/Concrete Block

Fiber Insulation Board

Chipboard

Gypsum Board

Plywood

Aerated Concrete

Plasterboard

User Specified Value

Calcium Silicate Board 

Alumina Silicate Block

Glass Fiber Insulation

Expanded Polystyrene

Click Here to Calculate this Sheet 

and Return to THIEF

Concrete

19-43
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

AND SMOKE LAYER HEIGHT IN A ROOM FIRE

WITH NATURAL VENTILATION

Version 1805.1

(English Units)

hk Tg Tg Tg Tg

(min) (sec) (kW/m2

-K) (°K) (°K) (°C) (°F)

0 0.00 - - 294.11 21.11 70.00

1 60 0.22 94.50 388.61 115.61 240.10

2 120 0.16 106.07 400.18 127.18 260.93

3 180 0.13 113.49 407.60 134.60 274.28

4 240 0.11 119.06 413.17 140.17 284.31

5 300 0.10 123.57 417.68 144.68 292.43

10 600 0.07 138.71 432.82 159.82 319.67

15 900 0.06 148.40 442.52 169.52 337.13

20 1200 0.05 155.69 449.80 176.80 350.25

25 1500 0.04 161.59 455.70 182.70 360.87

30 1800 0.04 166.58 460.69 187.69 369.84

35 2100 0.04 170.91 465.02 192.02 377.64

40 2400 0.03 174.76 468.87 195.87 384.57

45 2700 0.03 178.22 472.33 199.33 390.80

50 3000 0.03 181.38 475.49 202.49 396.49

55 3300 0.03 184.29 478.40 205.40 401.71

60 3600 0.03 186.98 481.09 208.09 406.56

Results Time After Ignition (t)

0

50

100

150

200

250

300

350

400

450

0 10 20 30 40 50 60

Temperature (°F)

Time (min)

Hot Gas Layer Temperature

Natural Ventilation (MQH Method)

19-44
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

AND SMOKE LAYER HEIGHT IN A ROOM FIRE

WITH NATURAL VENTILATION

Version 1805.1

(English Units)

Results

Time g Constant (k)

Smoke Layer 

Height

Smoke Layer 

Height

(min) (kg/m3

) (kW/m-K) z (m) z (ft)

0 1.20 0.063 3.00 9.84

1 0.91 0.084 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

2 0.88 0.086 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

3 0.87 0.088 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

4 0.85 0.089 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

5 0.85 0.090 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

10 0.82 0.093 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

15 0.80 0.095 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

20 0.78 0.097 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

25 0.77 0.098 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

30 0.77 0.099 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

35 0.76 0.100 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

40 0.75 0.101 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

45 0.75 0.102 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

50 0.74 0.102 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

55 0.74 0.103 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

60 0.73 0.104 2.10 6.90 CAUTION: SMOKE IS EXITING OUT VENT

The above calculations are based on principles developed in the SFPE Handbook of Fire Protection Engineering, 3rd Edition, 2002. Calculations are based on 

certain assumptions and have inherent limitations. The results of such calculations may or may not have reasonable predictive capabilities for a given situation 

and should only be interpreted by an informed user. Although each calculation in the spreadsheet has been verified with the results of hand calculation, there is 

no absolute guarantee of the accuracy of these calculations. Any questions, comments, concerns, and suggestions, or to report an error(s) in the spreadsheet, 

please send an email to David.Stroup@nrc.gov and Naeem.Iqbal@nrc.gov or MarkHenry.Salley@nrc.gov.

NOTE:

Caution! The smoke layer height is a conservative estimate and is only intended to provide an indication where 

the hot gas layer is located. Calculated smoke layer height below the vent height are not creditable since the 

calculation is not accounting for the smoke exiting the vent.

0

2

4

6

8

10

12

0 10 20 30 40 50 60

Height from Floor (ft)

Time (min)

Smoke Layer Height

Natural Ventilation (Method of Yamana and Tanaka)

19-45
CHAPTER 19. ESTIMATING THE THERMALLY-INDUCED

ELECTRICAL FAILURE (THIEF)

OF CABLES

Version 1805.1

(English Units)

in 0.00749299 m

lb/ft Do Not Enter Any 0.37948 kg/m

in Values in the 0.001143 m o

F Green Boxes! 294.26 K

o

F 473.15 K

s They are entered

in automatically 0.005207 m

in based on the 0.0889 m

kg/m3 cable selection.

All subsequent output values are calculated by the spreadsheet and based on values specified in the input parameters. This spreadsheet is protected 

and secure to avoid errors due to a wrong entry in a cell(s). The chapter in the NUREG should be read before an analysis is made.

Failure Temperature

Maximum Time

Conduit Thickness

Conduit Outside Diameter

Project / Inspection 

Title:

Warning: You MUST Click the Calculate Button Below when Finished Entering or Changing Data!

Cable Function (Control, Instrumentation or Power)

Cable Diameter

Cable Mass per Unit Length

392

NUREG-1805 Supplement 1 Example 19.11-3b

INPUT PARAMETERS

Cable Density

Cable Insulation Type (Thermoplastic or Thermoset)

Cable Jacket Thickness

The following calculations estimate the time to failure of cables exposed to a specified hot gas layer.

Parameters in YELLOW CELLS are Entered by the User.

Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU or SELECT CABLE BUTTON.

Ambient Air Temperature

Number of Conductors

Cable Location

Wire Gauge (AWG)

4000

0.21

3.50

Thermoplastic

Control

12

0.59

0.26

0.045

70

7

Conduit - Rigid

Click to Select Source for Exposure Gas Temperature Profile:

2151.45

Calculate

Select Cable

Natural Ventilation - Method of McCaffrey, Quintiere, Harkleroad (MQH)

Forced Ventilation - Method of Foote, Pagni, and Alvares (FPA)

Forced Ventilation - Method of Deal and Beyler

Room Fire with Closed Door

Within Fire Plume

User Defined

Selecting one of 

these items will 

automatically 

transfer you to the 

appropriate 

spreadsheet to 

calculate the 

exposure gas 

temperature profile

19-46
CHAPTER 19. ESTIMATING THE THERMALLY-INDUCED

ELECTRICAL FAILURE (THIEF)

OF CABLES

Version 1805.1

(English Units)

EXPOSURE GAS TEMPERATURE PROFILE

Time (s)

274.28

284.31

Answer: Cable does not reach failure temperature in 4000.3 seconds

240

337.13

180

292.43

319.67 432.97

350.25

1800

60

260.93

0

120

Gas Temperature (oF)

240.10

Gas Temperature (oK)

70.00

369.84

2100

2400

360.87

300

600

900

1500

1200

377.64

384.57

401.71

406.56

2700

3000

390.80

396.49

442.67

449.95

455.85

3300

3600

460.84

465.17

294.26

388.76

400.33

407.75

413.32

417.83

469.02

472.48

475.64

478.55

481.24

Failure Range

0

50

100

150

200

250

300

350

400

450

500

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Temperature (°F)

Time (s)

RESULTS

Exposing Temp Cable Temp Conduit Temp

19-47
19-48 

Example Problem 19.11-4 

(Cable Type – Thermoplastic vs. Thermoset – Forced Ventilation)

Problem Statement 

Consider a concrete compartment that is 16.40 ft (5.00 m) wide x 16.40 ft (5.00 m) long x 11.48 

ft (3.50 m) high (wc x Ic x hc) and forced ventilation at a rate of 1000.00 cfm. The fire is constant 

with a HRR of 500kW. Compute the time to cable failure under two scenarios: 

(a) Thermoplastic cable located in a cable tray with the following parameters 

- Control 

- 14 AWG 

- 9 conductors 

- PE insulation 

- PVC jacket 

- Dekoron 

- Model : 1735 

(b) Thermoset cable is located in the same cable tray with the following parameters 

- Control 

- 14 AWG 

- 9 conductors 

- XLPE insulation 

- CSPE jacket 

- Rockbestos-Surprenant 

- Model : Firewall III ® 

Example 19.11-4. Concrete Compartment with Forced Ventilation. 
19-49 

Solution

Purpose: 

(1) Determine the time to failure and compare the results of cables with 

similar physical construction, but different insulation (differing 

chemical properties). 

Assumptions: 

(1) The cable is surrounded by a uniform temperature hot gas layer. 

(2) The cable properties do not change with temperature increase. 

(3) Failure is indicated when the temperature inside the cable jacket 

exceeds 392°F (200°C) for the thermoplastic cable and 752°F 

(400°C) for the thermoset cable. 

Spreadsheet (FDTs

) Information: 

 Use the following FDTs

: 

(a) 02.2_Temperature_FV_Sup1.xls (click on Temperature_FV) 

(b) 19_THIEF_Thermally_Induced_Electrical_Failure_of_Cables_ 

Sup1.xls (click on THIEF) 

FDTs

 Input Parameters 

 -Gas temperature around the cable as a function time: 

 Use 02.2_Temperature_FV_Sup1.xls and the parameters presented 

 above to determine the gas temperature (same for both scenarios) 

On the THIEF spreadsheet, select: Forced Ventilation – Method of Deal and 

Beyler or Forced Ventilation – Method of Foote, Pagni, and Alvares (FPA) 

-Press “Select Cable” Button 

-Choose appropriate cable from list 

 (a) Control – 14 AWG – 9 conductor – Dekoron – 1735 – PE – PVC 

(b) Control – 14 AWG – 9 conductor – Rockbestos-Surprenant – XLPE 

 - CSPE 

-Choose appropriate Cable Location (“Cable Tray”) 

-Press “Calculate” Button 

Results* 

 FPA Method Deal and Beyler 

Thermoplastic cable failure time (minutes) 31.8 30.9 

Thermoset cable failure time (minutes) No Failure No Failure 

*see spreadsheets 

The results show a thermoplastic cable failing prior to a thermoset cable of the same cable 

conductor configuration. This example illustrates the added thermal protection of a thermoset 

(TS) cable relative to a less thermally robust thermoplastic (TP) cable. The difference is a direct 

result of the difference between formulations of the polymeric insulating materials used in the 

two different cables. 
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(English Units)

16.40 ft 5.00 m

16.40 ft 5.00 m

11.48 ft 3.50 m

12.00 in 0.3048 m

70.00 21.11 °C

294.11 K

1.00 kJ/kg-K

1.20 kg/m3

2.9

0.0016

0.75

2400

Interior Lining Thermal Inertia (kc)

Interior Lining Thermal Conductivity (k)

Interior Lining Specific Heat (c)

Interior Lining Density ()

(kW/m2

-K)2-sec

kW/m-K

kJ/kg-K

kg/m3

COMPARTMENT INFORMATION

AMBIENT CONDITIONS

Compartment Width (wc)

Compartment Length (lc)

Compartment Height (hc)

All subsequent output values are calculated by the spreadsheet and based on values specified in the input parameters. This spreadsheet is protected 

Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU for the Material Selected.

COMPARTMENT WITH THERMALLY THICK/THIN BOUNDARIES 

The following calculations estimate the hot gas layer temperature and smoke layer height in enclosure fire.

Parameters in YELLOW CELLS are Entered by the User.

Project / Inspection 

Title: NUREG-1805 Supplement 1 Example 19-11.4a

Ambient Air Temperature (Ta)

Specific Heat of Air (cp)

Ambient Air Density (a)

Interior Lining Thickness ()

and secure to avoid errors due to a wrong entry in a cell(s). The chapter in the NUREG should be read before an analysis is made.

INPUT PARAMETERS

Note: Ambient Air Density (a) will automatically correct with Ambient Air Temperature (Ta) Input

°F

THERMAL PROPERTIES OF COMPARTMENT ENCLOSING SURFACES FOR

19-50
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(English Units)

kc k c 

(kW/m2

-K)2-sec (kW/m-K) (kJ/kg-K) (kg/m3)

500 0.206 0.895 2710

197 0.054 0.465 7850

2.9 0.0016 0.75 2400

1.7 0.0008 0.8 2600

1.6 0.00076 0.8 2710

1.2 0.00073 0.84 1900

0.18 0.00017 1.1 960

0.16 0.00012 2.5 540

0.16 0.00053 1.25 240

0.15 0.00015 1.25 800

0.12 0.00026 0.96 500

0.12 0.00016 0.84 950

0.098 0.00013 1.12 700

0.036 0.00014 1 260

0.0018 0.000037 0.8 60

0.001 0.000034 1.5 20

Enter Value Enter Value Enter Value Enter Value

1000.00 cfm 0.472 m3

/sec

0.566 kg/sec

500.00 kW

COMPARTMENT MASS VENTILATION FLOW RATE

Chipboard

Aerated Concrete

Plasterboard

Calcium Silicate Board 

Alumina Silicate Block

Glass Fiber Insulation

Reference: Klote, J., J. Milke, Principles of Smoke Management, 2002 Page 270.

Fire Heat Release Rate (Q)

FIRE SPECIFICATIONS

Aluminum (pure)

Steel (0.5% Carbon)

Concrete

Brick

Fiber Insulation Board

Forced Ventilation Flow Rate (m)

User Specified Value

Glass, Plate

Brick/Concrete Block

THERMAL PROPERTIES FOR COMMON INTERIOR LINING MATERIALS

Expanded Polystyrene

Material

Gypsum Board

Plywood

Scroll to desired material

Click on selection

Select Material

Click Here to Calculate this Sheet 

and Return to THIEF

Concrete

19-51
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(English Units)

Results Time After Ignition (t) hk Tg/Ta Tg Tg Tg Tg 

(min) (sec) (kW/m2

-K) (°K) (°K) (°C) (°F)

0 0 - - - 294.11 21.11 70.00

1 60 0.22 0.35 102.58 396.69 123.69 254.64

2 120 0.16 0.40 116.21 410.32 137.32 279.18

3 180 0.13 0.43 125.01 419.12 146.12 295.01

4 240 0.11 0.45 131.65 425.76 152.76 306.97

5 300 0.10 0.47 137.05 431.16 158.16 316.69

10 600 0.07 0.53 155.26 449.37 176.37 349.47

15 900 0.06 0.57 167.01 461.12 188.12 370.62

20 1200 0.05 0.60 175.89 470.00 197.00 386.60

25 1500 0.04 0.62 183.10 477.21 204.21 399.58

30 1800 0.04 0.64 189.21 483.32 210.32 410.57

35 2100 0.04 0.66 194.53 488.64 215.64 420.16

40 2400 0.03 0.68 199.26 493.37 220.37 428.67

45 2700 0.03 0.69 203.53 497.64 224.64 436.36

50 3000 0.03 0.71 207.43 501.54 228.54 443.37

55 3300 0.03 0.72 211.02 505.13 232.13 449.83

60 3600 0.03 0.73 214.35 508.46 235.46 455.83

Tg = Tg - Ta

Tg = Tg + Ta

Tg/Ta = 0.63(Q/mcpTa)

0.72(hkAT/mcp)-0.36

Compartment Hot Gas Layer Temperature With Forced Ventilation

0

50

100

150

200

250

300

350

400

450

500

0 10 20 30 40 50 60

Temperature (°F)

Time (min)

Hot Gas Layer Temperature

Forced Ventilation - FPA Method

19-52
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(English Units)

Results hk Tg Tg Tg Tg 

(min) (sec) (kW/m2

-K) (°K) (°K) (°C) (°F)

0 0 - - 294.11 21.11 70.00

1 60 0.09 44.99 339.10 66.10 150.98

2 120 0.06 62.31 356.42 83.42 182.16

3 180 0.05 75.12 369.23 96.23 205.22

4 240 0.04 85.61 379.73 106.73 224.11

5 300 0.04 94.64 388.75 115.75 240.35

10 600 0.03 128.15 422.26 149.26 300.66

15 900 0.02 151.99 446.10 173.10 343.58

20 1200 0.02 170.95 465.06 192.06 377.70

25 1500 0.02 186.85 480.96 207.96 406.33

30 1800 0.02 200.63 494.74 221.74 431.14

35 2100 0.01 212.83 506.94 233.94 453.10

40 2400 0.01 223.80 517.91 244.91 472.84

45 2700 0.01 233.78 527.89 254.89 490.81

50 3000 0.01 242.95 537.06 264.06 507.30

55 3300 0.01 251.43 545.54 272.54 522.57

60 3600 0.01 259.32 553.43 280.43 536.78

Time After Ignition (t)

0

100

200

300

400

500

600

0 10 20 30 40 50 60

Temperature (°F)

Time (min)

Hot Gas Layer Temperature

Forced Ventilation - Deal and Beyler Method

19-53
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(English Units)

Prepared by: Date:

Checked by: Date: Organization:

Additional Information:

NOTE:

Summary of Results

The above calculations are based on principles developed in the SFPE Handbook of Fire Protection Engineering, 2nd Edition, 1995. Calculations 

are based on certain assumptions and have inherent limitations. The results of such calculations may or may not have reasonable predictive 

capabilities for a given situation, and should only be interpreted by an informed user. Although each calculation in the spreadsheet has been 

verified with the results of hand calculation, there is no absolute guarantee of the accuracy of these calculations. Any questions, comments, 

concerns, and suggestions, or to report an error(s) in the spreadsheets, please send an email to David.Stroup@nrc.gov and Naeem.Iqbal@nrc.gov 

or MarkHenry.Salley@nrc.gov.

Organization:

0

100

200

300

400

500

600

0 10 20 30 40 50 60

Temperature (°F)

Time (min)

Hot Gas Layer Temperature

Forced Ventilation

FPA Method

Deal and Beyler Method

19-54
CHAPTER 19. ESTIMATING THE THERMALLY-INDUCED

ELECTRICAL FAILURE (THIEF)

OF CABLES

Version 1805.1

(English Units)

in 0.00825498 m

lb/ft Do Not Enter Any 0.36907 kg/m

in Values in the 0.001524 m o

F Green Boxes! 294.26 K

o

F 473.15 K

s They are entered

in automatically 0 m

in based on the 0 m

kg/m3 cable selection.

All subsequent output values are calculated by the spreadsheet and based on values specified in the input parameters. This spreadsheet is protected 

and secure to avoid errors due to a wrong entry in a cell(s). The chapter in the NUREG should be read before an analysis is made.

Failure Temperature

Maximum Time

Conduit Thickness

Conduit Outside Diameter

Project / Inspection 

Title:

Warning: You MUST Click the Calculate Button Below when Finished Entering or Changing Data!

Cable Function (Control, Instrumentation or Power)

Cable Diameter

Cable Mass per Unit Length

392

NUREG-1805 Supplement 1 Example 19.11-4a

INPUT PARAMETERS

Cable Density

Cable Insulation Type (Thermoplastic or Thermoset)

Cable Jacket Thickness

The following calculations estimate the time to failure of cables exposed to a specified hot gas layer.

Parameters in YELLOW CELLS are Entered by the User.

Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU or SELECT CABLE BUTTON.

Ambient Air Temperature

Number of Conductors

Cable Location

Wire Gauge (AWG)

4000

0.00

0.00

Thermoplastic

Control

14

0.65

0.25

0.060

70

9

Cable Tray

Click to Select Source for Exposure Gas Temperature Profile:

1723.93

Calculate

Select Cable

Natural Ventilation - Method of McCaffrey, Quintiere, Harkleroad (MQH)

Forced Ventilation - Method of Foote, Pagni, and Alvares (FPA)

Forced Ventilation - Method of Deal and Beyler

Room Fire with Closed Door

Within Fire Plume

User Defined

Selecting one of 

these items will 

automatically 

transfer you to the 

appropriate 

spreadsheet to 

calculate the 

exposure gas 

temperature profile

19-55
CHAPTER 19. ESTIMATING THE THERMALLY-INDUCED

ELECTRICAL FAILURE (THIEF)

OF CABLES

Version 1805.1

(English Units)

EXPOSURE GAS TEMPERATURE PROFILE

Time (s)

295.01

306.97

Answer: Cable fails at 31.8 minutes

240

370.62

180

316.69

349.47 449.52

386.60

1800

60

279.18

0

120

Gas Temperature (oF)

254.64

Gas Temperature (oK)

70.00

410.57

2100

2400

399.58

300

600

900

1500

1200

420.16

428.67

449.83

455.83

2700

3000

436.36

443.37

461.27

470.15

477.36

3300

3600

483.47

488.79

294.26

396.84

410.47

419.27

425.91

431.31

493.52

497.79

501.69

505.28

508.61

Failure Range

0

50

100

150

200

250

300

350

400

450

500

0 500 1000 1500 2000 2500

Temperature (°F)

Time (s)

RESULTS

Exposing Temp Cable Temp Conduit Temp

19-56
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(English Units)

16.40 ft 5.00 m

16.40 ft 5.00 m

11.48 ft 3.50 m

12.00 in 0.3048 m

70.00 21.11 °C

294.11 K

1.00 kJ/kg-K

1.20 kg/m3

2.9

0.0016

0.75

2400

Interior Lining Thermal Inertia (kc)

Interior Lining Thermal Conductivity (k)

Interior Lining Specific Heat (c)

Interior Lining Density ()

(kW/m2

-K)2-sec

kW/m-K

kJ/kg-K

kg/m3

COMPARTMENT INFORMATION

AMBIENT CONDITIONS

Compartment Width (wc)

Compartment Length (lc)

Compartment Height (hc)

All subsequent output values are calculated by the spreadsheet and based on values specified in the input parameters. This spreadsheet is protected 

Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU for the Material Selected.

COMPARTMENT WITH THERMALLY THICK/THIN BOUNDARIES 

The following calculations estimate the hot gas layer temperature and smoke layer height in enclosure fire.

Parameters in YELLOW CELLS are Entered by the User.

Project / Inspection 

Title: NUREG-1805 Supplement 1 Example 19-11.4b

Ambient Air Temperature (Ta)

Specific Heat of Air (cp)

Ambient Air Density (a)

Interior Lining Thickness ()

and secure to avoid errors due to a wrong entry in a cell(s). The chapter in the NUREG should be read before an analysis is made.

INPUT PARAMETERS

Note: Ambient Air Density (a) will automatically correct with Ambient Air Temperature (Ta) Input

°F

THERMAL PROPERTIES OF COMPARTMENT ENCLOSING SURFACES FOR

19-57
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(English Units)

kc k c 

(kW/m2

-K)2-sec (kW/m-K) (kJ/kg-K) (kg/m3)

500 0.206 0.895 2710

197 0.054 0.465 7850

2.9 0.0016 0.75 2400

1.7 0.0008 0.8 2600

1.6 0.00076 0.8 2710

1.2 0.00073 0.84 1900

0.18 0.00017 1.1 960

0.16 0.00012 2.5 540

0.16 0.00053 1.25 240

0.15 0.00015 1.25 800

0.12 0.00026 0.96 500

0.12 0.00016 0.84 950

0.098 0.00013 1.12 700

0.036 0.00014 1 260

0.0018 0.000037 0.8 60

0.001 0.000034 1.5 20

Enter Value Enter Value Enter Value Enter Value

1000.00 cfm 0.472 m3

/sec

0.566 kg/sec

500.00 kW

COMPARTMENT MASS VENTILATION FLOW RATE

Chipboard

Aerated Concrete

Plasterboard

Calcium Silicate Board 

Alumina Silicate Block

Glass Fiber Insulation

Reference: Klote, J., J. Milke, Principles of Smoke Management, 2002 Page 270.

Fire Heat Release Rate (Q)

FIRE SPECIFICATIONS

Aluminum (pure)

Steel (0.5% Carbon)

Concrete

Brick

Fiber Insulation Board

Forced Ventilation Flow Rate (m)

User Specified Value

Glass, Plate

Brick/Concrete Block

THERMAL PROPERTIES FOR COMMON INTERIOR LINING MATERIALS

Expanded Polystyrene

Material

Gypsum Board

Plywood

Scroll to desired material

Click on selection

Select Material

Click Here to Calculate this Sheet 

and Return to THIEF

Concrete

19-58
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(English Units)

Results Time After Ignition (t) hk Tg/Ta Tg Tg Tg Tg 

(min) (sec) (kW/m2

-K) (°K) (°K) (°C) (°F)

0 0 - - - 294.11 21.11 70.00

1 60 0.22 0.35 102.58 396.69 123.69 254.64

2 120 0.16 0.40 116.21 410.32 137.32 279.18

3 180 0.13 0.43 125.01 419.12 146.12 295.01

4 240 0.11 0.45 131.65 425.76 152.76 306.97

5 300 0.10 0.47 137.05 431.16 158.16 316.69

10 600 0.07 0.53 155.26 449.37 176.37 349.47

15 900 0.06 0.57 167.01 461.12 188.12 370.62

20 1200 0.05 0.60 175.89 470.00 197.00 386.60

25 1500 0.04 0.62 183.10 477.21 204.21 399.58

30 1800 0.04 0.64 189.21 483.32 210.32 410.57

35 2100 0.04 0.66 194.53 488.64 215.64 420.16

40 2400 0.03 0.68 199.26 493.37 220.37 428.67

45 2700 0.03 0.69 203.53 497.64 224.64 436.36

50 3000 0.03 0.71 207.43 501.54 228.54 443.37

55 3300 0.03 0.72 211.02 505.13 232.13 449.83

60 3600 0.03 0.73 214.35 508.46 235.46 455.83

Tg = Tg - Ta

Tg = Tg + Ta

Tg/Ta = 0.63(Q/mcpTa)

0.72(hkAT/mcp)-0.36

Compartment Hot Gas Layer Temperature With Forced Ventilation

0

50

100

150

200

250

300

350

400

450

500

0 10 20 30 40 50 60

Temperature (°F)

Time (min)

Hot Gas Layer Temperature

Forced Ventilation - FPA Method

19-59
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(English Units)

Results hk Tg Tg Tg Tg 

(min) (sec) (kW/m2

-K) (°K) (°K) (°C) (°F)

0 0 - - 294.11 21.11 70.00

1 60 0.09 44.99 339.10 66.10 150.98

2 120 0.06 62.31 356.42 83.42 182.16

3 180 0.05 75.12 369.23 96.23 205.22

4 240 0.04 85.61 379.73 106.73 224.11

5 300 0.04 94.64 388.75 115.75 240.35

10 600 0.03 128.15 422.26 149.26 300.66

15 900 0.02 151.99 446.10 173.10 343.58

20 1200 0.02 170.95 465.06 192.06 377.70

25 1500 0.02 186.85 480.96 207.96 406.33

30 1800 0.02 200.63 494.74 221.74 431.14

35 2100 0.01 212.83 506.94 233.94 453.10

40 2400 0.01 223.80 517.91 244.91 472.84

45 2700 0.01 233.78 527.89 254.89 490.81

50 3000 0.01 242.95 537.06 264.06 507.30

55 3300 0.01 251.43 545.54 272.54 522.57

60 3600 0.01 259.32 553.43 280.43 536.78

Time After Ignition (t)

0

100

200

300

400

500

600

0 10 20 30 40 50 60

Temperature (°F)

Time (min)

Hot Gas Layer Temperature

Forced Ventilation - Deal and Beyler Method

19-60
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(English Units)

Prepared by: Date:

Checked by: Date: Organization:

Additional Information:

NOTE:

Summary of Results

The above calculations are based on principles developed in the SFPE Handbook of Fire Protection Engineering, 2nd Edition, 1995. Calculations 

are based on certain assumptions and have inherent limitations. The results of such calculations may or may not have reasonable predictive 

capabilities for a given situation, and should only be interpreted by an informed user. Although each calculation in the spreadsheet has been 

verified with the results of hand calculation, there is no absolute guarantee of the accuracy of these calculations. Any questions, comments, 

concerns, and suggestions, or to report an error(s) in the spreadsheets, please send an email to David.Stroup@nrc.gov and Naeem.Iqbal@nrc.gov 

or MarkHenry.Salley@nrc.gov.

Organization:

0

100

200

300

400

500

600

0 10 20 30 40 50 60

Temperature (°F)

Time (min)

Hot Gas Layer Temperature

Forced Ventilation

FPA Method

Deal and Beyler Method

19-61
CHAPTER 19. ESTIMATING THE THERMALLY-INDUCED

ELECTRICAL FAILURE (THIEF)

OF CABLES

Version 1805.1

(English Units)

in 0.00825498 m

lb/ft Do Not Enter Any 0.36907 kg/m

in Values in the 0.001524 m o

F Green Boxes! 294.26 K

o

F 473.15 K

s They are entered

in automatically 0 m

in based on the 0 m

kg/m3 cable selection.

All subsequent output values are calculated by the spreadsheet and based on values specified in the input parameters. This spreadsheet is protected 

and secure to avoid errors due to a wrong entry in a cell(s). The chapter in the NUREG should be read before an analysis is made.

Failure Temperature

Maximum Time

Conduit Thickness

Conduit Outside Diameter

Project / Inspection 

Title:

Warning: You MUST Click the Calculate Button Below when Finished Entering or Changing Data!

Cable Function (Control, Instrumentation or Power)

Cable Diameter

Cable Mass per Unit Length

392

NUREG-1805 Supplement 1 Example 19.11-4b

INPUT PARAMETERS

Cable Density

Cable Insulation Type (Thermoplastic or Thermoset)

Cable Jacket Thickness

The following calculations estimate the time to failure of cables exposed to a specified hot gas layer.

Parameters in YELLOW CELLS are Entered by the User.

Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU or SELECT CABLE BUTTON.

Ambient Air Temperature

Number of Conductors

Cable Location

Wire Gauge (AWG)

4000

0.00

0.00

Thermoplastic

Control

14

0.65

0.25

0.060

70

9

Cable Tray

Click to Select Source for Exposure Gas Temperature Profile:

1723.93

Calculate

Select Cable

Natural Ventilation - Method of McCaffrey, Quintiere, Harkleroad (MQH)

Forced Ventilation - Method of Foote, Pagni, and Alvares (FPA)

Forced Ventilation - Method of Deal and Beyler

Room Fire with Closed Door

Within Fire Plume

User Defined

Selecting one of 

these items will 

automatically 

transfer you to the 

appropriate 

spreadsheet to 

calculate the 

exposure gas 

temperature profile

19-62
CHAPTER 19. ESTIMATING THE THERMALLY-INDUCED

ELECTRICAL FAILURE (THIEF)

OF CABLES

Version 1805.1

(English Units)

EXPOSURE GAS TEMPERATURE PROFILE

Time (s)

205.22

224.11

Answer: Cable fails at 30.9 minutes

240

343.58

180

240.35

300.66 422.41

377.70

1800

60

182.16

0

120

Gas Temperature (oF)

150.98

Gas Temperature (oK)

70.00

431.14

2100

2400

406.33

300

600

900

1500

1200

453.10

472.84

522.57

536.78

2700

3000

490.81

507.30

446.25

465.21

481.11

3300

3600

494.89

507.09

294.26

339.25

356.57

369.38

379.88

388.90

518.06

528.04

537.21

545.69

553.58

Failure Range

0

50

100

150

200

250

300

350

400

450

500

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Temperature (°F)

Time (s)

RESULTS

Exposing Temp Cable Temp Conduit Temp

19-63
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(English Units)

16.40 ft 5.00 m

16.40 ft 5.00 m

11.48 ft 3.50 m

12.00 in 0.3048 m

70.00 21.11 °C

294.11 K

1.00 kJ/kg-K

1.20 kg/m3

2.9

0.0016

0.75

2400

Interior Lining Thermal Inertia (kc)

Interior Lining Thermal Conductivity (k)

Interior Lining Specific Heat (c)

Interior Lining Density ()

(kW/m2

-K)2-sec

kW/m-K

kJ/kg-K

kg/m3

COMPARTMENT INFORMATION

AMBIENT CONDITIONS

Compartment Width (wc)

Compartment Length (lc)

Compartment Height (hc)

All subsequent output values are calculated by the spreadsheet and based on values specified in the input parameters. This spreadsheet is protected 

Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU for the Material Selected.

COMPARTMENT WITH THERMALLY THICK/THIN BOUNDARIES 

The following calculations estimate the hot gas layer temperature and smoke layer height in enclosure fire.

Parameters in YELLOW CELLS are Entered by the User.

Project / Inspection 

Title: NUREG-1805 Supplement 1 Example 19-11.4c

Ambient Air Temperature (Ta)

Specific Heat of Air (cp)

Ambient Air Density (a)

Interior Lining Thickness ()

and secure to avoid errors due to a wrong entry in a cell(s). The chapter in the NUREG should be read before an analysis is made.

INPUT PARAMETERS

Note: Ambient Air Density (a) will automatically correct with Ambient Air Temperature (Ta) Input

°F

THERMAL PROPERTIES OF COMPARTMENT ENCLOSING SURFACES FOR

19-64
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(English Units)

kc k c 

(kW/m2

-K)2-sec (kW/m-K) (kJ/kg-K) (kg/m3)

500 0.206 0.895 2710

197 0.054 0.465 7850

2.9 0.0016 0.75 2400

1.7 0.0008 0.8 2600

1.6 0.00076 0.8 2710

1.2 0.00073 0.84 1900

0.18 0.00017 1.1 960

0.16 0.00012 2.5 540

0.16 0.00053 1.25 240

0.15 0.00015 1.25 800

0.12 0.00026 0.96 500

0.12 0.00016 0.84 950

0.098 0.00013 1.12 700

0.036 0.00014 1 260

0.0018 0.000037 0.8 60

0.001 0.000034 1.5 20

Enter Value Enter Value Enter Value Enter Value

1000.00 cfm 0.472 m3

/sec

0.566 kg/sec

500.00 kW

COMPARTMENT MASS VENTILATION FLOW RATE

Chipboard

Aerated Concrete

Plasterboard

Calcium Silicate Board 

Alumina Silicate Block

Glass Fiber Insulation

Reference: Klote, J., J. Milke, Principles of Smoke Management, 2002 Page 270.

Fire Heat Release Rate (Q)

FIRE SPECIFICATIONS

Aluminum (pure)

Steel (0.5% Carbon)

Concrete

Brick

Fiber Insulation Board

Forced Ventilation Flow Rate (m)

User Specified Value

Glass, Plate

Brick/Concrete Block

THERMAL PROPERTIES FOR COMMON INTERIOR LINING MATERIALS

Expanded Polystyrene

Material

Gypsum Board

Plywood

Scroll to desired material

Click on selection

Select Material

Click Here to Calculate this Sheet 

and Return to THIEF

Concrete

19-65
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(English Units)

Results Time After Ignition (t) hk Tg/Ta Tg Tg Tg Tg 

(min) (sec) (kW/m2

-K) (°K) (°K) (°C) (°F)

0 0 - - - 294.11 21.11 70.00

1 60 0.22 0.35 102.58 396.69 123.69 254.64

2 120 0.16 0.40 116.21 410.32 137.32 279.18

3 180 0.13 0.43 125.01 419.12 146.12 295.01

4 240 0.11 0.45 131.65 425.76 152.76 306.97

5 300 0.10 0.47 137.05 431.16 158.16 316.69

10 600 0.07 0.53 155.26 449.37 176.37 349.47

15 900 0.06 0.57 167.01 461.12 188.12 370.62

20 1200 0.05 0.60 175.89 470.00 197.00 386.60

25 1500 0.04 0.62 183.10 477.21 204.21 399.58

30 1800 0.04 0.64 189.21 483.32 210.32 410.57

35 2100 0.04 0.66 194.53 488.64 215.64 420.16

40 2400 0.03 0.68 199.26 493.37 220.37 428.67

45 2700 0.03 0.69 203.53 497.64 224.64 436.36

50 3000 0.03 0.71 207.43 501.54 228.54 443.37

55 3300 0.03 0.72 211.02 505.13 232.13 449.83

60 3600 0.03 0.73 214.35 508.46 235.46 455.83

Tg = Tg - Ta

Tg = Tg + Ta

Tg/Ta = 0.63(Q/mcpTa)

0.72(hkAT/mcp)-0.36

Compartment Hot Gas Layer Temperature With Forced Ventilation

0

50

100

150

200

250

300

350

400

450

500

0 10 20 30 40 50 60

Temperature (°F)

Time (min)

Hot Gas Layer Temperature

Forced Ventilation - FPA Method

19-66
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(English Units)

Results hk Tg Tg Tg Tg 

(min) (sec) (kW/m2

-K) (°K) (°K) (°C) (°F)

0 0 - - 294.11 21.11 70.00

1 60 0.09 44.99 339.10 66.10 150.98

2 120 0.06 62.31 356.42 83.42 182.16

3 180 0.05 75.12 369.23 96.23 205.22

4 240 0.04 85.61 379.73 106.73 224.11

5 300 0.04 94.64 388.75 115.75 240.35

10 600 0.03 128.15 422.26 149.26 300.66

15 900 0.02 151.99 446.10 173.10 343.58

20 1200 0.02 170.95 465.06 192.06 377.70

25 1500 0.02 186.85 480.96 207.96 406.33

30 1800 0.02 200.63 494.74 221.74 431.14

35 2100 0.01 212.83 506.94 233.94 453.10

40 2400 0.01 223.80 517.91 244.91 472.84

45 2700 0.01 233.78 527.89 254.89 490.81

50 3000 0.01 242.95 537.06 264.06 507.30

55 3300 0.01 251.43 545.54 272.54 522.57

60 3600 0.01 259.32 553.43 280.43 536.78

Time After Ignition (t)

0

100

200

300

400

500

600

0 10 20 30 40 50 60

Temperature (°F)

Time (min)

Hot Gas Layer Temperature

Forced Ventilation - Deal and Beyler Method

19-67
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(English Units)

Prepared by: Date:

Checked by: Date: Organization:

Additional Information:

NOTE:

Summary of Results

The above calculations are based on principles developed in the SFPE Handbook of Fire Protection Engineering, 2nd Edition, 1995. Calculations 

are based on certain assumptions and have inherent limitations. The results of such calculations may or may not have reasonable predictive 

capabilities for a given situation, and should only be interpreted by an informed user. Although each calculation in the spreadsheet has been 

verified with the results of hand calculation, there is no absolute guarantee of the accuracy of these calculations. Any questions, comments, 

concerns, and suggestions, or to report an error(s) in the spreadsheets, please send an email to David.Stroup@nrc.gov and Naeem.Iqbal@nrc.gov 

or MarkHenry.Salley@nrc.gov.

Organization:

0

100

200

300

400

500

600

0 10 20 30 40 50 60

Temperature (°F)

Time (min)

Hot Gas Layer Temperature

Forced Ventilation

FPA Method

Deal and Beyler Method

19-68
CHAPTER 19. ESTIMATING THE THERMALLY-INDUCED

ELECTRICAL FAILURE (THIEF)

OF CABLES

Version 1805.1

(English Units)

in 0.00787398 m

lb/ft Do Not Enter Any 0.38692 kg/m

in Values in the 0.001524 m o

F Green Boxes! 294.26 K

o

F 673.15 K

s They are entered

in automatically 0 m

in based on the 0 m

kg/m3 cable selection.

All subsequent output values are calculated by the spreadsheet and based on values specified in the input parameters. This spreadsheet is protected 

and secure to avoid errors due to a wrong entry in a cell(s). The chapter in the NUREG should be read before an analysis is made.

Failure Temperature

Maximum Time

Conduit Thickness

Conduit Outside Diameter

Project / Inspection 

Title:

Warning: You MUST Click the Calculate Button Below when Finished Entering or Changing Data!

Cable Function (Control, Instrumentation or Power)

Cable Diameter

Cable Mass per Unit Length

752

NUREG-1805 Supplement 1 Example 19.11-4c

INPUT PARAMETERS

Cable Density

Cable Insulation Type (Thermoplastic or Thermoset)

Cable Jacket Thickness

The following calculations estimate the time to failure of cables exposed to a specified hot gas layer.

Parameters in YELLOW CELLS are Entered by the User.

Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU or SELECT CABLE BUTTON.

Ambient Air Temperature

Number of Conductors

Cable Location

Wire Gauge (AWG)

4000

0.00

0.00

Thermoset

Control

14

0.62

0.26

0.060

70

9

Cable Tray

Click to Select Source for Exposure Gas Temperature Profile:

1986.49

Calculate

Select Cable

Natural Ventilation - Method of McCaffrey, Quintiere, Harkleroad (MQH)

Forced Ventilation - Method of Foote, Pagni, and Alvares (FPA)

Forced Ventilation - Method of Deal and Beyler

Room Fire with Closed Door

Within Fire Plume

User Defined

Selecting one of 

these items will 

automatically 

transfer you to the 

appropriate 

spreadsheet to 

calculate the 

exposure gas 

temperature profile

19-69
CHAPTER 19. ESTIMATING THE THERMALLY-INDUCED

ELECTRICAL FAILURE (THIEF)

OF CABLES

Version 1805.1

(English Units)

EXPOSURE GAS TEMPERATURE PROFILE

Time (s)

295.01

306.97

Answer: Cable does not reach failure temperature in 4000 seconds

240

370.62

180

316.69

349.47 449.52

386.60

1800

60

279.18

0

120

Gas Temperature (oF)

254.64

Gas Temperature (oK)

70.00

410.57

2100

2400

399.58

300

600

900

1500

1200

420.16

428.67

449.83

455.83

2700

3000

436.36

443.37

461.27

470.15

477.36

3300

3600

483.47

488.79

294.26

396.84

410.47

419.27

425.91

431.31

493.52

497.79

501.69

505.28

508.61

Failure Range

0

100

200

300

400

500

600

700

800

900

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Temperature (°F)

Time (s)

RESULTS

Exposing Temp Cable Temp Conduit Temp

19-70
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(English Units)

16.40 ft 5.00 m

16.40 ft 5.00 m

11.48 ft 3.50 m

12.00 in 0.3048 m

70.00 21.11 °C

294.11 K

1.00 kJ/kg-K

1.20 kg/m3

2.9

0.0016

0.75

2400

Interior Lining Thermal Inertia (kc)

Interior Lining Thermal Conductivity (k)

Interior Lining Specific Heat (c)

Interior Lining Density ()

(kW/m2

-K)2-sec

kW/m-K

kJ/kg-K

kg/m3

COMPARTMENT INFORMATION

AMBIENT CONDITIONS

Compartment Width (wc)

Compartment Length (lc)

Compartment Height (hc)

All subsequent output values are calculated by the spreadsheet and based on values specified in the input parameters. This spreadsheet is protected 

Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU for the Material Selected.

COMPARTMENT WITH THERMALLY THICK/THIN BOUNDARIES 

The following calculations estimate the hot gas layer temperature and smoke layer height in enclosure fire.

Parameters in YELLOW CELLS are Entered by the User.

Project / Inspection 

Title: NUREG-1805 Supplement 1 Example 19-11.4d

Ambient Air Temperature (Ta)

Specific Heat of Air (cp)

Ambient Air Density (a)

Interior Lining Thickness ()

and secure to avoid errors due to a wrong entry in a cell(s). The chapter in the NUREG should be read before an analysis is made.

INPUT PARAMETERS

Note: Ambient Air Density (a) will automatically correct with Ambient Air Temperature (Ta) Input

°F

THERMAL PROPERTIES OF COMPARTMENT ENCLOSING SURFACES FOR

19-71
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(English Units)

kc k c 

(kW/m2

-K)2-sec (kW/m-K) (kJ/kg-K) (kg/m3)

500 0.206 0.895 2710

197 0.054 0.465 7850

2.9 0.0016 0.75 2400

1.7 0.0008 0.8 2600

1.6 0.00076 0.8 2710

1.2 0.00073 0.84 1900

0.18 0.00017 1.1 960

0.16 0.00012 2.5 540

0.16 0.00053 1.25 240

0.15 0.00015 1.25 800

0.12 0.00026 0.96 500

0.12 0.00016 0.84 950

0.098 0.00013 1.12 700

0.036 0.00014 1 260

0.0018 0.000037 0.8 60

0.001 0.000034 1.5 20

Enter Value Enter Value Enter Value Enter Value

1000.00 cfm 0.472 m3

/sec

0.566 kg/sec

500.00 kW

COMPARTMENT MASS VENTILATION FLOW RATE

Chipboard

Aerated Concrete

Plasterboard

Calcium Silicate Board 

Alumina Silicate Block

Glass Fiber Insulation

Reference: Klote, J., J. Milke, Principles of Smoke Management, 2002 Page 270.

Fire Heat Release Rate (Q)

FIRE SPECIFICATIONS

Aluminum (pure)

Steel (0.5% Carbon)

Concrete

Brick

Fiber Insulation Board

Forced Ventilation Flow Rate (m)

User Specified Value

Glass, Plate

Brick/Concrete Block

THERMAL PROPERTIES FOR COMMON INTERIOR LINING MATERIALS

Expanded Polystyrene

Material

Gypsum Board

Plywood

Scroll to desired material

Click on selection

Select Material

Click Here to Calculate this Sheet 

and Return to THIEF

Concrete

19-72
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(English Units)

Results Time After Ignition (t) hk Tg/Ta Tg Tg Tg Tg 

(min) (sec) (kW/m2

-K) (°K) (°K) (°C) (°F)

0 0 - - - 294.11 21.11 70.00

1 60 0.22 0.35 102.58 396.69 123.69 254.64

2 120 0.16 0.40 116.21 410.32 137.32 279.18

3 180 0.13 0.43 125.01 419.12 146.12 295.01

4 240 0.11 0.45 131.65 425.76 152.76 306.97

5 300 0.10 0.47 137.05 431.16 158.16 316.69

10 600 0.07 0.53 155.26 449.37 176.37 349.47

15 900 0.06 0.57 167.01 461.12 188.12 370.62

20 1200 0.05 0.60 175.89 470.00 197.00 386.60

25 1500 0.04 0.62 183.10 477.21 204.21 399.58

30 1800 0.04 0.64 189.21 483.32 210.32 410.57

35 2100 0.04 0.66 194.53 488.64 215.64 420.16

40 2400 0.03 0.68 199.26 493.37 220.37 428.67

45 2700 0.03 0.69 203.53 497.64 224.64 436.36

50 3000 0.03 0.71 207.43 501.54 228.54 443.37

55 3300 0.03 0.72 211.02 505.13 232.13 449.83

60 3600 0.03 0.73 214.35 508.46 235.46 455.83

Tg = Tg - Ta

Tg = Tg + Ta

Tg/Ta = 0.63(Q/mcpTa)

0.72(hkAT/mcp)-0.36

Compartment Hot Gas Layer Temperature With Forced Ventilation

0

50

100

150

200

250

300

350

400

450

500

0 10 20 30 40 50 60

Temperature (°F)

Time (min)

Hot Gas Layer Temperature

Forced Ventilation - FPA Method

19-73
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(English Units)

Results hk Tg Tg Tg Tg 

(min) (sec) (kW/m2

-K) (°K) (°K) (°C) (°F)

0 0 - - 294.11 21.11 70.00

1 60 0.09 44.99 339.10 66.10 150.98

2 120 0.06 62.31 356.42 83.42 182.16

3 180 0.05 75.12 369.23 96.23 205.22

4 240 0.04 85.61 379.73 106.73 224.11

5 300 0.04 94.64 388.75 115.75 240.35

10 600 0.03 128.15 422.26 149.26 300.66

15 900 0.02 151.99 446.10 173.10 343.58

20 1200 0.02 170.95 465.06 192.06 377.70

25 1500 0.02 186.85 480.96 207.96 406.33

30 1800 0.02 200.63 494.74 221.74 431.14

35 2100 0.01 212.83 506.94 233.94 453.10

40 2400 0.01 223.80 517.91 244.91 472.84

45 2700 0.01 233.78 527.89 254.89 490.81

50 3000 0.01 242.95 537.06 264.06 507.30

55 3300 0.01 251.43 545.54 272.54 522.57

60 3600 0.01 259.32 553.43 280.43 536.78

Time After Ignition (t)

0

100

200

300

400

500

600

0 10 20 30 40 50 60

Temperature (°F)

Time (min)

Hot Gas Layer Temperature

Forced Ventilation - Deal and Beyler Method

19-74
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(English Units)

Prepared by: Date:

Checked by: Date: Organization:

Additional Information:

NOTE:

Summary of Results

The above calculations are based on principles developed in the SFPE Handbook of Fire Protection Engineering, 2nd Edition, 1995. Calculations 

are based on certain assumptions and have inherent limitations. The results of such calculations may or may not have reasonable predictive 

capabilities for a given situation, and should only be interpreted by an informed user. Although each calculation in the spreadsheet has been 

verified with the results of hand calculation, there is no absolute guarantee of the accuracy of these calculations. Any questions, comments, 

concerns, and suggestions, or to report an error(s) in the spreadsheets, please send an email to David.Stroup@nrc.gov and Naeem.Iqbal@nrc.gov 

or MarkHenry.Salley@nrc.gov.

Organization:

0

100

200

300

400

500

600

0 10 20 30 40 50 60

Temperature (°F)

Time (min)

Hot Gas Layer Temperature

Forced Ventilation

FPA Method

Deal and Beyler Method

19-75
CHAPTER 19. ESTIMATING THE THERMALLY-INDUCED

ELECTRICAL FAILURE (THIEF)

OF CABLES

Version 1805.1

(English Units)

in 0.00787398 m

lb/ft Do Not Enter Any 0.38692 kg/m

in Values in the 0.001524 m o

F Green Boxes! 294.26 K

o

F 673.15 K

s They are entered

in automatically 0 m

in based on the 0 m

kg/m3 cable selection.

All subsequent output values are calculated by the spreadsheet and based on values specified in the input parameters. This spreadsheet is protected 

and secure to avoid errors due to a wrong entry in a cell(s). The chapter in the NUREG should be read before an analysis is made.

Failure Temperature

Maximum Time

Conduit Thickness

Conduit Outside Diameter

Project / Inspection 

Title:

Warning: You MUST Click the Calculate Button Below when Finished Entering or Changing Data!

Cable Function (Control, Instrumentation or Power)

Cable Diameter

Cable Mass per Unit Length

752

NUREG-1805 Supplement 1 Example 19.11-4d

INPUT PARAMETERS

Cable Density

Cable Insulation Type (Thermoplastic or Thermoset)

Cable Jacket Thickness

The following calculations estimate the time to failure of cables exposed to a specified hot gas layer.

Parameters in YELLOW CELLS are Entered by the User.

Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU or SELECT CABLE BUTTON.

Ambient Air Temperature

Number of Conductors

Cable Location

Wire Gauge (AWG)

4000

0.00

0.00

Thermoset

Control

14

0.62

0.26

0.060

70

9

Cable Tray

Click to Select Source for Exposure Gas Temperature Profile:

1986.49

Calculate

Select Cable

Natural Ventilation - Method of McCaffrey, Quintiere, Harkleroad (MQH)

Forced Ventilation - Method of Foote, Pagni, and Alvares (FPA)

Forced Ventilation - Method of Deal and Beyler

Room Fire with Closed Door

Within Fire Plume

User Defined

Selecting one of 

these items will 

automatically 

transfer you to the 

appropriate 

spreadsheet to 

calculate the 

exposure gas 

temperature profile

19-76
CHAPTER 19. ESTIMATING THE THERMALLY-INDUCED

ELECTRICAL FAILURE (THIEF)

OF CABLES

Version 1805.1

(English Units)

EXPOSURE GAS TEMPERATURE PROFILE

Time (s)

205.22

224.11

Answer: Cable does not reach failure temperature in 4000 seconds

240

343.58

180

240.35

300.66 422.41

377.70

1800

60

182.16

0

120

Gas Temperature (oF)

150.98

Gas Temperature (oK)

70.00

431.14

2100

2400

406.33

300

600

900

1500

1200

453.10

472.84

522.57

536.78

2700

3000

490.81

507.30

446.25

465.21

481.11

3300

3600

494.89

507.09

294.26

339.25

356.57

369.38

379.88

388.90

518.06

528.04

537.21

545.69

553.58

Failure Range

0

100

200

300

400

500

600

700

800

900

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Temperature (°F)

Time (s)

RESULTS

Exposing Temp Cable Temp Conduit Temp

19-77
19-78 

Example Problem 19.11-5 (SI Units) 

(Cable Selection when Specific Cable is not on THIEF cable list)

Problem Statement 

Consider the same concrete compartment used in the previous problem (Example Problem 

19.11-4): 

 5.00 m (16.40 ft) wide x 5.00 m (16.40 ft) long x 3.50 m (11.48 ft) high (wc x Ic x hc) 

 Force ventilation rate of 0.47 m3

/s (1000 cfm) 

 Fire is constant with a HRR of 500 kW. 

The cable to be analyzed is located in a cable tray near the ceiling of the compartment and has 

the following identification: 

 “Lui–Monninger Wire and Cable Company CONTROL CABLE 19/C 10 AWG PE/PVC 90°C 

Type TC” 

This cable is not included in the THIEF list of cables; the cable manufacture has gone out of 

business with no records available online and the licensee doesn’t have records available for 

this cable. Use the THIEF spreadsheet to calculate times to failure for “generic” cables with 

similar construction. It is also of interest to determine how much the time to failure can be 

increased by enclosing the cable in a conduit. 

Example 19.11-5. Concrete Compartment with Forced Ventilation. 

5.00 m

5.00 m 

0.47 m3/s

3.50 m 
19-79 

Solution

Purpose: 

(1) Determine the time to failure and compare the results of similar electrical 

cables located in a cable tray. 

Assumptions: 

(1) The cable is surrounded by a uniform temperature hot gas layer. 

(2) The cable properties do not change with temperature increase. 

(3) Failure is indicated when the temperature inside the cable jacket exceeds 

200 °C (392 °F) (thermoplastic cable). 

Spreadsheet (FDTs

) Information: 

 Use the following FDTs

: 

(a) 02.2_Temperature_FV_Sup1_SI.xls (click on Temperature_FV) 

(b) 19_THIEF_Thermally_Induced_Electrical_Failure_of_Cables_ 

Sup1_SI.xls (click on THIEF) 

FDTs

 Input Parameters: 

 -Gas temperature around the cable as a function time: 

o Use 02.2_Temperature_FV_Sup1_SI.xls and the parameters presented 

above to determine the gas temperature 

o On the THIEF spreadsheet, select: Forced Ventilation – Method of Deal 

and Beyler or Forced Ventilation – Method of Foote, Pagni, and Alvares 

(FPA) 

-Press “Select Cable” Button 

-Choose the “Generic” cable with TP insulation from the list for 10 AWG and 19 

conductors 

-Choose appropriate Cable Location (“Cable Tray”) or 63 mm “Rigid”conduit 

-Press “Calculate” Button 

Results* 

Cable Location FPA Method 

(Minutes) 

Deal and Beyler 

(Minutes) 

Cable Tray 48.7 42.4 

Conduit No Failure 63 

*see spreadsheets 

As the results show, some variability exists between the different cable times to failure. 

A conservative approach would be to use the results of the cable that is most similar to the 

cable being analyzed (same insulation and jacket materials) and that has the shortest time to 

failure. In this example, cable 4 - General Cable – 20/10 – PE/PVC would be the best choice for 

representing the cable under analysis. The Deal and Beyler method results in a realistically 

conservative cable failure time of 42.4 minutes for the Lui-Monninger 10 AWG 19/C cable. 

 
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(SI Units)

5.00 m m

5.00 m m

3.50 m m

30.00 cm 0.3 m

21.00 294.00 °C

K

1.00 kJ/kg-K

1.20 kg/m3

2.9

0.0016

0.75

2400

THERMAL PROPERTIES OF COMPARTMENT ENCLOSING SURFACES FOR

Interior Lining Thermal Inertia (kc)

Interior Lining Thermal Conductivity (k)

Specific Heat of Air (cp)

Ambient Air Density (a)

Interior Lining Thickness ()

and secure to avoid errors due to a wrong entry in a cell(s). The chapter in the NUREG should be read before an analysis is made.

INPUT PARAMETERS

Note: Ambient Air Density (a) will automatically correct with Ambient Air Temperature (Ta) Input

°C

Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU for the Material Selected.

COMPARTMENT WITH THERMALLY THICK/THIN BOUNDARIES 

The following calculations estimate the hot gas layer temperature and smoke layer height in enclosure fire.

Parameters in YELLOW CELLS are Entered by the User.

All subsequent output values are calculated by the spreadsheet and based on values specified in the input parameters. This spreadsheet is protected 

Project / Inspection 

Title: NUREG-1805 Supplement 1 Example 19.11-5a

Ambient Air Temperature (Ta)

COMPARTMENT INFORMATION

AMBIENT CONDITIONS

Compartment Width (wc)

Compartment Length (lc)

Compartment Height (hc)

Interior Lining Specific Heat (c)

Interior Lining Density ()

(kW/m2

-K)2-sec

kW/m-K

kJ/kg-K

kg/m3

19-80
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(SI Units)

kc k c 

(kW/m2

-K)2-sec (kW/m-K) (kJ/kg-K) (kg/m3)

500 0.206 0.895 2710

197 0.054 0.465 7850

2.9 0.0016 0.75 2400

1.7 0.0008 0.8 2600

1.6 0.00076 0.8 2710

1.2 0.00073 0.84 1900

0.18 0.00017 1.1 960

0.16 0.00012 2.5 540

0.16 0.00053 1.25 240

0.15 0.00015 1.25 800

0.12 0.00026 0.96 500

0.12 0.00016 0.84 950

0.098 0.00013 1.12 700

0.036 0.00014 1 260

0.0018 0.000037 0.8 60

0.001 0.000034 1.5 20

Enter Value Enter Value Enter Value Enter Value

0.47 0.564 m3

/sec

kg/sec

500.00 kW

Scroll to desired material

Click on selection

Brick/Concrete Block

THERMAL PROPERTIES FOR COMMON INTERIOR LINING MATERIALS

Expanded Polystyrene

Material

Gypsum Board

Plywood

Select Material

Fire Heat Release Rate (Q)

FIRE SPECIFICATIONS

Aluminum (pure)

Steel (0.5% Carbon)

Concrete

Brick

Fiber Insulation Board

Forced Ventilation Flow Rate (m)

User Specified Value

Glass, Plate

m3

/s

COMPARTMENT MASS VENTILATION FLOW RATE

Chipboard

Aerated Concrete

Plasterboard

Calcium Silicate Board 

Alumina Silicate Block

Glass Fiber Insulation

Reference: Klote, J., J. Milke, Principles of Smoke Management, 2002 Page 270.

Click Here to Calculate this

Sheet and Return to THIEF

Concrete

19-81
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(SI Units)

Results Time After Ignition (t) hk Tg/Ta Tg Tg Tg Tg 

(min) (sec) (kW/m2

-K) (°K) (°K) (°C) (°F)

0 0 - - - 294.00 21.00 69.80

1 60 0.22 0.35 102.69 396.69 123.69 254.64

2 120 0.16 0.40 116.33 410.33 137.33 279.20

3 180 0.13 0.43 125.14 419.14 146.14 295.05

4 240 0.11 0.45 131.79 425.79 152.79 307.03

5 300 0.10 0.47 137.19 431.19 158.19 316.75

10 600 0.07 0.53 155.42 449.42 176.42 349.56

15 900 0.06 0.57 167.19 461.19 188.19 370.74

20 1200 0.05 0.60 176.08 470.08 197.08 386.74

25 1500 0.04 0.62 183.29 477.29 204.29 399.73

30 1800 0.04 0.64 189.41 483.41 210.41 410.74

35 2100 0.04 0.66 194.74 488.74 215.74 420.33

40 2400 0.03 0.68 199.47 493.47 220.47 428.85

45 2700 0.03 0.69 203.75 497.75 224.75 436.55

50 3000 0.03 0.71 207.65 501.65 228.65 443.57

55 3300 0.03 0.72 211.24 505.24 232.24 450.04

60 3600 0.03 0.73 214.58 508.58 235.58 456.04

Tg = Tg + Ta

Compartment Hot Gas Layer Temperature With Forced Ventilation

Tg/Ta = 0.63(Q/mcpTa)

0.72(hkAT/mcp)-0.36

Tg = Tg - Ta

0

50

100

150

200

250

300

350

400

450

500

0 10 20 30 40 50 60

Temperature (°C)

Time (min)

Hot Gas Layer Temperature

Forced Ventilation - FPA Method

19-82
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(SI Units)

Results hk Tg Tg Tg Tg 

(min) (sec) (kW/m2

-K) (°K) (°K) (°C) (°F)

0 0 - - 294.00 21.00 69.80

1 60 0.09 44.98 338.98 65.98 150.76

2 120 0.06 62.30 356.30 83.30 181.93

3 180 0.05 75.11 369.11 96.11 205.00

4 240 0.04 85.61 379.61 106.61 223.89

5 300 0.04 94.63 388.63 115.63 240.14

10 600 0.03 128.16 422.16 149.16 300.49

15 900 0.02 152.02 446.02 173.02 343.44

20 1200 0.02 171.00 465.00 192.00 377.60

25 1500 0.02 186.93 480.93 207.93 406.27

30 1800 0.02 200.72 494.72 221.72 431.10

35 2100 0.01 212.94 506.94 233.94 453.10

40 2400 0.01 223.93 517.93 244.93 472.87

45 2700 0.01 233.93 527.93 254.93 490.87

50 3000 0.01 243.11 537.11 264.11 507.39

55 3300 0.01 251.60 545.60 272.60 522.69

60 3600 0.01 259.52 553.52 280.52 536.93

Time After Ignition (t)

0

100

200

300

400

500

600

0 10 20 30 40 50 60

Temperature (°C)

Time (min)

Hot Gas Layer Temperature

Forced Ventilation - Deal and Beyler Method

19-83
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(SI Units)

Prepared by: Date:

Checked by: Date:

Organization:

The above calculations are based on principles developed in the SFPE Handbook of Fire Protection Engineering, 2nd Edition, 1995. Calculations 

are based on certain assumptions and have inherent limitations. The results of such calculations may or may not have reasonable predictive 

capabilities for a given situation, and should only be interpreted by an informed user. Although each calculation in the spreadsheet has been 

verified with the results of hand calculation, there is no absolute guarantee of the accuracy of these calculations. Any questions, comments, 

concerns, and suggestions, or to report an error(s) in the spreadsheets, please send an email to David.Stroup@nrc.gov and Naeem.Iqbal@nrc.gov 

or MarkHenry.Salley@nrc.gov.

NOTE:

Summary of Results

Organization:

Additional Information:

0

100

200

300

400

500

600

0 10 20 30 40 50 60

Temperature 

(°C=IF(THIEF!$E$29="","",THIEF!$E$29))

Time (min)

Hot Gas Layer Temperature

Forced Ventilation

FPA Method

Deal and Beyler Method

19-84
CHAPTER 19. ESTIMATING THE THERMALLY-INDUCED

ELECTRICAL FAILURE (THIEF)

OF CABLES

Version 1805.1

(SI Units)

mm 0.013335 m

kg/m Do Not Enter Any 1.38399 kg/m

mm Values in the 0.001524 m o

C Green Boxes! 294.00 K

o

C 473.00 K

s They are entered

mm automatically 0 m

mm based on the 0 m

kg/m3 cable selection.

Failure Temperature

Maximum Time

Conduit Thickness

Conduit Outside Diameter

Project / Inspection 

Title: NUREG-1805 Supplement 1 Example 19.11-5a

Cable Mass per Unit Length

200

4000

0.00

0.00

All subsequent output values are calculated by the spreadsheet and based on values specified in the input parameters. This spreadsheet is protected 

and secure to avoid errors due to a wrong entry in a cell(s). The chapter in the NUREG should be read before an analysis is made.

Click to Select Source for Exposure Gas Temperature Profile:

INPUT PARAMETERS

Cable Density

Cable Insulation Type (Thermoplastic or Thermoset)

Cable Function (Control, Instrumentation or Power)

Cable Diameter

The following calculations estimate the time to failure of cables exposed to a specified hot gas layer.

Parameters in YELLOW CELLS are Entered by the User.

Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU or SELECT CABLE BUTTON.

Cable Jacket Thickness

Ambient Air Temperature

Number of Conductors

Cable Location

Wire Gauge (AWG)

Warning: You MUST Click the Calculate Button Below when Finished Entering or Changing Data!

2477.41

Thermoplastic

Control

10

26.67

1.38

1.524

21

19

Cable Tray

Calculate

Select Cable

Natural Ventilation - Method of McCaffrey, Quintiere, Harkleroad (MQH)

Forced Ventilation - Method of Foote, Pagni, and Alvares (FPA)

Forced Ventilation - Method of Deal and Beyler

Room Fire with Closed Door

Within Fire Plume

User Defined

Selecting one of 

these items will 

automatically 

transfer you to the 

appropriate 

spreadsheet to 

calculate the 

exposure gas 

temperature profile

19-85
CHAPTER 19. ESTIMATING THE THERMALLY-INDUCED

ELECTRICAL FAILURE (THIEF)

OF CABLES

Version 1805.1

(SI Units)

Answer: Cable fails at 48.7 minutes

EXPOSURE GAS TEMPERATURE PROFILE

Time (s)

146.14

152.79

137.33

240

188.19

0

Gas Temperature (oC) Gas Temperature (oK)

158.19

176.42 449.57

120

60

180

197.08

21.00

123.69

1800 210.41

2100

2400

204.29

300

600

900

1500

1200

215.74

220.47

232.24

235.58

2700

3000

224.75

228.65

493.62

461.34

470.23

477.44

3300

3600

483.56

488.89

294.15

396.84

410.48

419.29

425.94

431.34

497.90

501.80

505.39

508.73

Failure Range

0

50

100

150

200

250

300

0 500 1000 1500 2000 2500 3000 3500

Temperature (°C)

Time (s)

RESULTS

Exposing Temp Cable Temp Conduit Temp

19-86
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(SI Units)

5.00 m m

5.00 m m

3.50 m m

30.00 cm 0.3 m

21.00 294.00 °C

K

1.00 kJ/kg-K

1.20 kg/m3

2.9

0.0016

0.75

2400

THERMAL PROPERTIES OF COMPARTMENT ENCLOSING SURFACES FOR

Interior Lining Thermal Inertia (kc)

Interior Lining Thermal Conductivity (k)

Specific Heat of Air (cp)

Ambient Air Density (a)

Interior Lining Thickness ()

and secure to avoid errors due to a wrong entry in a cell(s). The chapter in the NUREG should be read before an analysis is made.

INPUT PARAMETERS

Note: Ambient Air Density (a) will automatically correct with Ambient Air Temperature (Ta) Input

°C

Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU for the Material Selected.

COMPARTMENT WITH THERMALLY THICK/THIN BOUNDARIES 

The following calculations estimate the hot gas layer temperature and smoke layer height in enclosure fire.

Parameters in YELLOW CELLS are Entered by the User.

All subsequent output values are calculated by the spreadsheet and based on values specified in the input parameters. This spreadsheet is protected 

Project / Inspection 

Title: NUREG-1805 Supplement 1 Example 19.11-5b

Ambient Air Temperature (Ta)

COMPARTMENT INFORMATION

AMBIENT CONDITIONS

Compartment Width (wc)

Compartment Length (lc)

Compartment Height (hc)

Interior Lining Specific Heat (c)

Interior Lining Density ()

(kW/m2

-K)2-sec

kW/m-K

kJ/kg-K

kg/m3

19-87
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(SI Units)

kc k c 

(kW/m2

-K)2-sec (kW/m-K) (kJ/kg-K) (kg/m3)

500 0.206 0.895 2710

197 0.054 0.465 7850

2.9 0.0016 0.75 2400

1.7 0.0008 0.8 2600

1.6 0.00076 0.8 2710

1.2 0.00073 0.84 1900

0.18 0.00017 1.1 960

0.16 0.00012 2.5 540

0.16 0.00053 1.25 240

0.15 0.00015 1.25 800

0.12 0.00026 0.96 500

0.12 0.00016 0.84 950

0.098 0.00013 1.12 700

0.036 0.00014 1 260

0.0018 0.000037 0.8 60

0.001 0.000034 1.5 20

Enter Value Enter Value Enter Value Enter Value

0.47 0.564 m3

/sec

kg/sec

500.00 kW

Scroll to desired material

Click on selection

Brick/Concrete Block

THERMAL PROPERTIES FOR COMMON INTERIOR LINING MATERIALS

Expanded Polystyrene

Material

Gypsum Board

Plywood

Select Material

Fire Heat Release Rate (Q)

FIRE SPECIFICATIONS

Aluminum (pure)

Steel (0.5% Carbon)

Concrete

Brick

Fiber Insulation Board

Forced Ventilation Flow Rate (m)

User Specified Value

Glass, Plate

m3

/s

COMPARTMENT MASS VENTILATION FLOW RATE

Chipboard

Aerated Concrete

Plasterboard

Calcium Silicate Board 

Alumina Silicate Block

Glass Fiber Insulation

Reference: Klote, J., J. Milke, Principles of Smoke Management, 2002 Page 270.

Click Here to Calculate this

Sheet and Return to THIEF

Concrete

19-88
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(SI Units)

Results Time After Ignition (t) hk Tg/Ta Tg Tg Tg Tg 

(min) (sec) (kW/m2

-K) (°K) (°K) (°C) (°F)

0 0 - - - 294.00 21.00 69.80

1 60 0.22 0.35 102.69 396.69 123.69 254.64

2 120 0.16 0.40 116.33 410.33 137.33 279.20

3 180 0.13 0.43 125.14 419.14 146.14 295.05

4 240 0.11 0.45 131.79 425.79 152.79 307.03

5 300 0.10 0.47 137.19 431.19 158.19 316.75

10 600 0.07 0.53 155.42 449.42 176.42 349.56

15 900 0.06 0.57 167.19 461.19 188.19 370.74

20 1200 0.05 0.60 176.08 470.08 197.08 386.74

25 1500 0.04 0.62 183.29 477.29 204.29 399.73

30 1800 0.04 0.64 189.41 483.41 210.41 410.74

35 2100 0.04 0.66 194.74 488.74 215.74 420.33

40 2400 0.03 0.68 199.47 493.47 220.47 428.85

45 2700 0.03 0.69 203.75 497.75 224.75 436.55

50 3000 0.03 0.71 207.65 501.65 228.65 443.57

55 3300 0.03 0.72 211.24 505.24 232.24 450.04

60 3600 0.03 0.73 214.58 508.58 235.58 456.04

Tg = Tg + Ta

Compartment Hot Gas Layer Temperature With Forced Ventilation

Tg/Ta = 0.63(Q/mcpTa)

0.72(hkAT/mcp)-0.36

Tg = Tg - Ta

0

50

100

150

200

250

300

350

400

450

500

0 10 20 30 40 50 60

Temperature (°C)

Time (min)

Hot Gas Layer Temperature

Forced Ventilation - FPA Method

19-89
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(SI Units)

Results hk Tg Tg Tg Tg 

(min) (sec) (kW/m2

-K) (°K) (°K) (°C) (°F)

0 0 - - 294.00 21.00 69.80

1 60 0.09 44.98 338.98 65.98 150.76

2 120 0.06 62.30 356.30 83.30 181.93

3 180 0.05 75.11 369.11 96.11 205.00

4 240 0.04 85.61 379.61 106.61 223.89

5 300 0.04 94.63 388.63 115.63 240.14

10 600 0.03 128.16 422.16 149.16 300.49

15 900 0.02 152.02 446.02 173.02 343.44

20 1200 0.02 171.00 465.00 192.00 377.60

25 1500 0.02 186.93 480.93 207.93 406.27

30 1800 0.02 200.72 494.72 221.72 431.10

35 2100 0.01 212.94 506.94 233.94 453.10

40 2400 0.01 223.93 517.93 244.93 472.87

45 2700 0.01 233.93 527.93 254.93 490.87

50 3000 0.01 243.11 537.11 264.11 507.39

55 3300 0.01 251.60 545.60 272.60 522.69

60 3600 0.01 259.52 553.52 280.52 536.93

Time After Ignition (t)

0

100

200

300

400

500

600

0 10 20 30 40 50 60

Temperature (°C)

Time (min)

Hot Gas Layer Temperature

Forced Ventilation - Deal and Beyler Method

19-90
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(SI Units)

Prepared by: Date:

Checked by: Date:

Organization:

The above calculations are based on principles developed in the SFPE Handbook of Fire Protection Engineering, 2nd Edition, 1995. Calculations 

are based on certain assumptions and have inherent limitations. The results of such calculations may or may not have reasonable predictive 

capabilities for a given situation, and should only be interpreted by an informed user. Although each calculation in the spreadsheet has been 

verified with the results of hand calculation, there is no absolute guarantee of the accuracy of these calculations. Any questions, comments, 

concerns, and suggestions, or to report an error(s) in the spreadsheets, please send an email to David.Stroup@nrc.gov and Naeem.Iqbal@nrc.gov 

or MarkHenry.Salley@nrc.gov.

NOTE:

Summary of Results

Organization:

Additional Information:

0

100

200

300

400

500

600

0 10 20 30 40 50 60

Temperature 

(°C=IF(THIEF!$E$29="","",THIEF!$E$29))

Time (min)

Hot Gas Layer Temperature

Forced Ventilation

FPA Method

Deal and Beyler Method

19-91
CHAPTER 19. ESTIMATING THE THERMALLY-INDUCED

ELECTRICAL FAILURE (THIEF)

OF CABLES

Version 1805.1

(SI Units)

mm 0.013335 m

kg/m Do Not Enter Any 1.38399 kg/m

mm Values in the 0.001524 m o

C Green Boxes! 294.00 K

o

C 473.00 K

s They are entered

mm automatically 0 m

mm based on the 0 m

kg/m3 cable selection.

Failure Temperature

Maximum Time

Conduit Thickness

Conduit Outside Diameter

Project / Inspection 

Title: NUREG-1805 Supplement 1 Example 19.11-5b

Cable Mass per Unit Length

200

4000

0.00

0.00

All subsequent output values are calculated by the spreadsheet and based on values specified in the input parameters. This spreadsheet is protected 

and secure to avoid errors due to a wrong entry in a cell(s). The chapter in the NUREG should be read before an analysis is made.

Click to Select Source for Exposure Gas Temperature Profile:

INPUT PARAMETERS

Cable Density

Cable Insulation Type (Thermoplastic or Thermoset)

Cable Function (Control, Instrumentation or Power)

Cable Diameter

The following calculations estimate the time to failure of cables exposed to a specified hot gas layer.

Parameters in YELLOW CELLS are Entered by the User.

Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU or SELECT CABLE BUTTON.

Cable Jacket Thickness

Ambient Air Temperature

Number of Conductors

Cable Location

Wire Gauge (AWG)

Warning: You MUST Click the Calculate Button Below when Finished Entering or Changing Data!

2477.41

Thermoplastic

Control

10

26.67

1.38

1.524

21

19

Cable Tray

Calculate

Select Cable

Natural Ventilation - Method of McCaffrey, Quintiere, Harkleroad (MQH)

Forced Ventilation - Method of Foote, Pagni, and Alvares (FPA)

Forced Ventilation - Method of Deal and Beyler

Room Fire with Closed Door

Within Fire Plume

User Defined

Selecting one of 

these items will 

automatically 

transfer you to the 

appropriate 

spreadsheet to 

calculate the 

exposure gas 

temperature profile

19-92
CHAPTER 19. ESTIMATING THE THERMALLY-INDUCED

ELECTRICAL FAILURE (THIEF)

OF CABLES

Version 1805.1

(SI Units)

Answer: Cable fails at 42.4 minutes

EXPOSURE GAS TEMPERATURE PROFILE

Time (s)

96.11

106.61

83.30

240

173.02

0

Gas Temperature (oC) Gas Temperature (oK)

115.63

149.16 422.31

120

60

180

192.00

21.00

65.98

1800 221.72

2100

2400

207.93

300

600

900

1500

1200

233.94

244.93

272.60

280.52

2700

3000

254.93

264.11

518.08

446.17

465.15

481.08

3300

3600

494.87

507.09

294.15

339.13

356.45

369.26

379.76

388.78

528.08

537.26

545.75

553.67

Failure Range

0

50

100

150

200

250

300

0 500 1000 1500 2000 2500 3000

Temperature (°C)

Time (s)

RESULTS

Exposing Temp Cable Temp Conduit Temp

19-93
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(SI Units)

5.00 m m

5.00 m m

3.50 m m

30.00 cm 0.3 m

21.00 294.00 °C

K

1.00 kJ/kg-K

1.20 kg/m3

2.9

0.0016

0.75

2400

Interior Lining Specific Heat (c)

Interior Lining Density ()

(kW/m2

-K)2-sec

kW/m-K

kJ/kg-K

kg/m3

COMPARTMENT INFORMATION

AMBIENT CONDITIONS

Compartment Width (wc)

Compartment Length (lc)

Compartment Height (hc)

All subsequent output values are calculated by the spreadsheet and based on values specified in the input parameters. This spreadsheet is protected 

Project / Inspection 

Title: NUREG-1805 Supplement 1 Example 19.11-5c

Ambient Air Temperature (Ta)

Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU for the Material Selected.

COMPARTMENT WITH THERMALLY THICK/THIN BOUNDARIES 

The following calculations estimate the hot gas layer temperature and smoke layer height in enclosure fire.

Parameters in YELLOW CELLS are Entered by the User.

Specific Heat of Air (cp)

Ambient Air Density (a)

Interior Lining Thickness ()

and secure to avoid errors due to a wrong entry in a cell(s). The chapter in the NUREG should be read before an analysis is made.

INPUT PARAMETERS

Note: Ambient Air Density (a) will automatically correct with Ambient Air Temperature (Ta) Input

°C

THERMAL PROPERTIES OF COMPARTMENT ENCLOSING SURFACES FOR

Interior Lining Thermal Inertia (kc)

Interior Lining Thermal Conductivity (k)

19-94
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(SI Units)

kc k c 

(kW/m2

-K)2-sec (kW/m-K) (kJ/kg-K) (kg/m3)

500 0.206 0.895 2710

197 0.054 0.465 7850

2.9 0.0016 0.75 2400

1.7 0.0008 0.8 2600

1.6 0.00076 0.8 2710

1.2 0.00073 0.84 1900

0.18 0.00017 1.1 960

0.16 0.00012 2.5 540

0.16 0.00053 1.25 240

0.15 0.00015 1.25 800

0.12 0.00026 0.96 500

0.12 0.00016 0.84 950

0.098 0.00013 1.12 700

0.036 0.00014 1 260

0.0018 0.000037 0.8 60

0.001 0.000034 1.5 20

Enter Value Enter Value Enter Value Enter Value

0.47 0.564 m3

/sec

kg/sec

500.00 kW

m3

/s

COMPARTMENT MASS VENTILATION FLOW RATE

Chipboard

Aerated Concrete

Plasterboard

Calcium Silicate Board 

Alumina Silicate Block

Glass Fiber Insulation

Reference: Klote, J., J. Milke, Principles of Smoke Management, 2002 Page 270.

Fire Heat Release Rate (Q)

FIRE SPECIFICATIONS

Aluminum (pure)

Steel (0.5% Carbon)

Concrete

Brick

Fiber Insulation Board

Forced Ventilation Flow Rate (m)

User Specified Value

Glass, Plate

Brick/Concrete Block

THERMAL PROPERTIES FOR COMMON INTERIOR LINING MATERIALS

Expanded Polystyrene

Material

Gypsum Board

Plywood

Select Material

Scroll to desired material

Click on selection

Click Here to Calculate this

Sheet and Return to THIEF

Concrete

19-95
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(SI Units)

Results Time After Ignition (t) hk Tg/Ta Tg Tg Tg Tg 

(min) (sec) (kW/m2

-K) (°K) (°K) (°C) (°F)

0 0 - - - 294.00 21.00 69.80

1 60 0.22 0.35 102.69 396.69 123.69 254.64

2 120 0.16 0.40 116.33 410.33 137.33 279.20

3 180 0.13 0.43 125.14 419.14 146.14 295.05

4 240 0.11 0.45 131.79 425.79 152.79 307.03

5 300 0.10 0.47 137.19 431.19 158.19 316.75

10 600 0.07 0.53 155.42 449.42 176.42 349.56

15 900 0.06 0.57 167.19 461.19 188.19 370.74

20 1200 0.05 0.60 176.08 470.08 197.08 386.74

25 1500 0.04 0.62 183.29 477.29 204.29 399.73

30 1800 0.04 0.64 189.41 483.41 210.41 410.74

35 2100 0.04 0.66 194.74 488.74 215.74 420.33

40 2400 0.03 0.68 199.47 493.47 220.47 428.85

45 2700 0.03 0.69 203.75 497.75 224.75 436.55

50 3000 0.03 0.71 207.65 501.65 228.65 443.57

55 3300 0.03 0.72 211.24 505.24 232.24 450.04

60 3600 0.03 0.73 214.58 508.58 235.58 456.04

Tg Tg = - Ta

Tg = Tg + Ta

Compartment Hot Gas Layer Temperature With Forced Ventilation

Tg/Ta = 0.63(Q/mcpTa)

0.72(hkAT/mcp)-0.36

0

50

100

150

200

250

300

350

400

450

500

0 10 20 30 40 50 60

Temperature (°C)

Time (min)

Hot Gas Layer Temperature

Forced Ventilation - FPA Method

19-96
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(SI Units)

Results hk Tg Tg Tg Tg 

(min) (sec) (kW/m2

-K) (°K) (°K) (°C) (°F)

0 0 - - 294.00 21.00 69.80

1 60 0.09 44.98 338.98 65.98 150.76

2 120 0.06 62.30 356.30 83.30 181.93

3 180 0.05 75.11 369.11 96.11 205.00

4 240 0.04 85.61 379.61 106.61 223.89

5 300 0.04 94.63 388.63 115.63 240.14

10 600 0.03 128.16 422.16 149.16 300.49

15 900 0.02 152.02 446.02 173.02 343.44

20 1200 0.02 171.00 465.00 192.00 377.60

25 1500 0.02 186.93 480.93 207.93 406.27

30 1800 0.02 200.72 494.72 221.72 431.10

35 2100 0.01 212.94 506.94 233.94 453.10

40 2400 0.01 223.93 517.93 244.93 472.87

45 2700 0.01 233.93 527.93 254.93 490.87

50 3000 0.01 243.11 537.11 264.11 507.39

55 3300 0.01 251.60 545.60 272.60 522.69

60 3600 0.01 259.52 553.52 280.52 536.93

Time After Ignition (t)

0

100

200

300

400

500

600

0 10 20 30 40 50 60

Temperature (°C)

Time (min)

Hot Gas Layer Temperature

Forced Ventilation - Deal and Beyler Method

19-97
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(SI Units)

Prepared by: Date:

Checked by: Date: Organization:

Additional Information:

NOTE:

Summary of Results

The above calculations are based on principles developed in the SFPE Handbook of Fire Protection Engineering, 2nd Edition, 1995. Calculations 

are based on certain assumptions and have inherent limitations. The results of such calculations may or may not have reasonable predictive 

capabilities for a given situation, and should only be interpreted by an informed user. Although each calculation in the spreadsheet has been 

verified with the results of hand calculation, there is no absolute guarantee of the accuracy of these calculations. Any questions, comments, 

concerns, and suggestions, or to report an error(s) in the spreadsheets, please send an email to David.Stroup@nrc.gov and Naeem.Iqbal@nrc.gov 

or MarkHenry.Salley@nrc.gov.

Organization:

0

100

200

300

400

500

600

0 10 20 30 40 50 60

Temperature 

(°C=IF(THIEF!$E$29="","",THIEF!$E$29))

Time (min)

Hot Gas Layer Temperature

Forced Ventilation

FPA Method

Deal and Beyler Method

19-98
CHAPTER 19. ESTIMATING THE THERMALLY-INDUCED

ELECTRICAL FAILURE (THIEF)

OF CABLES

Version 1805.1

(SI Units)

mm 0.013335 m

kg/m Do Not Enter Any 1.38399 kg/m

mm Values in the 0.001524 m o

C Green Boxes! 294.00 K

o

C 473.00 K

s They are entered

mm automatically 0.0049 m

mm based on the 0.073 m

kg/m3 cable selection.

Failure Temperature

Maximum Time

Conduit Thickness

Conduit Outside Diameter

Project / Inspection 

Title: NUREG-1805 Supplement 1 Example 19.11-5c

Cable Mass per Unit Length

200

4000

4.90

73.00

All subsequent output values are calculated by the spreadsheet and based on values specified in the input parameters. This spreadsheet is protected 

and secure to avoid errors due to a wrong entry in a cell(s). The chapter in the NUREG should be read before an analysis is made.

Click to Select Source for Exposure Gas Temperature Profile:

INPUT PARAMETERS

Cable Density

Cable Insulation Type (Thermoplastic or Thermoset)

Cable Function (Control, Instrumentation or Power)

Cable Diameter

The following calculations estimate the time to failure of cables exposed to a specified hot gas layer.

Parameters in YELLOW CELLS are Entered by the User.

Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU or SELECT CABLE BUTTON.

Cable Jacket Thickness

Ambient Air Temperature

Number of Conductors

Cable Location

Wire Gauge (AWG)

Warning: You MUST Click the Calculate Button Below when Finished Entering or Changing Data!

2477.41

Thermoplastic

Control

10

26.67

1.38

1.524

21

19

Conduit - Rigid

Calculate

Select Cable

Natural Ventilation - Method of McCaffrey, Quintiere, Harkleroad (MQH)

Forced Ventilation - Method of Foote, Pagni, and Alvares (FPA)

Forced Ventilation - Method of Deal and Beyler

Room Fire with Closed Door

Within Fire Plume

User Defined

Selecting one of 

these items will 

automatically 

transfer you to the 

appropriate 

spreadsheet to 

calculate the 

exposure gas 

temperature profile

19-99
CHAPTER 19. ESTIMATING THE THERMALLY-INDUCED

ELECTRICAL FAILURE (THIEF)

OF CABLES

Version 1805.1

(SI Units)

Answer: Cable does not reach failure temperature in 4000.3 seconds

EXPOSURE GAS TEMPERATURE PROFILE

Time (s)

146.14

152.79

137.33

240

188.19

0

Gas Temperature (oC) Gas Temperature (oK)

158.19

176.42 449.57

120

60

180

197.08

21.00

123.69

1800 210.41

2100

2400

204.29

300

600

900

1500

1200

215.74

220.47

232.24

235.58

2700

3000

224.75

228.65

493.62

461.34

470.23

477.44

3300

3600

483.56

488.89

294.15

396.84

410.48

419.29

425.94

431.34

497.90

501.80

505.39

508.73

Failure Range

0

50

100

150

200

250

300

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Temperature (°C)

Time (s)

RESULTS

Exposing Temp Cable Temp Conduit Temp

19-100
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(SI Units)

5.00 m m

5.00 m m

3.50 m m

30.00 cm 0.3 m

21.00 294.00 °C

K

1.00 kJ/kg-K

1.20 kg/m3

2.9

0.0016

0.75

2400

Interior Lining Specific Heat (c)

Interior Lining Density ()

(kW/m2

-K)2-sec

kW/m-K

kJ/kg-K

kg/m3

COMPARTMENT INFORMATION

AMBIENT CONDITIONS

Compartment Width (wc)

Compartment Length (lc)

Compartment Height (hc)

All subsequent output values are calculated by the spreadsheet and based on values specified in the input parameters. This spreadsheet is protected 

Project / Inspection 

Title: NUREG-1805 Supplement 1 Example 19.11-5d

Ambient Air Temperature (Ta)

Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU for the Material Selected.

COMPARTMENT WITH THERMALLY THICK/THIN BOUNDARIES 

The following calculations estimate the hot gas layer temperature and smoke layer height in enclosure fire.

Parameters in YELLOW CELLS are Entered by the User.

Specific Heat of Air (cp)

Ambient Air Density (a)

Interior Lining Thickness ()

and secure to avoid errors due to a wrong entry in a cell(s). The chapter in the NUREG should be read before an analysis is made.

INPUT PARAMETERS

Note: Ambient Air Density (a) will automatically correct with Ambient Air Temperature (Ta) Input

°C

THERMAL PROPERTIES OF COMPARTMENT ENCLOSING SURFACES FOR

Interior Lining Thermal Inertia (kc)

Interior Lining Thermal Conductivity (k)

19-101
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(SI Units)

kc k c 

(kW/m2

-K)2-sec (kW/m-K) (kJ/kg-K) (kg/m3)

500 0.206 0.895 2710

197 0.054 0.465 7850

2.9 0.0016 0.75 2400

1.7 0.0008 0.8 2600

1.6 0.00076 0.8 2710

1.2 0.00073 0.84 1900

0.18 0.00017 1.1 960

0.16 0.00012 2.5 540

0.16 0.00053 1.25 240

0.15 0.00015 1.25 800

0.12 0.00026 0.96 500

0.12 0.00016 0.84 950

0.098 0.00013 1.12 700

0.036 0.00014 1 260

0.0018 0.000037 0.8 60

0.001 0.000034 1.5 20

Enter Value Enter Value Enter Value Enter Value

0.47 0.564 m3

/sec

kg/sec

500.00 kW

m3

/s

COMPARTMENT MASS VENTILATION FLOW RATE

Chipboard

Aerated Concrete

Plasterboard

Calcium Silicate Board 

Alumina Silicate Block

Glass Fiber Insulation

Reference: Klote, J., J. Milke, Principles of Smoke Management, 2002 Page 270.

Fire Heat Release Rate (Q)

FIRE SPECIFICATIONS

Aluminum (pure)

Steel (0.5% Carbon)

Concrete

Brick

Fiber Insulation Board

Forced Ventilation Flow Rate (m)

User Specified Value

Glass, Plate

Brick/Concrete Block

THERMAL PROPERTIES FOR COMMON INTERIOR LINING MATERIALS

Expanded Polystyrene

Material

Gypsum Board

Plywood

Select Material

Scroll to desired material

Click on selection

Click Here to Calculate this

Sheet and Return to THIEF

Concrete

19-102
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(SI Units)

Results Time After Ignition (t) hk Tg/Ta Tg Tg Tg Tg 

(min) (sec) (kW/m2

-K) (°K) (°K) (°C) (°F)

0 0 - - - 294.00 21.00 69.80

1 60 0.22 0.35 102.69 396.69 123.69 254.64

2 120 0.16 0.40 116.33 410.33 137.33 279.20

3 180 0.13 0.43 125.14 419.14 146.14 295.05

4 240 0.11 0.45 131.79 425.79 152.79 307.03

5 300 0.10 0.47 137.19 431.19 158.19 316.75

10 600 0.07 0.53 155.42 449.42 176.42 349.56

15 900 0.06 0.57 167.19 461.19 188.19 370.74

20 1200 0.05 0.60 176.08 470.08 197.08 386.74

25 1500 0.04 0.62 183.29 477.29 204.29 399.73

30 1800 0.04 0.64 189.41 483.41 210.41 410.74

35 2100 0.04 0.66 194.74 488.74 215.74 420.33

40 2400 0.03 0.68 199.47 493.47 220.47 428.85

45 2700 0.03 0.69 203.75 497.75 224.75 436.55

50 3000 0.03 0.71 207.65 501.65 228.65 443.57

55 3300 0.03 0.72 211.24 505.24 232.24 450.04

60 3600 0.03 0.73 214.58 508.58 235.58 456.04

Tg Tg = - Ta

Tg = Tg + Ta

Compartment Hot Gas Layer Temperature With Forced Ventilation

Tg/Ta = 0.63(Q/mcpTa)

0.72(hkAT/mcp)-0.36

0

50

100

150

200

250

300

350

400

450

500

0 10 20 30 40 50 60

Temperature (°C)

Time (min)

Hot Gas Layer Temperature

Forced Ventilation - FPA Method

19-103
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(SI Units)

Results hk Tg Tg Tg Tg 

(min) (sec) (kW/m2

-K) (°K) (°K) (°C) (°F)

0 0 - - 294.00 21.00 69.80

1 60 0.09 44.98 338.98 65.98 150.76

2 120 0.06 62.30 356.30 83.30 181.93

3 180 0.05 75.11 369.11 96.11 205.00

4 240 0.04 85.61 379.61 106.61 223.89

5 300 0.04 94.63 388.63 115.63 240.14

10 600 0.03 128.16 422.16 149.16 300.49

15 900 0.02 152.02 446.02 173.02 343.44

20 1200 0.02 171.00 465.00 192.00 377.60

25 1500 0.02 186.93 480.93 207.93 406.27

30 1800 0.02 200.72 494.72 221.72 431.10

35 2100 0.01 212.94 506.94 233.94 453.10

40 2400 0.01 223.93 517.93 244.93 472.87

45 2700 0.01 233.93 527.93 254.93 490.87

50 3000 0.01 243.11 537.11 264.11 507.39

55 3300 0.01 251.60 545.60 272.60 522.69

60 3600 0.01 259.52 553.52 280.52 536.93

Time After Ignition (t)

0

100

200

300

400

500

600

0 10 20 30 40 50 60

Temperature (°C)

Time (min)

Hot Gas Layer Temperature

Forced Ventilation - Deal and Beyler Method

19-104
CHAPTER 2. PREDICTING HOT GAS LAYER TEMPERATURE

IN A ROOM FIRE

WITH FORCED VENTILATION 

Version 1805.1

(SI Units)

Prepared by: Date:

Checked by: Date: Organization:

Additional Information:

NOTE:

Summary of Results

The above calculations are based on principles developed in the SFPE Handbook of Fire Protection Engineering, 2nd Edition, 1995. Calculations 

are based on certain assumptions and have inherent limitations. The results of such calculations may or may not have reasonable predictive 

capabilities for a given situation, and should only be interpreted by an informed user. Although each calculation in the spreadsheet has been 

verified with the results of hand calculation, there is no absolute guarantee of the accuracy of these calculations. Any questions, comments, 

concerns, and suggestions, or to report an error(s) in the spreadsheets, please send an email to David.Stroup@nrc.gov and Naeem.Iqbal@nrc.gov 

or MarkHenry.Salley@nrc.gov.

Organization:

0

100

200

300

400

500

600

0 10 20 30 40 50 60

Temperature 

(°C=IF(THIEF!$E$29="","",THIEF!$E$29))

Time (min)

Hot Gas Layer Temperature

Forced Ventilation

FPA Method

Deal and Beyler Method

19-105
CHAPTER 19. ESTIMATING THE THERMALLY-INDUCED

ELECTRICAL FAILURE (THIEF)

OF CABLES

Version 1805.1

(SI Units)

mm 0.013335 m

kg/m Do Not Enter Any 1.38399 kg/m

mm Values in the 0.001524 m o

C Green Boxes! 294.00 K

o

C 473.00 K

s They are entered

mm automatically 0.0049 m

mm based on the 0.073 m

kg/m3 cable selection.

Failure Temperature

Maximum Time

Conduit Thickness

Conduit Outside Diameter

Project / Inspection 

Title: NUREG-1805 Supplement 1 Example 19.11-5d

Cable Mass per Unit Length

200

4000

4.90

73.00

All subsequent output values are calculated by the spreadsheet and based on values specified in the input parameters. This spreadsheet is protected 

and secure to avoid errors due to a wrong entry in a cell(s). The chapter in the NUREG should be read before an analysis is made.

Click to Select Source for Exposure Gas Temperature Profile:

INPUT PARAMETERS

Cable Density

Cable Insulation Type (Thermoplastic or Thermoset)

Cable Function (Control, Instrumentation or Power)

Cable Diameter

The following calculations estimate the time to failure of cables exposed to a specified hot gas layer.

Parameters in YELLOW CELLS are Entered by the User.

Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU or SELECT CABLE BUTTON.

Cable Jacket Thickness

Ambient Air Temperature

Number of Conductors

Cable Location

Wire Gauge (AWG)

Warning: You MUST Click the Calculate Button Below when Finished Entering or Changing Data!

2477.41

Thermoplastic

Control

10

26.67

1.38

1.524

21

19

Conduit - Rigid

Calculate

Select Cable

Natural Ventilation - Method of McCaffrey, Quintiere, Harkleroad (MQH)

Forced Ventilation - Method of Foote, Pagni, and Alvares (FPA)

Forced Ventilation - Method of Deal and Beyler

Room Fire with Closed Door

Within Fire Plume

User Defined

Selecting one of 

these items will 

automatically 

transfer you to the 

appropriate 

spreadsheet to 

calculate the 

exposure gas 

temperature profile

19-106
CHAPTER 19. ESTIMATING THE THERMALLY-INDUCED

ELECTRICAL FAILURE (THIEF)

OF CABLES

Version 1805.1

(SI Units)

Answer: Cable fails at 63 minutes

EXPOSURE GAS TEMPERATURE PROFILE

Time (s)

96.11

106.61

83.30

240

173.02

0

Gas Temperature (oC) Gas Temperature (oK)

115.63

149.16 422.31

120

60

180

192.00

21.00

65.98

1800 221.72

2100

2400

207.93

300

600

900

1500

1200

233.94

244.93

272.60

280.52

2700

3000

254.93

264.11

518.08

446.17

465.15

481.08

3300

3600

494.87

507.09

294.15

339.13

356.45

369.26

379.76

388.78

528.08

537.26

545.75

553.67

Failure Range

0

50

100

150

200

250

300

0 500 1000 1500 2000 2500 3000 3500 4000

Temperature (°C)

Time (s)

RESULTS

Exposing Temp Cable Temp Conduit Temp

19-107
19-108 

Example Problem 19.11-6 (SI Units) 

(Cable Within Plume)

Problem Statement 

Consider a concrete compartment that is 5.00 m (16.40 ft) wide x 5.00 m (16.40 ft) long x 3.5 m 

(11.48 ft) high (wc x Ic x hc). A cable tray is located 1.83 m (6 ft) above a burning electrical 

cabinet. The fire is constant with a HRR of 250kW and a combustible area of 0.28 m2

 (3 ft2). 

Compute the time to cable failure using a thermoplastic cable located in the cable tray with the 

following parameters: 

- Control 

- 14 AWG 

- 9 conductors 

- PE insulation 

- PVC jacket 

- Dekoron 

- Model : 1735 

Solution

Purpose: 

(1) Determine the time to failure of the cable. 

Assumptions: 

(1) The cable is surrounded by a uniform temperature fire plume. 

(2) The cable properties do not change with temperature increase. 

(3) Failure is indicated when the temperature inside the cable jacket 

exceeds 200 °C (392 °F) for the thermoplastic cable. 

Spreadsheet (FDTs

) Information: 

 Use the following FDTs

: 

(a) 09_Plume_Temperature_Calculations_Sup1_SI.xls 

(b) 19_THIEF_Thermally_Induced_Electrical_Failure_of_Cables_ 

Sup1_SI.xls (click on THIEF) 

FDTs

 Input Parameters 

 -Gas temperature around the cable as a function time: 

Use 09_Plume_Tempearture_Calculations_Sup1_SI.xls and the parameters 

presented above to determine the plume centerline temperature 

On the THIEF spreadsheet, select: Plume_Calculations 

-Press “Select Cable” Button 

-Choose appropriate cable from list 

 Control – 14 AWG – 9 conductor – Dekoron – 1735 – PE – PVC 

-Choose appropriate Cable Location (“Cable Tray”) 

-Press “Calculate” Button 
19-109 

Results* 

Thermoplastic cable failure time (minutes) 3.9 

*see spreadsheets 

The results show a thermoplastic cable failing in 3.9 minutes. 

 
CHAPTER 9. ESTIMATING CENTERLINE TEMPERATURE

OF A

BUOYANT FIRE PLUME

Version 1805.1

(SI Units)

250.00

1.83 m

0.28 m2

21.00 294.00 °C

°K

1.00

1.20

9.81

Convective Heat Release Fraction c) 0.70

kg/m3

m2

°C

kJ/kg-K

Area of Combustible Fuel (Ac)

Ambient Air Temperature (Ta)

Ambient Air Density (a)

Parameters should be specified ONLY IN THE YELLOW INPUT PARAMETER BOXES.

All subsequent output values are calculated by the spreadsheet and based on values specified in the input parameters. This spreadsheet is protected 

and secure to avoid errors due to a wrong entry in a cell(s). The chapter in the NUREG should be read before an analysis is made.

NUREG-1805 Supplement 1 Example 19.11-6

Heat Release Rate of the Fire (Q)

Elevation Above the Fire Source (z)

kW

m

INPUT PARAMETERS

m/sec2

NOTE: Ambient Air Density (a) will automatically correct with Ambient Air Temperature (Ta) Input

Acceleration of Gravity (g)

Project / Inspection 

Title:

AMBIENT CONDITIONS

Specific Heat of Air (cp)

The following calculations estimate the centerline plume temperature in a compartment fire.

Click Here to Calculate this

Sheet and Return to THIEF

19-110
CHAPTER 9. ESTIMATING CENTERLINE TEMPERATURE

OF A

BUOYANT FIRE PLUME

Version 1805.1

(SI Units)

L =

Where,

L =

Q =

D =

L = 

Answer

Prepared by: Date:

Checked by: Date:

°F

Tp(centerline) - Ta =

Additional Information:

Organization:

Organization:

Mean Flame Height Calculation

Tp(centerline) =

9.1 (Ta/g cp

2

a

2

)

1/3 Qc

2/3 (z - z0)

-5/3

NOTE:

mean flame height (m)

m

 -1.02D + 0.235 (Q2/5)

Centerline Plume Temperature Calculation

heat release rate of fire (kW)

fire diameter (m)

°C 661.27

1.53

°K

The above calculations are based on principles developed in the SFPE Handbook of Fire Protection Engineering, 2nd Edition, 1995. Calculations 

are based on certain assumptions and have inherent limitations. The results of such calculations may or may not have reasonable predictive 

capabilities for a given situation, and should only be interpreted by an informed user. Although each calculation in the spreadsheet has been 

verified with the results of hand calculation, there is no absolute guarantee of the accuracy of these calculations. Any questions, comments, 

concerns, and suggestions, or to report an error(s) in the spreadsheets, please send an email to David.Stroup@nrc.gov and Naeem.Iqbal@nrc.gov 

or MarkHenry.Salley@nrc.gov.

622.59

°K

Tp(centerline) = 349.59

Tp(centerline) - Ta = 328.59

19-111
CHAPTER 19. ESTIMATING THE THERMALLY-INDUCED

ELECTRICAL FAILURE (THIEF)

OF CABLES

Version 1805.1

(SI Units)

mm 0.008255 m

kg/m Do Not Enter Any 0.36906 kg/m

mm Values in the 0.001524 m o

C Green Boxes! 294.00 K

o

C 473.00 K

s They are entered

mm automatically 0 m

mm based on the 0 m

kg/m3 cable selection.

Failure Temperature

Maximum Time

Conduit Thickness

Conduit Outside Diameter

Project / Inspection 

Title: NUREG-1805 Supplement 1 Example 19.11-6

Cable Mass per Unit Length

200

4000

0.00

0.00

All subsequent output values are calculated by the spreadsheet and based on values specified in the input parameters. This spreadsheet is protected 

and secure to avoid errors due to a wrong entry in a cell(s). The chapter in the NUREG should be read before an analysis is made.

Click to Select Source for Exposure Gas Temperature Profile:

INPUT PARAMETERS

Cable Density

Cable Insulation Type (Thermoplastic or Thermoset)

Cable Function (Control, Instrumentation or Power)

Cable Diameter

The following calculations estimate the time to failure of cables exposed to a specified hot gas layer.

Parameters in YELLOW CELLS are Entered by the User.

Parameters in GREEN CELLS are Automatically Selected from the DROP DOWN MENU or SELECT CABLE BUTTON.

Cable Jacket Thickness

Ambient Air Temperature

Number of Conductors

Cable Location

Wire Gauge (AWG)

Warning: You MUST Click the Calculate Button Below when Finished Entering or Changing Data!

1723.93

Thermoplastic

Control

14

16.51

0.37

1.524

21

9

Cable Tray

Calculate

Select Cable

Natural Ventilation - Method of McCaffrey, Quintiere, Harkleroad (MQH)

Forced Ventilation - Method of Foote, Pagni, and Alvares (FPA)

Forced Ventilation - Method of Deal and Beyler

Room Fire with Closed Door

Within Fire Plume

User Defined

Selecting one of 

these items will 

automatically 

transfer you to the 

appropriate 

spreadsheet to 

calculate the 

exposure gas 

temperature profile

19-112
CHAPTER 19. ESTIMATING THE THERMALLY-INDUCED

ELECTRICAL FAILURE (THIEF)

OF CABLES

Version 1805.1

(SI Units)

Answer: Cable fails at 3.9 minutes

EXPOSURE GAS TEMPERATURE PROFILE

Time (s)

349.59

349.59

0

Gas Temperature (oC) Gas Temperature (oK)

2000

10

4000

21.00

349.59

294.15

622.74

622.74

622.74

Failure Range

0

50

100

150

200

250

300

350

400

0 50 100 150 200 250 300

Temperature (°C)

Time (s)

RESULTS

Exposing Temp Cable Temp Conduit Temp

19-113




UNITED STATES 

NUCLEAR REGULATORY COMMISSION

WASHINGTON, DC 20555-0001

--------------------

OFFICIAL BUSINESS
NUREG-1805

Supplement 1, Vol. 1

Fire Dynamics Tools FDTs Quantitative Fire Hazard Analysis Methods for the 

U.S. Nuclear Regulatory Commission Fire Protection Inspection Program