NISTIR 7482 

Thermal Performance of Fire Resistive Materials 

II. A Multi-Layer One-Dimensional Heat Transfer 

Model for Fire Resistive Materials Protecting a 

Substrate

Slug calorimeter

SpecimenSpecimen

Guard

insulation

Guard

insulation

Q direction

heating

cooling

Retaining

plate

Experimental

setup

Kuldeep R. Prasad 

Dale P. Bentz 
NISTIR 7482 

Thermal Performance of Fire Resistive Materials 

II. A Multi-Layer One-Dimensional Heat Transfer 

Model for Fire Resistive Materials Protecting a 

Substrate

Kuldeep R. Prasad 

Dale P. Bentz 

Building and Fire Research Laboratory 

National Institute of Standards and Technology 

Gaithersburg, MD 20899-8615 

February 2008 

U.S. Department of Commerce 

Carlos M. Gutierrez, Secretary

National Institute of Standards and Technology 

James M. Turner, Acting Director 

ii
Abstract 

This report is the second of a three-part series concerning the characterization and 

modeling of the thermal performance of fire resistive materials (FRMs). These materials 

are currently qualified and certified based on lab-scale fire tests such as those described 

in the American Society for Testing and Materials (ASTM) E119 Standard Test Methods 

for Fire Tests of Building Construction and Materials [1]. While these tests provide an 

“hourly” rating for the FRM, these ratings have no direct quantitative relationship to the 

performance of an FRM in an actual fire, e.g., a 2 h rating does not mean that the FRM 

will protect the steel (or other substrate) for 2 h in a real world fire. Computational heat 

transfer models offer the potential to bridge the gap between laboratory testing and field 

performance. However, these models, whether basic one-dimensional or more complex 

three-dimensional versions, depend critically on having accurate values for the 

thermophysical properties of the FRM (and substrate) as a function of temperature, to be 

used as inputs along with the system geometry and fire and heat transfer boundary 

conditions. In part I of this series, procedures for determining a consistent set of these 

thermophysical properties were presented. Now, in part II, a computational onedimensional multi-layer model for the heat transfer from the fire, through the FRM, to the 

substrate is developed and verified by comparison to the results of a series of slug 

calorimeter experiments, previously conducted in the Building and Fire Research 

Laboratory (BFRL). Ultimately, similar performance simulations will be executed for 

ASTM E119-type tests and even real fires. 

iii
iv
Table of Contents 

Abstract..............................................................................................................................iii 

List of Figures.................................................................................................................... vi 

List of Tables.................................................................................................................... vii 

1 Introduction...................................................................................................................... 1 

2 Experimental Setup – Mini-furnace and Slug Calorimeter.............................................. 2 

2.1 Mini-furnace ............................................................................................................. 2 

2.2 Slug Calorimeter....................................................................................................... 5 

3 Modeling of the Slug Calorimeter Experiment................................................................ 6 

4 Material Properties Used in Modeling............................................................................. 8 

5 Results.............................................................................................................................. 9 

5.1 First Heating/Cooling Cycle ..................................................................................... 9 

5.2 Second Heating/Cooling Cycle............................................................................... 13 

5.3 Different Furnaces .................................................................................................. 17 

6 Summary and Future Research ...................................................................................... 19 

7 Acknowledgements........................................................................................................ 20 

8 References...................................................................................................................... 20 

v
List of Figures 

Figure 1. Schematics of the slug calorimeter test setup: left- schematic of a cross section 

through the middle of the basic slug calorimeter setup, and right- schematic of an 

overhead view of a completed sandwich specimen mounted and ready for testing in 

the mini-furnace.......................................................................................................... 3 

Figure 2. Comparison of measured furnace temperatures for the original furnace and the 

mini-furnace when programmed with the same set of linear temperature ramps. TC1 

and TC2 indicate two different locations of sensing thermocouple in the minifurnace as described in the text................................................................................... 3 

Figure 3. Comparison of measured furnace and outer FRM surface temperatures for a) 

the original furnace and b) the mini-furnace, when programmed with the same set of 

linear temperature ramps............................................................................................. 4 

Figure 4. Experimental and model predicted exterior FRM surface (top) and slug 

temperatures (bottom) vs. time for the first heating/cooling cycle in the slug 

calorimeter for the standard density FRM. ............................................................... 10 

Figure 5. Experimental and model predicted exterior FRM surface (top) and slug 

temperatures (bottom) vs. time for the first heating/cooling cycle in the slug 

calorimeter for the medium density FRM................................................................. 11 

Figure 6. Experimental and model predicted exterior FRM surface (top) and slug 

temperatures (bottom) vs. time for the first heating/cooling cycle in the slug 

calorimeter for the high density FRM....................................................................... 12 

Figure 7. Experimental and model predicted exterior FRM surface (top) and slug 

temperatures (bottom) vs. time for the second heating/cooling cycle in the slug 

calorimeter for the standard density FRM. ............................................................... 14 

Figure 8. Experimental and model predicted exterior FRM surface (top) and slug 

temperatures (bottom) vs. time for the second heating/cooling cycle in the slug 

calorimeter for the medium density FRM................................................................. 15 

Figure 9. Experimental and model predicted exterior FRM surface (top) and slug 

temperatures (bottom) vs. time for the second heating/cooling cycle in the slug 

calorimeter for the high density FRM....................................................................... 16 

Figure 10. Experimental and model predicted exterior FRM surface (top) and slug 

temperatures (bottom) vs. time for the first heating/cooling cycle in the slug 

calorimeter in the original furnace for a standard density (specific gravity = 0.31) 

FRM. ......................................................................................................................... 18 

vi
List of Tables 

Table 1. Specific Gravities (with standard deviations from the twin specimens) of the 

Three Evaluated FRMs............................................................................................... 8 

vii
viii
1 Introduction 

 In recent years, computer modeling has been successfully applied in bridging the gap 

between laboratory measurements and field performance predictions for a wide variety of 

materials. A prime example of this were the simulations conducted as part of the investigation of 

the World Trade Center progressive collapse led by the Building and Fire Research Laboratory 

(BFRL) of the National Institute of Standards and Technology (NIST) [2]. This current series of 

NIST internal reports specifically addresses the modeling of heat transfer from a fire (or furnace) 

through a fire resistive material (FRM) to the (steel) substrate that the FRM is protecting. The 

necessary characterization of the FRMs and substrate materials was outlined in part I of this 

series [3]. In part II, the details of a one-dimensional multi-layer heat transfer model are 

presented and the model is verified by comparison against a variety of slug calorimeter 

experiments performed previously in BFRL. In part III, extensions of the modeling to American 

Society for Testing and Materials (ASTM) E-119 [1] standard fire tests and real world fires will 

be considered. 

1
2 Experimental Setup – Mini-furnace and Slug Calorimeter 

2.1 Mini-furnace 

 Originally, slug calorimeter experiments were conducted in an electrically-heated box 

furnace with a working volume of 360 mm by 360 mm by 360 mm, a maximum operating 

temperature of 1773 K, and heating provided from exposed heating elements on all four vertical 

faces of the interior [4, 5]. However, it soon became desirable to demonstrate that equivalent 

measurements could be achieved using a smaller and less expensive furnace. The mini-furnace 

constructed to meet this objective has a working volume of 250 mm by 250 mm by 300 mm and 

is constructed from a set of four ceramic fiber elements. As shown in Figure 1, only two of the 

elements (sides) contain active heating, while the other two elements (front and back) function as 

passive insulators. The active heating elements measure 356 mm x 305 mm x 50 mm, while the 

passive elements are 254 mm x 305 mm x 50 mm. The top and bottom of the furnace consist of 

50 mm thick “plates” of the same high temperature insulation that is utilized as the guard 

insulation in the slug calorimeter setup [4, 5]. This mini-furnace has been used extensively and 

reliably for more than one year. The two active heating elements are connected to a control 

panel from which the temperature of the furnace can be programmed as a series of linear ramps, 

for example. Type N thermocouples, used to monitor the temperatures of the outer FRM surface, 

the steel slug, and the furnace, are connected to a simple Universal Serial Bus (USB)-based data 

acquisition unit (with cold junction compensation) that can monitor up to eight channels 

simultaneously, and conveniently outputs the values into a spreadsheet. The uncertainty of the 

Type N thermocouples has been presented previously [4]. For example, measurement in ice 

water yielded an average standard deviation of 0.05 K among a set of five thermocouples. At 

higher temperatures, the uncertainty increases to 1 K [4]. Recently, the slug calorimeter 

experimental method developed in BFRL has been standardized by ASTM as ASTM E2584 

“Standard Practice for Thermal Conductivity of Materials Using a Thermal Capacitance (Slug) 

Calorimeter” [6]. 

 Several comparisons were made between the original and mini furnaces to ensure compatible 

performance. Figure 2 shows the furnace temperatures achieved during a single heating/cooling 

cycle when both furnaces were programmed with the same set of piecewise linear temperature 

ramps for the heating portion, followed by natural cooling. Specifically, the furnace setpoints 

were 538 °C after 45 min, 704 °C after 70 min, 843 °C after 90 min, 927 °C after 105 min, and 

1010 °C after 2 h. At the maximum points in the temperature/time curves shown in Figure 2, the 

furnaces were turned off and the temperatures continually monitored during natural cooling. For 

the mini-furnace, results are shown for two different locations of the measurement thermocouple 

(37.5 mm and 87.5 mm from the heating element surface) while the thermocouple for 

temperature control was maintained at a distance of 37.5 mm in both cases, indicating the 

uniformity of the temperature distribution within the mini-furnace. Due to its larger working 

volume, the original furnace exhibits a slight lag behind the temperature rise observed in the 

mini-furnace. Because the two furnaces are in different local environments, the mini-furnace 

being housed in a fume hood and the original furnace in a large open-bay laboratory, their 

cooling responses are also different. But, for all practical purposes, it appears that either furnace 

2
may be utilized to produce a heating/cooling curve that matches the temperature setpoints 

presented above. Slug calorimeter Specimen

Specimen

Guard

insulation

Guard

insulation

Q direction

heating

cooling

Retaining

plate

Active heating elementActive heating element

Passive element

Passive element

Figure 1. Schematics of the slug calorimeter test setup: left- schematic of a cross section through the middle 

of the basic slug calorimeter setup, and right- schematic of an overhead view of a completed sandwich 

specimen mounted and ready for testing in the mini-furnace. 

0

200

400

600

800

1000

1 10 100 1000

Time (min)

Temperature ( oC)

Original Furnace

Minifurnace (TC 1)

Minifurnace (TC 2)

Figure 2. Comparison of measured furnace temperatures for the original furnace and the mini-furnace when 

programmed with the same set of linear temperature ramps. TC1 and TC2 indicate two different locations of 

sensing thermocouple in the mini-furnace as described in the text. 

 One other difference between the two furnaces was noted during the course of these 

experiments. Because the heating elements in the original furnace are exposed, they will transfer 

considerable energy via radiation to the Inconel retaining plates located on the exterior of the 

slug calorimeter setup (Figure 1). Thus, at the later stages of the heating curve, as shown in 

3
Figure 3, the temperature of the outer surfaces of the FRM specimens (and these retaining plates) 

actually may exceed that of the furnace environment. For the mini-furnace, where the heating 

elements are embedded in the ceramic fiber boards, this (radiation) effect is not observed, as the 

temperature of the outer FRM surface always remains below that of the furnace environment 

during heating (Figure 3). From a practical viewpoint, either of these cases is reasonable, as long 

as the temperatures of the steel slug and outer FRM surface are monitored throughout the 

heating/cooling cycles. However, as will be shown later, from a modeling viewpoint, the 

covered elements of the mini-furnace are preferable, as the enhanced radiation between the open 

elements and the retaining plates is not easily incorporated into a model, where it is generally 

expected that during heating, the furnace temperature will always be higher than the outer FRM 

specimen temperature. 

a)

Original furnace with 4-sided heating and 

exposed elements

0

200

400

600

800

1000

1 10 100 1000

Time (min)

Temperature ( oC)

Furnace

Outer specimen

b) 

Minifurnace with 2-sided heating and covered 

elements

0

200

400

600

800

1000

1 10 100 1000

Time (min)

Temperature ( oC)

Furnace

Outer specimen

Figure 3. Comparison of measured furnace and outer FRM surface temperatures for a) the original furnace 

and b) the mini-furnace, when programmed with the same set of linear temperature ramps. 

4
2.2 Slug Calorimeter 

 The details of the slug calorimeter experimental setup have been provided in references 

[4] and [5]. The steel slug consists of a 152.4 mm by 152.4 mm by 12.7 mm AISI 304 stainless 

steel plate into which three thermocouple holes have been milled. It has a mass of 2340 g. The 

two major faces of the slug are covered with samples of the FRM to be evaluated, each 

nominally 25 mm thick. The remaining sides of the stainless steel slug (and those of the 

samples) are surrounded by a high temperature guard (microporous) insulation material [4, 5] 

(Figure 1). The assembled specimen is held together by two high temperature retaining plates 

and a set of eight bolts that are external to (outside of) the guard insulation. For the results 

presented in this report, the retaining plates were continuous, but contained a set of four 

centralized slots (2.4 mm by 98 mm) to allow for the escape of steam and gases. The calorimeter 

can also be assembled with retaining plates containing a 150 mm by 150 mm central square hole 

for when intumescent or other expansive FRMs are to be evaluated. 

 When ready for testing, the specimen is placed in a high temperature furnace and exposed 

to programmed heating/cooling cycles. Generally, the heating cycle is programmed as a series of 

linear ramps (such as the one provided in the previous section) and the cooling is natural (e.g., 

not imposed). The temperatures of the slug and the sample (exposed) surfaces are monitored and 

recorded over time. From this temperature/time data, the apparent thermal conductivity of the 

samples as a function of mean sample temperature during multiple heating/cooling cycles can be 

obtained from a previously derived analytical solution [4-6]. 

5
3 Modeling of the Slug Calorimeter Experiment 

 A numerical tool was developed to model the slug calorimeter experimental setup. As 

discussed in the previous section, the experimental setup consists of a slug calorimeter placed 

inside a furnace and subjected to a prescribed heating and cooling cycle. The slug consists of a 

12.7 mm thick stainless steel plate covered with a layer of 25 mm thick FRM on its two major 

faces, and is protected with a high temperature guard insulation material on all the remaining 

faces. The assembled specimen is held together by two high temperature retaining plates. The 

temperature of the steel slug is measured during the course of the experiments and is a function 

of the thickness and thermo-physical properties of the FRM as well as the imposed heating and 

cooling cycle (instantaneous furnace temperature). Before proceeding to formulate the present 

problem of heat and moisture transfer including chemical reactions and phase changes, several 

important assumptions can be made to simplify the formulation. These assumptions are 

discussed in the next three paragraphs. 

 When the slug assembly is placed inside a furnace, the exterior faces of the assembly are 

subjected to convective and radiative heating from the furnace walls. Energy can conduct 

through the retaining plates and the guard insulation material. Since the thermal conductivity of 

the retaining plates was significantly higher than that of the guard insulation material, it can be 

assumed that heating of the FRM material and steel slug effectively occurs entirely through 

energy that was conducted through the metal retaining plates. The slug experiment can therefore 

be modeled simply as a one dimensional transport of mass and energy through multiple material 

layers. 

 As the FRM is heated for the first time, the material can undergo (generally) endothermic 

phase changes / chemical reactions. Evaporation of free water and de-hydration reactions in the 

FRM can result in the production of free water vapor. This free water vapor could in turn 

migrate (diffuse / convect) through the porous fire resistive material. It is conceivable that this 

free water vapor can condense in the cooler portions of the slug setup. Modeling water-vapor 

migration through porous materials is a difficult and challenging problem that is beyond the 

scope of the present report. In the current work, we will account only for the energy associated 

with the phase changes / chemical reactions and neglect the subsequent mass transport of water 

vapor through the FRM. 

 A further simplification can be based on symmetry arguments, noting that the slug is 

placed symmetrically in the furnace, the thickness of the FRM is approximately equal on both 

sides, and the incident fluxes on both sides are also identical. Use of the symmetry argument 

reduces the cost of the computations by reducing the size of the computational domain. 

 Consider a small volume element of a slab of homogeneous material of unit area A and of 

thickness Δx. The equation for conservation of energy for the control volume can be written as 

x

q

x

T k

xt

h R

∂

∂ ⎟ −

⎠

⎞ ⎜

⎝

⎛

∂

∂ − ∂∂ −= ∂∂ ρ )( , (1) 

6
where ρ is the density of the control volume, h is the enthalpy, T is the local temperature and qR

is the radiative flux. The left hand side of the energy equation is the rate of accumulation of 

enthalpy in the control volume. The first term on the right hand side shows the net rate of heat 

addition due to thermal conduction into the control volume, while the second term on the right 

hand side represents the net rate of heat added due to the incident radiative flux on the control 

volume. The equations states that the net enthalpy change of the material in a control volume is 

equal to the net amount of heat entering by conduction plus the contribution due to radiative 

heating of the volume. 

 The partial differential equation expressing conservation of energy was discretized using 

a control volume approach to derive the finite difference form of the equations. The method of 

discretization ensures local energy conservation and requires approximation of only first order 

derivatives (rather than higher order derivatives). The goal of the numerical procedure was to 

predict the temperature T at the cell center. The discretized form of the above equation was 

solved for each material layer. A second order explicit Runge-Kutta scheme was used for time 

stepping. Although the stability characteristics of these methods are more restrictive than 

implicit methods, explicit Runge-Kutta techniques [7] result in more accurate solutions than 

implicit schemes of comparable order. 

 A unique solution to the governing equations requires the specification of initial and 

boundary conditions. The initial temperature distribution in the layers (retaining plate, FRM and 

stainless steel slug) was specified to match that of each experiment being modeled. The density 

and thermal conductivities for each material must also be defined and may or may not be a 

function of temperature. The enthalpy for each material must be defined as a function of 

temperature and can be obtained by integrating the specific heat curve and including the heat of 

reaction [3]. The incident radiative flux varying as a function of time must also be specified to 

start the calculation. Boundary conditions were also specified at the edges of the computational 

domain. At the gas-solid interface, the conductive heat flux into the retaining plate must equal 

the net radiative and convective flux reaching the surface. At the symmetry (middle) boundary, 

the energy flux was set to zero (adiabatic boundary condition). The procedure described in this 

section has been previously used for modeling the thermal performance of fire fighters protective 

clothing and has been discussed in detail in reference [7]. 

 Computational grids should be constructed so as to concentrate the maximum number of 

grid points in the FRM layer, since it is the material of lowest thermal conductivity and also the 

only reactive material in the simulation. Grid density in the stainless steel slug and the retaining 

plate can be relatively coarse due to high thermal conductivities and specific heats for these 

materials. The numerical procedure chooses an appropriate time step for the time marching 

procedure depending on grid density, temperature and other thermo-physical properties. Typical 

computations were performed with approximately five grid points each in the steel plate and the 

retaining plate and twenty grid points in the FRM. A grid convergence study was conducted by 

doubling the number of grid points to make sure that the solutions were grid-independent. A 

typical computational cost was approximately 90 seconds on a single 3.8 GHz processor running 

Linux. 

7
4 Material Properties Used in Modeling 

 Each FRM being evaluated using the model was characterized with respect to its density, 

heat capacity, apparent thermal conductivity, and enthalpies of (projected) reactions according to 

the methodology outlined in part I of this series [3]. In that report, example properties of five 

different FRMs and two types of steel, including the AISI 304 stainless steel plate used for the 

slug calorimeter, were provided. Based on the measured mass loss for each FRM during a high 

temperature (slug calorimeter) exposure, its local density was varied during the first heating 

cycle as a linear function of the local FRM temperature. Each FRM was represented as two 

separate materials in the program database, an original material (whose density was a function of 

temperature and whose enthalpy included reactions and phase changes) and a “burnt” material of 

constant (burnt) density and heat capacity, with no further reaction or phase change contributions 

to the enthalpy. In the program, a conversion was made for each FRM, from its “original” 

properties to its “burnt” properties, when the maximum furnace temperature was achieved during 

the first heating/cooling cycle. For any simulations of the second heating/cooling cycle, the 

“burnt” material properties were employed. 

 To illustrate the predictive capability of the model for a variety of FRM materials, 

standard, medium and high density products were tested in the slug calorimeter and modeled 

using the software described previously. One of the tested products was gypsum-based, while 

the other two were based on a (portland) cementitious binder. Table 1 provides the specific 

gravities of these three materials. Several other FRMs have also been successfully modeled 

using this approach, but the focus of this report will be on these three representative products. 

Table 1. Specific Gravities (with standard deviations from the twin specimens) of the Three Evaluated FRMs 

Product Original Specific Gravity 

Standard density 0.36 ± 0.01 

Medium density 0.45 ± 0.01 

High density 0.77 ± 0.01 

8
5 Results 

5.1 First Heating/Cooling Cycle 

 The experimental results and model predictions for the first heating/cooling cycle are 

compared in Figures 4, 5, and 6 for FRMs of standard, medium, and high density, respectively. 

In each figure, separate plots are included for the FRM (exterior) surface temperature and the 

slug temperature. It is observed that the FRM surface temperature predictions are in excellent 

agreement with the experimental values for the full heating/cooling curves. Specifically, in 

Figures 4, 5, and 6, the differences in peak surface temperatures between experiment and model 

are 2.8 oC, 9.9 oC, and 10.9 oC, respectively. This agreement suggests that an appropriate choice 

has been made for the heat transfer coefficient governing energy transfer between the furnace 

environment and the retaining plates. Because the retaining plates have a high thermal 

conductivity relative to any of the FRMs, the exterior FRM surface temperature is nearly 

identical to that of the retaining plates in the simulations conducted in this study. 

 Regarding the slug temperature predictions, as shown in Figures 4 through 6, an 

acceptable prediction is provided by the model, particularly for temperatures exhibited during the 

cooling portion of the heating/cooling curves. For two of the three materials presented in these 

figures, the peak temperature of the slug is slightly underpredicted by the modeling. Specifically, 

in Figures 4, 5, and 6, the differences in peak slug temperatures between experiment and model 

are 29.1 oC, 1.4 oC, and 23.7 oC, respectively. In addition, for each material, the agreement 

between model and experiment for slug temperatures less than 100 oC during heating is not 

particularly good. Initially, the measured slug temperature is significantly higher than the 

predicted one, followed by a slight plateau region in the measured results, when the slug 

achieves a temperature of about 100 °C. No such plateau is produced by the modeling. It is 

hypothesized that both the difference between measured and model temperatures at these lower 

temperatures and the presence of this plateau in the experimental results are due to mass 

transport and subsequent evaporation (boiling) of condensed moisture released as the gypsumbased or cementitious binders of the different FRMs dehydrate (only) during the first heating 

cycle in the furnace. As this dehydration front penetrates into the FRM from the exterior surface, 

steam is driven towards the interior of the FRM specimen (and the slug surface), where it may 

first recondense when it reaches a local environment with a temperature below 100 °C and then 

evaporates as that local temperature is raised above 100 °C due to heat transfer from the furnace 

(or fire) through the FRM. The initial mass transfer of the steam/hot water results in 

experimental slug temperatures above those predicted by the model, while its ultimate 

evaporation absorbs energy (at the slug surface), such that the temperature rise of the slug in the 

experiment plateaus near 100 °C and is less than that predicted by the model. The net effect, 

however, appears to be fairly well accounted for in the model by including the enthalpies of 

dehydration (and decarbonation) of the binder components of the various FRM materials. The 

hypothesis that these differences are due to dehydration reactions and mass transport is further 

supported by the fact that these effects are not observed at all during the second heating/cooling 

cycle (Figures 7 through 9), as the FRM has completely reacted and all moisture has been 

completely removed during the first heating/cooling cycle. 

9
0

200

400

600

800

1000

0 200 400 600 800 1000 1200

Time (min)

FRM Surface Temperature ( oC)

Simulation

Experiment

0

100

200

300

400

500

600

700

800

0 200 400 600 800 1000 1200

Time (min)

Slug Temperature ( oC)

Simulation

Experiment

Figure 4. Experimental and model predicted exterior FRM surface (top) and slug temperatures (bottom) vs. 

time for the first heating/cooling cycle in the slug calorimeter for the standard density FRM. 

10
0

200

400

600

800

1000

0 200 400 600 800 1000 1200

Time (min)

FRM Surface Temperature ( oC)

Simulation

Experiment

0

100

200

300

400

500

600

700

800

0 200 400 600 800 1000 1200

Time (min)

Slug Temperature ( oC)

Simulation

Experiment

Figure 5. Experimental and model predicted exterior FRM surface (top) and slug temperatures (bottom) vs. 

time for the first heating/cooling cycle in the slug calorimeter for the medium density FRM. 

11
0

200

400

600

800

1000

0 200 400 600 800 1000 1200

Time (min)

FRM Surface Temperature ( oC)

Simulation

Experiment

0

100

200

300

400

500

600

700

800

0 200 400 600 800 1000 1200

Time (min)

Slug Temperature ( oC)

Simulation

Experiment

Figure 6. Experimental and model predicted exterior FRM surface (top) and slug temperatures (bottom) vs. 

time for the first heating/cooling cycle in the slug calorimeter for the high density FRM. 

12
5.2 Second Heating/Cooling Cycle 

 The experimental results and model predictions for the second heating/cooling cycle are 

compared in Figures 7, 8, and 9 for FRMs of standard, medium, and high density, respectively. 

In each case, excellent agreement is observed between the model and experimental results for 

both the FRM surface and the stainless steel slug temperatures. For these simulations, the 

differences in peak surface temperatures between experiment and model are 3.0 oC, 12.5 oC, and 

7.8 oC, for the standard, medium, and high density FRMs, respectively. For the peak slug 

temperatures, the corresponding differences are 6.3 oC, 1.2 oC, and 4.6 oC, respectively. During 

the 2nd heating curve, no indication of a temperature plateau near 100 °C is observed, suggesting 

that all dehydration reactions went to completion during the first heating cycle and that all of the 

free and bound water was effectively removed from the FRM (and the slug calorimeter setup) 

during the first heating/cooling cycle, as noted previously. 

13
0

200

400

600

800

1000

0 200 400 600 800 1000 1200

Time (min)

FRM Surface Temperature ( oC)

Simulation

Experiment

0

200

400

600

800

0 200 400 600 800 1000 1200

Time (min)

Slug Temperature ( oC)

Simulation

Experiment

Figure 7. Experimental and model predicted exterior FRM surface (top) and slug temperatures (bottom) vs. 

time for the second heating/cooling cycle in the slug calorimeter for the standard density FRM. 

14
0

200

400

600

800

1000

0 200 400 600 800 1000 1200

Time (min)

FRM Surface Temperature ( oC)

Simulation

Experiment

0

100

200

300

400

500

600

700

800

0 200 400 600 800 1000 1200

Time (min)

Slug Temperature ( oC)

Simulation

Experiment

Figure 8. Experimental and model predicted exterior FRM surface (top) and slug temperatures (bottom) vs. 

time for the second heating/cooling cycle in the slug calorimeter for the medium density FRM. 

15
0

200

400

600

800

1000

0 200 400 600 800 1000 1200

Time (min)

FRM Surface Temperature ( oC)

Simulation

Experiment

0

100

200

300

400

500

600

700

800

0 200 400 600 800 1000 1200

Time (min)

Slug Temperature ( oC)

Simulation

Experiment

Figure 9. Experimental and model predicted exterior FRM surface (top) and slug temperatures (bottom) vs. 

time for the second heating/cooling cycle in the slug calorimeter for the high density FRM. 

16
5.3 Different Furnaces 

 As was mentioned previously, the open heating elements present in the original furnace 

result in a different energy transfer between the furnace “walls” and the slug calorimeter’s 

retaining plates. The additional radiative transfer between the glowing elements and the metal 

plates complicates any modeling of the experimental results, as shown in Figure 10. For this 

furnace, the simulation results consistently underestimate both the experimental exterior FRM 

surface and slug temperatures for much of the heating portion of the heating/cooling cycle. 

Specifically, the maximum surface and slug temperatures are underestimated by 31 oC and 72 oC, 

respectively. While the heat transfer coefficient between the furnace and the retaining plates 

could be adjusted (increased) to improve the agreement between experiment and simulation, the 

increase of the retaining plate (FRM surface) temperature above that of the furnace will not be 

obtained in the current configuration of the model, regardless of what value is employed for the 

heat transfer coefficient. An extended model that accounted for the energy transfer between the 

individual heating elements and the metal retaining plates would be required when the heating 

elements are directly exposed. Fortunately, for the insulated heating elements employed in the 

mini-furnace, it appears that such energy transfer is negligible and thus, the slug calorimeter 

experiment can be successfully modeled using the one-dimensional multi-layer heat transfer 

model presented in this report. 

17
0

200

400

600

800

1000

0 200 400 600 800 1000 1200

Time (min)

FRM Surface Temperature ( oC)

Simulation

Experiment

0

100

200

300

400

500

600

700

800

0 200 400 600 800 1000 1200

Time (min)

Slug Temperature ( oC)

Simulation

Experiment

Figure 10. Experimental and model predicted exterior FRM surface (top) and slug temperatures (bottom) vs. 

time for the first heating/cooling cycle in the slug calorimeter in the original furnace for a standard density 

(specific gravity = 0.31) FRM. 

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6 Summary and Future Research 

 This report has demonstrated the capability of a multi-layer thermal performance model 

to simulate the results of a slug calorimeter experiment exposure in a high temperature furnace. 

By including the enthalpy of the FRM as a function of temperature, along with its thermal 

conductivity and mass loss, adequate predictions of the stainless steel slug temperature during 

both the first and second heating/cooling cycles could be produced for a furnace exposure where 

the heating elements were encased within the furnace walls. Conversely, results for a furnace 

with exposed elements differed significantly from the experimental measurements, most likely 

due to enhanced radiative transfer between these elements and the metal retaining plates used to 

immobilize the slug calorimeter specimen. Future studies will extend the modeling to consider 

actual ASTM E119 fire exposures, beginning with testing of structural steel columns protected 

by an FRM. If these efforts are successful, it is envisioned that the model will be incorporated 

into a computational toolkit to be made available to the general public from NIST. Further 

refinements of the model could also be considered, such as including a mass transfer component 

to simulate the moisture movement that occurs during the first heating cycle of the slug 

calorimeter. To accurately model this phenomena, in addition to the moisture release rates 

(dehydration kinetics), gas and liquid permeabilities of the FRM as a function of temperature 

would also be needed. The initial one-dimensional heat transfer model for firefighter’s clothing 

[7] already includes the appropriate basic equations to simulate such moisture movement. 

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7 Acknowledgements 

 The authors would like to acknowledge the financial and technical support of the current 

industrial members of the National Institute of Standards and Technology/industry consortium 

on Performance Assessment and Optimization of Fire Resistive Materials: the American Iron and 

Steel Institute, Isolatek International, PPG Industries, and W.R. Grace & Co.- Conn.

8 References 

[1] ASTM E119, “Standard Test Methods for Fire Tests of Building Construction and 

Materials,” ASTM Annual Book of Standards, ASTM International, West Conshohocken 

2007. 

[2] NIST NCSTAR 1: Federal Building and Fire Safety Investigation of the World Trade Center 

Disaster: Final Report on the Collapse of the World Trade Center Towers, U.S. Department 

of Commerce, September 2005. 

[3] Bentz, D.P., Prasad, K.R., “Thermal Performance of Fire Resistive Materials I. 

Characterization of Fire Resistive Materials with Respect to Thermal Performance Models,” 

NISTIR 7401, U.S. Department of Commerce, February 2007. 

[4] Bentz, D.P., Flynn, D.R., Kim, J.H., and Zarr, R.R., “A Slug Calorimeter for Evaluating the 

Thermal Performance of Fire Resistive Materials,” Fire and Materials, Vol. 30 (4), 257-270 

(2006). 

[5] Bentz, D.P., “Combination of Transient Plane Source and Slug Calorimeter Measurements to 

Estimate the Thermal Properties of Fire Resistive Materials,” Journal of Testing and 

Evaluation, Vol. 35 (3), 240-244, (2007). 

[6] ASTM E2584, “Standard Practice for Thermal Conductivity of Materials Using a Thermal 

Capacitance (Slug) Calorimeter,” ASTM Annual Book of Standards, ASTM International, 

West Conshohocken 2007. 

[7] Prasad, K., Twilley, W., and Lawson, J.R., “Thermal Performance of Fire Fighters’ 

Protective Clothing. 1. Numerical Study of Transient Heat and Water Vapor Transfer,” 

NISTIR 6881, U.S. Department of Commerce, August 2002. 

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