NBSIR 77-1260

A Computer Program for the

Thermal Analysis of the Fire

Endurance of Construction

Walls

Francis C. W. Fung

Center for Fire Research

Institute for Applied Technology

National Bureau of Standards

Washington, D.C. 20234

May 1977

Final Report

Issued June 1 977

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

NBSIR 77-1260

A COMPUTER PROGRAM FOR THE

THERMAL ANALYSIS OF THE FIRE

ENDURANCE OF CONSTRUCTION

WALLS

Francis C. W. Fung

Center for Fire Research

Institute for Applied Technology

National Bureau of Standards

Washington, D.C. 20234

May 1977

Final Report

Issued June 1 977

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Dr. Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director
s.
CONTENTS

Page

LIST OF FIGURES iv

LIST OF TABLES i v

1. INTRODUCTION 1

2. GOVERNING EQUATION AND BOUNDARY CONDITIONS 3

4. DISCUSSION OF NUMERICAL PROGRAM

3. PROBLEM FORMULATION AND FINITE DIFFERENCE EQUATIONS 7

4. DISCUSSION OF NUMERICAL PROGRAM 12

5. SAMPLE CASES CALCULATED 13

5.1. Description of Panels 13

5.2. Thermal Properties 16

5.3. Input Data 17

6. DISCUSSION OF RESULTS AND CONCLUSIONS 19

7. ACKNOWLEDGMENT 19

8. REFERENCES 21

APPENDIX - PROGRAM LISTING 31

iii
LIST OF FIGURES

Page

Figure 1. Solid-Air-Solid Interface 3 Figure 2. Solid-to-Surrounding Interface 5 Figure 3. Symmetry Plane 5 Figure 4. Solid-to-Solid Interface 6 Figure 5. Furnace-to-First-Solid Interface 6 Figure 6. A Composite Wall with N Layers, m Air Spaces 7 Figure 7. Sketch of Finite Differencing Network in a Solid Layer ... 8 Figure 8. Thermal Response of Gypsum Wood Wall, Case 1 22

Figure 9. Thermal Response of Gypsum Wood Wall, Case 2 23

Figure 10. Thermal Response of Bulkhead 2B 24

Figure 11. Thermal Response of Bulkhead 3 25

Figure 12. Thermal Response of Bulkhead 3C 26

Figure 13. Thermal Response of Bulkhead 3F 27

Figure 14. Thermal Response of Bulkhead 4 28

Figure 15. Thermal Response of Bulkhead 5B1 29

Figure 16. Flow Chart of Transient Heat Transfer Through Composite

Walls with Arbitrary Air Gaps 30

LIST OF TABLES

Table 1. Comparison of Fire Endurance Times by Experiment and

Calculations. . 20

IV
A COMPUTER PROGRAM FOR THE THERMAL ANALYSIS OF THE

FIRE ENDURANCE OF CONSTRUCTION WALLS

Francis C. W. Fung

Abstract

A general one-dimensional transient heat and mass transfer

numerical program has been developed for composite building con- structions. Since typical building constructions consist of a series of composite layers and intermediate air layers, transient

heat transfer is modeled by conduction through solids and by

radiation and convection through air spaces. In addition the

program has built-in features for ease of application to

building constructions where various combinations of solid-tosolid and solid-to-air interfaces are encountered. The com- plete Fortran language program as used on the NBS Univac 1108

computer is given. A discussion of the program and instruction

for its use are facilitated by the aid of examples. Numerical

solutions using the present program compare favorably with experimental data in standard fire endurance tests.

Key words: Composite building constructions; convection;

experimental data; fire endurance; heat generation or absorption;

numerical solutions; radiation; one-dimensional; thermal con- duction; transient heat transfer.

1. INTRODUCTION

The fire performance of building constructions is generally evaluated

by a large scale laboratory fire endurance test (ASTM E 119) in which one surface is exposed to furnace gases with a prescribed increasing temperature

history simulating the burnout of combustibles. The fire endurance rating

of the construction is the time period during which it withstands the fire

exposure without (a) structural failure, (b) the development of cracks

through which flames or hot gases can pass, or (c) the temperature rise on the

unexposed surface exceeding, a prescribed limit (250 °F average rise or 325 °F

rise at a single point) . Where the failure criterion is due to heat transmission alone, heat transfer analysis can provide a means for prediction and

design

.

1
Since typical building constructions consist of a series of composite

layers and intermediate air layers, transient heat transfer is modeled by

conduction through solids and by radiation and convection through air spaces.

In addition, the program has built-in features for ease of application to

building constructions where various combinations of solid-to-solid and solidto-air interfaces are encountered. For each solid layer, the present program

has provisions for phase changes, heat generation and absorption, and thermal

property variation with temperature commonly found in building materials.

Through the air spaces the modes of heat transfer include radiation and con- vection with temperature-dependent air properties.

A number of special analog and numerical programs for fire endurance

evaluation have been in existence for some time [1-4]more flexible and

general finite difference program was developed by Krokosky as recently as 1970 [5]

,

which also contains a review of the existing thermal analysis

programs for fire endurance evaluation.

The present numerical program was also developed to incorporate into

fire endurance analyses the following features which are desirable and yet

not readily available in existing programs:

1. Options to handle heat exposure on one or both sides of a structure.

2. Allowance for air infiltration, and heat generation and absorption

in air spaces.

3. For ease of application to building structures, a single input card,

using digits 1 and 0, is sufficient to instruct the computer the

specified number of solid layers and air spaces arranged in a given

problem.

4. Temperature-dependent thermal properties and known heat effects due

to chemical reactions of some common building materials are stored

in a subroutine and called by an input card, punched as 2331,

indicate coded materials stored in the subroutine.

5. The duration as well as the amount of heat represented by a phase

change or chemical reaction can be varied in any material.

Numbers in brackets refer to the literature references listed at the end

of this paper.

2
2 . GOVERNING EQUATION AND BOUNDARY CONDITIONS

The governing equation for one-dimensi'onal transient heat flow is the

well known heat diffusion equation. Including a term for internal heat

generation, this can be expressed as:

where

T = absolute temperature in solid

x = coordinate in direction of heat flow

k = heat conduction coefficient

g

= time rate of heat generation per unit volume in solid

p = density of solid

c = specific heat capacity of solid

0 = time.

Boundary Conditions [6,7] : The following types of boundary conditions need to be evaluated for the

general problem:

(a) solid to air

(b) energy balance in air space

(c) air to solid

(d) solid to surrounding

(e) solid to symmetry plane

(f) solid to solid

(g) furnace gases to first surface layer.

+ g ( 1 )

Ax

1 Ax 2

Solid 1 Solid 2

Figure 1. Solid-Air-Solid Interface

3
(a) Solid to Air (see fig. 1) [7]

PjCjAx ATj

A 0

AT

1 / 4 4 k

l Ax,

° E 12 ( T

1 T2

Ax. 5/4 1 - h(T

1 -T

a

) 7 + g x - ( 2 )

(b) Energy Balance in Air Space (see fig. 1)

AT - = h fT. -T

a

A. C__ P _ = hCTj-^) 574 - h(T

a-T

2

) 5/4

+ m C

pa

(T

1 -T2

) + J^g

a pa a A a -'a (3)

(c ) Air to Solid (see fig. 1)

P 2 C 2 Ax

2 AT

2 AT

A 0 = k

4 4 5/4 Ax

+ ae T -T + h (T -T„) ' + g

2 AX 12 \ a 2/ a 2 ' y

2 2 (4)

In the above equations the subscripts 1 and 2 indicate solid 1 and solid 2,

respectively, as shown in figure 1, and where

e

l 2

and

e

T

Ax

1

2

1

o

T

a k , k

l 2 g

are emissivity of surface 1 and of surface 2 surface temperatures as shown in figure 1 incremental length in x direction in solid 1 and solid 2 Stefan Boltzmann constant

temperature of air

heat conduction coefficient in solid 1, and 2 time rate of heat generation or absorption per unit volume in

solid 1 and 2 air gap spacing

specific heat capacity of air

density of air

4
m: rate of mass transfer per unit area due to pressure difference

g : rate of heat generation per unit volume in air space due to

combustibles

h: an empirical convection heat transfer constant,

h = .27 for vertical surface, and h = .38 for horizontal

surfaces [ 8]

.

Radiation

T T

o

Convection

Figure 2. Solid- to-Surrounding Interface

Solid

(d) Solid to Ambient (see fig. 2)

^

U - - *(T-To

, 5 ^ Ax

2

where the additional variables are:

T

q

: ambient temperature

e: emissivity of surface

T: surface temperature of solid

(5)

Solid

AX]

1

Symmetry plane

Ax

2

4

'A I

s /l Air Space Yi

/

Ax

Solid

Ax

2 Ax

Figure 3. Symmetry Plane

5
(e) Solid to Symmetry Plane (see fig. 3)

By symmetry, temperature on both solid surfaces that face each other are equal, however T >_ T

g

. So there will be heat transfer from solid to air. At

the interface we have:

pcAx AT

2 A 0 h (T g

Ax

2

At the air space we have,

AT

<5 5/4

a c P = h (T - T ) ' s pa a

A0 s

where

T: surface temperature of solids

T

g

: temperature of air in symmetry plane

distance from solid to symmetry plane

(6a)

(6b)

T

1 Solid 1

T

2Solid 2

Figure 4. Solid- to-Solid Interface

(f ) Solid to Solid (see fig. 4)

Consider interface between Solid 1 and Solid 2 as shown in figure 4.

Let Tj and T., be the interface temperature in each solid respectively. A

heat balance for the interface node can be expressed as T = T , and

2 1

P

i C

i

AT

A 0 + P c

2 2

Ax AT

2 2

2 A 0 + g. AT AT —1 + k —2 Ax 2 Ax

where subscript indicates conditions in solid layer 1 or 2

Radiation

Convection

Figure 5. Furnace-to-First- Solid Interface

"

Solid

( 7 )

6
(g) Furnace Gases to First Solid Surface (see fig. 5)

Consider heat transfer from furnace gases to first solid surface. The

main modes of heat transfer will be radiation and convection. A good approximation of ASTM E 119 fire curve is given by the following three formulas:

e T = 1692 g

- + 68 0

< 9 < 50 min (error + 2%)

2 T = 1667 + 1.260 - 0.0236(120-0) 50 min < 6 < 115 min

(no appreciable error)

T = 1667 + 1.260 115 min < 0 < 480 min

(linear exact)

Heat balance from furnace to first solid surface,

AT!

PC Ax

2 A ( ATAx

5 / 4 = k -r— + oe (T - T ) + h (T - T ) ' + g

Ax

2

( 8 )

where T„ is absolute furnace temperature

r

3. PROBLEM FORMULTION AND FINITE DIFFERENCE EQUATIONS

Consider general one-dimensional heat transfer problem containing N

solid layers and m air spaces in any order. To facilitate formulation and

discussion we introduce i, j, and k, three running indices.

Let

T^ j

: Temperature of jth node in ith solid

i: 1...N (number of solid layers)

j: l...n (number of nodes in solid layer

k: l...m (number of air spaces)

In figure 6, a general multi-layer configuration is shown, where numbers in

circles indicate the applicable equation at the given node as discussed in

the previous section.

Solid Solid Air Solid Solid Solid

Radiation i=l — i k i+1 — i=N

(D di © © © © © (I 1 s or

T

i i rv T. . T T

T+l o

TNn^

1 .

Convection d 1 > j

SL . 9. . 1 . y w

Figure 6. A Composite Wall with N Layers, m Air Spaces

(Numbers in circles indicate applicable equation

as discussed in section 2.)

7
To solve our problem numerically with the nonlinear heat diffusion equation

and associated complex system of boundary conditions we shall use forward

time differencing and central space differencing scheme. Figure 7 shows the

finite differencing network inside a solid layer.

1 1 1

1 1 1 II

1 1 1

1 1 1 ll

Ax . Ax Ax | Ax | Ax | Ax | Ax

9 ill 1 | 9 “1 1 il| I

| nth node

1 ! 2

1 3 I4i5 1 in j=l. . .n

1 1 1

|

1 1 1 ith solid layer

Figure 7. Sketch of Finite Differencing Network in a Solid Layer

Furthermore, let

T . : ak : Temperature of kth air spacing

e :: Time

A 0 :: Time increment

T! . :: Temperature at (0 + A0) of jth node in ith solid

£ . : 1

: Thickness of ith solid

£ . : ak : Thickness of kth air spacing

£

Ax. = —^ : 1 n-1 : Difference spacing for ith solid

g i,j :: Rate of heat generation per unit volume

k. . : 1.1

: Heat conduction coefficient

a . ; 1

: Heat diffusion coefficient

^ak 1: Rate of heat generation per unit volume in air space

0m

k

:: Rate of mass transfer per unit area

Applying our finite differencing scheme we have the following general

finite difference expressions corresponding to the previously discussed

governing equation and boundary conditions [6,7 and 9].

8
Governing Equation

T! . i/D M

i + T

i ( j +1

)

i 1_\ T . + Ili! .- 1

- M. ) ij k. .M. 1/ J 13 i

(9)

where

M.

1

(

Ax i)

a . A 0 l

From equation (9) we require > 2 for stability,

Solid to Air

T!

1 ,n

T. + =r i,n M.

/ \ r 4 3 ^i,n-l T. - R.

1 ,n

/ 1

|

2

[_

(T i,n>

- T i+1 /

} ]

- T , ) 5/4 g . Ax

1 /n 1 ak ; k . M.

1 , n 1

( 10 )

where

2 A 0 a e

1 2 Ax . p . c . 11 1

c . : 1

H . 1

Specific heat of ith layer

2A0h

p . c . Ax

11 1

Air Space Heat Balance

T’ak

= T . + P. (T -T , ak k i,n ak

5/4

- Qv (T . - T . , , ,)

5/4 + S, (T . _-T,

'K ak i+1 , 1k i ,n i+1 ,

(11

> + G , ) ak

where

p a

:

hA 0 a . c ak pa a

air density function of temperature

9
c : specific heat of air

pa r

hA 6 l , c p ak pa a

mA 6 'ak^a

ak

gak

A9

c P pa a

Air to Solid

T'. = T . , , , + R. i+1,1 i+1,1 i in [

(T in>* - <T

i + l,l , “] M

±+1

(T i+l,l T i+1,2 )

+ H . , (T , - T . , n ) i+l ak i+l,l

5/4

( 12 )

R., M . , , H.,, as defined before,

l ' i+l , i+l

Solid to Ambient

T

1 = t + -— (T N , n N , n M

1 N,n-1 ' n

G. t ( Ax. t

) 2 N ,n N

Tm ) - Rm (Tm

4 - T

4

) - H ( T - T ) N,n N N,n o N N,n o

kM M.- N ,n N

5/4

(13)

where

R

N

4xH

P N

CN

N

: emissivity of solid (last node to ambient)

IL, , k„T and M.. as defined before

N N , n T!

T

q

: ambient temperature

10
Solid to Symmetry Plane

T' = T + — (T - T 1 N,n N , n

v N,n-1 X N , n

;

c /, G. 7 (Ax..,)

t.t wm m 1 5 / 4 , N,n N

H

N

(TN,n V + }T M

N ,n n Wn" - V

where

T' = T + P (T - T ) 5 ^ 4 + R, (T 4 - T

4

) s s sN,n s N N,n s

T

g

: temperature at symmetry plane

hA0

s £ c p s pa a

£ g

: distance between solid surface and symmetry plane.

Solid to Solid

T! , , = T!

1 +1,1 i,n

T!

l ,n [

A . T . + A. ,-T. , + B.g. + B. ,,g. ,, , + D. (T.

l i,n l+l i+l,l i^i, n l+l^i+l,! i,n i,nD i+1 ,1

(T i+l ,1

T i+1 ,2]

(A

i + A

i+1 )

where

A.

1

p . c . Ax . 11 1

B . 1

Ax . A0

1

D . i,n

k. A 0 1 ,n Ax . l

(14a)

(14b)

(15)

11
i+1,1

k . , n A 0 l+l , 1 Ax i+1

g^ j

: rate of heat generation per unit volume in ith solid.

Furnace Gases to First Solid Surface

T,' n = T, , + R, (T 4 ~ T, 4

) + H, (T - T, J + 1,1 1,1 1 F 1,1 1' F 1,1'

G 1,1

AX

1 k l,lM

l

M

1 (T 1,1 Tl,2 } (16)

where

2 A 0 a z o X

1 1 C

1

emissivity of first surface (furnace gases to 1st solid)

furnace temperature, and

as defined before

4. DISCUSSION OF NUMERICAL PROGRAM

A flow chart of the main program is presented in figure 16. A listing of

the complete numerical program is also presented at the end of this report.

The logical sequence of the main program can be grasped readily by first

considering the flow chart.

The following is a list of input parameters as read in on data cards

(examples of which are shown at section 5.3).

NN : number of solid layers

N: number of nodes in each layer

M: number of air spaces

ID: sequence of numbers 1 or 0 , specifying the sequence of solid layers

and air spaces, e.g., 101011101 means solid-air-solid-air-solid-solidsol id- air- sol id.

12
IDD

sequence of numbers specifying the material of each solid layer,

e.g., 122321 means the six solid layers of the problem are of

materials 1, 2, 2, 3, 2, 1 in that order. Various temperature

dependent material properties are stored in Subroutine PROP.

AL(i): thickness of ith solid layer in feet

AI(i): thickness of air gap spacing in feet

GA(k): rate of heat generation per unit volume due to combustibles in kth

air space, Btu/ft 3 -hr.

DTHETA : Time increment in fraction of hour.

AMO: Volume rate of airflow through walls per unit area in ft 3 /ft 2 -hr

(m/p ) . GMl , GM2 , GM3 , etc: Heat absorption or release due to phase change in

material 1, 2 or 3 etc., Btu/ft 3 hr.

Subroutine PROP stores temperature dependent thermal properties and phase

change reactions of some common building materials. This subroutine can be

expanded as desired when new materials are encountered. When called from the

main program this subroutine supplies the thermal properties for the ith layer

of solid currently being calculated.

The function subroutines are self-explanatory. The comment statement at

the beginning of each function subroutine properly identifies it with the

corresponding equation and boundary conditions in section 3.

5. SAMPLE CASES CALCULATED

5.1. Description of Panels

Case 1 : Four solid layers (gypsum, wood, wood, gypsum), three air gaps, heat

from one side as shown.

G

5“

8 r

Air

3" w

1"

t 2 r

Air

3"

W

i"

t 2 r

Air

3

" G

JL"

( 8 (

where

G: Gypsum board

W: Plywood

13
Case 2 : Four solid layers (gypsum, wood, wood, gypsum), three air gaps,

heating from both sides as shown,

G

5"

8

Air

6"

w

1 " 2

Air

3

" W

i M 2

Air

6"

G

£8

where

G: Gypsum board

W: Plywood

2 Case 3 : Bulkhead 2B , four solid layers (marinite, mineral wool, aluminum,

marinite) , two air gaps, heat from one side as shown.

M

3"4

Air

6"

MW

1"

(

sk*

r~

>

Air M

i"

. . >

where

M : Marinite

MW: Mineral Wool

AL: Aluminum

Case 4 : Bulkhead 3, three solid layers (marinite, aluminum, marinite), two

air gaps, heat from one side as shown,

Tf

M

3"4

Air

, .

AL

5”

1 161

Air

6"

M

3"

1 4 r

where

M : Marinite

AL: Aluminum

^Assembly descriptions and details of the actual ASTM E 119 fire endurance

tests of this and following bulkheads are presented in reference [11].

14
Case 5

Bulkhead 3C , four solid layers (marinate, aluminum, mineral wool,

marinite) , two air gaps, heat from one side as shown,

M

A"

4

Air

i"

AL

5"

16 MW

i"

\ >

at

qr

M

i

2

where

M : Marinite

AL : Aluminum

MW: Mineral Wool

Case 6 : Bulkhead 3F , four solid layers (marinite, mineral wool, aluminum,

marinite), two air gaps, heat from one side as shown,

M

3"4

Air

i"

MW

i”

AL

5"

16

Air

6"

M

3"4

Case 7

Bulkhead 4, three solid layers (perforated steel, mineral wool,

aluminum) , one air gap, heat from one side as shown.

PS* Air MW AL

tf i.

2" i" 5

"

16 __

where

PS: Perforated steel sheet (#16 USCG, 3/16 inch diameter holes,

3/8 inch diameter holes, 3/8 inch center, 23% open area)

MW: Mineral wool

AL: Aluminum

Case 8 : Deck 5B1 , three solid layers (perforated steel, mineral wool,

aluminum) , heat from bottom as shown.

AL

*5*

, 16 MW ; 2

"

Air 9"

PS

15
5.2. Thermal Properties

The following thermal properties are taken from Ref. [1] and Ref. [10].

NBS property measurements are programmed into subroutine PROPT,

Gypsum Board

p 60 lb/ft

3

c = .26 Btu/lb °F

k = .125 Btu/hr ft °F 0 i T 1 200

= .075 Btu/hr ft °F 200 °F 1 T <. 400

= (-05 + 16,000 ) Btu/hr ft °F 400 °F 1 T 1 2000

e - .9

Heat of moisture desorption and calcination: 20,740 Btu/ft

Brick

p = 110 lb/ft 3

c = .216 Btu/lb °F

e = .9

k = 1.0 Btu/hr ft °F 0 < T £ 200 °F

= (.46 + 2T/10 , 000 ) Btu/hr ft °F 200 °F <_ T <_ 2000 °F

Heat of moisture desorption 5000 Btu/ft 3

Plywood

P = 31 lb/ft 3

c = .67 Btu/lb °F

e = .9

k = .065 Btu/hr ft °F

Heat of moisture desorption 1500 Btu/ft 3

Mineral Wool

P = 6.04 lb/ft 3

c = .2 Btu/lb °F

e = .9

k = .02 Btu/hr ft °F 0 < T 1 50 °F = . 02167 Btu/hr ft °F 50 °F <_ T <_ 75 °F

= . 0229 + 0.517 (T-100J/10, 000 75 °F <_ T £ 2000 °F

16
Aluminum

a = 3.33 ft 2 /hr

p = 169 lb/ft 3

c = .208 Btu/lb °

e = .09

k = .167 + 1.63 T/10,000 0 < T < 200 °F

= 117 + .13 (T-32) 200 < T < 2000 °F

Marinite

P 36 lb/ft 3

c = .25 Btu/lb °

0 < T < 200 °F = .25+3 (T-200)/10 ,000 200 °

< T < 2000 °F

E = .9

k = .063 Btu/hr ft °F 0 < T < 200 °F

= (.76 + 1.1 (T-100)/10,000)/12 200 °F < T < 2000 °F

5.3. Input Data

The following are the complete input data for the sample cases calculated.

Case 1 : Four solid layers, 3 air gaps, furnace on one side (gypsum-air-woodair-wood- air- gyp sum)

4531 68 . . 0 5380.0 1500.0 1.0

1010101

1331

.052 . 0417 . 0417 . 052

.25 0 . . 25 0 . .25 0 .

Case 2 : Four solid layers, 3 air gaps, furnace on both sides (gypsum

wood-air'-wood-air -gypsum)

4532 68.0 . 0 5380 .

1500.0 1.0

1010101

1331

.052 . 0417 . 0417 . 052

.5 0 . .25 0 . 0 .

17
Case 3

:

Bulkhead 2B, four solid layers, 2 air gaps, furnace on one side

(marinite-air-mineral wool-aluminum-air-marinite)

4321 68.0 . 0 . 0 101101

6456

.063 .083 0.052 . 083

. 5 .00 . 083 .00

1.0

Case 4 : Bulkhead 3, three solid layers, 2 air gaps, furnace on one side

(mar in ite-air- aluminum- air-mar ini te)

3321

10101

656

.063

. 083

68.0 .0 .0

.052 .063

. 0 .5 .

0

. 0 1.0

Case 5 : Bulkhead 3C , four solid layers, two air gaps furnace on one side

(mar in ite- air- aluminum-mineral wool -air-marini te)

4331 68 . 00 .00

101101

6546

. 063 . 05 .083 . 042

. 083 . 00 . 5 . 00

1.0

Case 6 : Bulkhead 3F , four solid layers, two air gaps, furnace on one side

(marinite-air-mineral wool-aluminum-air-marinite)

4321 68.0 .00

101101

6456

. 063 .083 . 052

.083 . 00 . 5

.00 .00 1.0

. 063

. 00

18
6. DISCUSSION OF RESULTS AND CONCLUSIONS

Comparison plots of calculated and measured temperatures from standard

fire endurance tests represented by the above sample cases are presented in

figures 8-15. Tests were conducted at the NBS large scale fire test center,

Washington, D.C. Complete specification of the bulkheads and decks and

descriptions of the tests are presented in a separate NBS report [11] . The

good agreement between calculations and actual fire endurance test measurements as shown in the comparison plots reflect the success of the mathematical modeling.

In the comparison plots, temperature- time histories were recorded for

each individual panel in a given wall construction for comparison with

computer calculations. The plots can be examined for details of the heat

transfer processes. For the purpose of fire endurance rating generally only

the temperature history of the unexposed surface is needed. Table 1 shows a comparison of the fire endurance times by experiment and calculation. The

criterion used in this table is the 250 °F average temperature rise condition

at the unexposed surface. The agreement of experimental results and theoretical predictions of fire endurance times is good. Based on those calculations one would recommend using the present computer program for the purposes

of fire endurance evaluation and design studies. Such applications would

result in considerable savings in both money and time. This program could

also be used to evaluate the performance of new materials.

Finally a word of caution in the use of a thermal analyzer program

with air gap heat balances such as the present program. Due to the low heat

capacity of air, one must exercise caution in selecting the incremental A0.

The iteration time, A0, used in the previous sample calculations are 1/720 or 1/1440 hour for cases which do not involve metal layers and 1/14400 hour for cases involving metals.

7 . ACKNOWLEDGMENT

The author wishes to acknowledge the contribution of Mr. Vernon Dantzler,

Applications Section, Computer Services Division, for coding the Fortran

program, and for his indispensible and cheerful help in modifying and updating

the Fortran program.

The author also wishes to thank Mr. J. Newton Breese for his part in preparing the graphs and the flow chart for reproduction.

19
Table 1. Comparison of Fire Endurance Times by Experiment and Calculations

Case

Description

Endurance Time

NoExperiment Calculation

1 4 layers, Gypsum, Wood, Wood,

Gypsum, 3 Air Gaps

Passed 1 hr Passed 1 hr

2 4 Layers, Gypsum, Wood, Wood,

Gypsum, 3 Air Gaps, fire on both

sides

Failed at

35 min

Failed at

37 min

3 4 Layers, Marinite, Mineral Wool

Aluminum, Marinite, 2 Air Gaps

Passed 1 hr Passed 1 hr

4 3 Layers, Marinite, Aluminum,

Marinite, 2 Air Gaps

Passed 1 hr Passed 1 hr

5 4 Layers, Marinite, Aluminum,

Mineral Wool, marinite, 2 Air

Gaps

Passed 1 hr Passed 1 hr

6 4 Layers, Marinite, Mineral Wool,

Aluminum, Marinite, 2 Air Gaps

Passed 1 hr Passed 1 hr

7 3 Layers, Perforated Steel,

Mineral Wool, Aluminum 1 Air Gap

Failed at

38 min

Failed at

36 min

8 3 Layers, Perforated Steel,

Mineral Wool, Aluminum, 1 Air

Gap

Failed at

30 min

Failed at

34 min

20
8 . REFERENCES

[1] Harmathy, T. Z., A Treatize on Theoretical Fire Endurance Rating, ASTM

Special Technical Publication No. 301, American Society for Testing and

Materials, Philadelphia, Pa., 10 (1961).

[2] Lawson, D. I. and McGuire, J. H. , The Solution of Transient Heat Flow

Problems by Analogous Electric Networks, Proceedings, Institution of

Mechanical Engineers, Vol. 167, 275-287 (1953).

[3] Robertson, A. F. and Gross, D., An Electrical Analog Method of Transient

Heat Flow Analysis, Journal of Research of the National Bureau of

Standards, Vol. 61, 105-115 (1958).

[4] Krokosky, E. M. , An Analog Simulator for Evaluating Materials Subjected

to the Standard ASTM Fire Curve, Journal of Materials, American Society of

Testing Materials, Vol. 2, No. 4, 801-816 (1967).

[5] Krokosky, E. M. , Fire Intensity-Resistance Evaluation, Journal of

the Structural Division, Proceedings of the American Society of Civil

Engineers, 2501-2519 (1970).

[6] Ozisik, M. N. , Boundary Value Problems of Heat Conduction, International

Textbook Company, Pennsylvania (1968).

[7] Kreith, F., Principles of Heat Transfer, International Textbook

Company, Pennsylvania (1967).

[8] McAdams, W. H. , Heat Transmission, 3rd ed. , McGraw Hill, New York (1954).

[9] Fox, L. , Numerical Solution of Ordinary and Partial Differential Equations,

Addison-Wesley , Massachusetts (1962).

[10] Nottage, H. G. , The Thermal Properties of Building Materials Used in Heat

Flow Calculations, Amer. Soc. of Heating and Vent. Engineers Research

Bulletin, Vol. 53, No. 2, 9 (1947).

[11] Parker, W. J. , Fire Endurance Tests of Aluminum Bulkhead and Deck

Assemblies, NBS Report 10813, Nat. Bur. Stand. (U.S.), Washington, D.C.,

3 (1972)

21
EXPERIMENTAL

CALCULATED

Ac ‘3dn±Vd3dW3i

22

Figure

8.

Thermal

Response

of

Gypsum

Wood

Wall,

Case
1400

23

Figure

9.

Thermal

Response

of

Gypsum

Wood

Wall,

Case
800

700

600

500

400

300

200

100

0

Bulkhead 2B

©

M

©@®

MWAL M

Ml Marinite

MW: Mineral Wool

AL: Aluminum

A: T.3,N

o: T

4,1

:T4,N

Calculation

Experiment

TIME, MIN.

Figure 10. Thermal Response of Bulkhead 2B

24
TEMPERATURE,

TIME, MIN

Figure 11. Thermal Response of Bulkhead 3.

25
800

700

600

500

400

300

200

100

0

Bulkhead 3C

®

M

© (D ©

AL MW M

f

\\

5!' |”

16 1

Ml Marinite

MW: Mineral Wool

AL! Aluminum

A T,

. N

O T-3,N

T4,N

Calculation

Experiment A

20 30 40

TIME,MIN.

Figure 12. Thermal Response of Bulkhead 3C.

26
TEMPERATURE

TIME, MIN

Figure 13. Thermal Response of Bulkhead 3F.

27
800

700

600

500

400

300

200

100

0

Bulkhead 4

PS: Perforated Steel

MW: Mineral Wool

AL! Aluminum

O: T,

3,N

Calculation

Experiment

TIME, MIN

Figure 14. Thermal Response of Bulkhead 4.

28
TEMPERATURE,

TIME, MIN

Figure 15. Thermal Response of Bulkhead 5B1.

29
©'

30

Figure

16.

Flow

Chart

of

Transient

Heat

Transfer

Through

Composite

Walls

with

Arbitrary

Air

Gaps.
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57
NBS-1 14A (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBSIR 77-1260

2. Gov’t Accession

No.

3. Recipient’s Accession No.

4. TITLE AND SUBTITLE

A Computer Program for the Thermal Analysis of the

Fire Endurance of Construction Walls

5. Publication Date June 1977

6. Performing Organization Code

7. AUTHOR(S) Francis C.W. Fung

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 4928678

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Same as No. 9

13. Type of Report & Period Covered

Final Report

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

A general one-dimensional transient heat and mass transfer

numerical program has been developed for composite building constructions

Since typical building constructions consist of a series of composite

layers and intermediate air layers transient heat transfer is modeled by

conduction through solids and by radiation and convection through air

spaces. In addition the program has built-in features for ease of

application to building constructions where various combinations of

solid-to-solid and solid-to-air interfaces are encountered. The complete

Fortran language program as used on the NBS Univac 1108 computer is

given. A discussion of the program and instruction for its use are

facilitated by the aid of examples. Numerical solutions using the

present program compare favorably with experimental data in standard

fire endurance tests.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons

)

Composite building constructions ; convection;

experimental data; fire endurance; heat generation or absorption; numerical

solutions; radiation; one-dimensional; thermal conduction; transient

heat transfer.

18. AVAILABILITY p^l Unlimited

For Official Distribution. Do Not Release to NTIS

Order From Sup. of Doc., U.S. Government Printing Office Washington, D.C. 20402, SD Cat. No. Cl 3 Order From National Technical Information Service (NTIS)

Springfield, Virginia 22151

19. SECURITY CLASS

(THIS REPORT)

UNCL ASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

61

22. Price

$4.50

USCOMM-DC 29042-P74