NBSIR 74-596

Radiative Heat Transfer From

Products of Combustion in Building

Corridor Fires

K. Bromberg and J. G. Quintiere

Center for Fire Research

Institute for Applied Technology

National Bureau of Standards

Washington, D. C. 20234

February 1975

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

NBSIR 74-596

RADIATIVE HEAT TRANSFER FROM

PRODUCTS OF COMBUSTION IN BUILDING

CORRIDOR FIRES

K. Bromberg and J. G. Quintiere

Center for Fire Research

Institute for Applied Technology

National Bureau of Standards

Washington, D. C. 20234

February 1975

U. S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts. Director

RADIATIVE HEAT TRANSFER FROM PRODUCTS

OF COMBUSTION IN BUILDING CORRIDOR FIRES

K. Bromberg and J. G. Quintiere

The contribution of radiative heat transfer

from hot combustion products to corridor floors is

examined. Data from full-scale corridor fire experiments is used to calculate emissivity and absorptivity of the combustion products. An empirical

model based on attenuation by absorption is used to

specify the absorption coefficient due to particulates in the products. In these experiments it is

shown that radiation from the combustion products is

just as significant as radiation from convectively

heated walls and ceiling of the corridor. Calculations show that the ratio of radiant heat transfer

to the floor due to ceiling emission to that by combustion product emission ranges from about 0.2 to

0.7. Also^ molecular gas radiation and particulate

radiation can both be significant for the combustion

products. Calculations show that the emissivity of

the gaseous combustion products alone would be about

0.3, but the inclusion of soot particles yields an

emissivity for the total combustion product mixture

of as high as 0.73, based on the experimental data

considered

.

Key words: Combustion products; full-scale fire;

radiative heat transfer.

1 . INTRODUCTION

Radiative transfer is an important mechanism in the spread

of fires in buildings. As a flame spreads over the surface of

a material, its rate of spread will depend on the radiant flux

received by the material. Also, as a fire grows in size within

a compartment, the magnitude of radiant flux falling on the

combustible contents will increase. This heating can lead to

increased burning rates for items involved in the fire and

spontaneous ignition for the remaining combustible items.

Thus, radiant heat transfer can initiate the rapid involvement

in fire (flashover) of the contents of a room.

In the growth of a fire within a building compartment,

several sources of radiant energy do arise. As a flame grows

in size, radiation emitted by it becomes significant. This

direct flame radiation will depend on the concentration and

nature of particles in the flame, as well as the temperature.

Another source of radiation in fires is from the heated surfaces. Hot combustion products will convectively heat the

1
ceiling and upper walls of a compartment. Although the temperature of these heated surfaces will be much less than flame

temperatures, resulting radiation to the floor can be significant because large areas of the walls and ceiling are heated

and the emissivity of these surfaces (which will become coated

with soot) is generally high. Finally, a third source of

radiation is the products of combustion which fill the upper

region of a compartment. As for radiation from flames, this

source of radiation depends on particulate concentration, gas

composition, thickness of the combustion product cloud, and

temperature

.

It is the purpose of this study to determine the significance of the combustion product layer along the ceiling on

radiative energy transfer to the floor. This layer can emit

radiant energy to the floor and can attenuate radiant energy

emitted from the ceiling. The relative contribution of ceiling

versus radiant transfer to the floor by ceiling and combustion

products was investigated by analyzing data from NBS corridor

fire experiments. In these experiments [1,2]^ hot combustion

products from a fully-involved room fire flow out along a

corridor. These hot combustion products heat the upper surfaces of the corridor, and radiant energy, originating from

these products directly or from the heated surfaces, is received

by the corridor floor. In these experiments, it has been found

that radiant energy transfer is essential for sustained flame

spread over a combustible floor covering. Based on data from

these experiments, an attempt will be made to discriminate

between the role of the combustion products and the heated

surfaces as a source of radiation.

2. CORRIDOR FIRE EXPERIMENTS

Data from two corridor fire experiments will be examined.

One experiment (348) ^ had a nylon carpet as the floor covering;

the other experiment (349) had an unvarnished red oak floor in

the corridor and a portion of the burn room. Temperature,

gas composition, and smoke measurements were made in these

experiments and will be used to estimate the combustion product radiation.

The smoke and gas composition data were taken from three

measuring stations as shown in figure 1. The concentration

measurements of CO2 , CO, and O2 were continuous (Birky [3]).

^Numbers in brackets correspond with the literature references

listed at the end of this paper.

^The numbers, 348 and 349, identify two experiments in a series

of NBS corridor fire experiments which were conducted to

investigate the fire hazards of floor covering materials.

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Smoke measurements taken at the exit corridor included light

obscuration and particulate measurements. The obscuration

apparatus continuously recorded the attenuation of light by a

photo-detector at a wavelength of approximately 0.52ym. This

device has an optical path length of 7.6 cm (3 in). The particulate measurements were made by sampling the combustion products at several times during the experiment for a duration of

about one minute each. Over each sampling period either solid

particulate concentration was measured or condensables in the

combustion products were collected. The solid particulates

were collected on a filter maintained at 150°C. The condensables we;re collected by a cold trap at -50°C and approximately

ninety percent was estimated to be water. The smoke data were

summarized in table 1.

Two time periods should be distinguished in these experiments. They are before and after rapid flame spread occurs

over the floor covering in the corridor. Rapid flame spread

occurs at 430 s in test 348 and 620 s in test 349. The effect

on gas temperature is shown in figure 2 for test 348.

Some measurements were examined in test 348 in order to

assess the source of radiant energy to the floor. Radiant

flux to the floor (measured with a sapphire window radiometer)

at 8 ft and combustion product and ceiling temperature at 10

ft were compared, along with attenuation by smoke, in figure

3. The sharp peak in radiation at 300 s appears to follow the

combustion product temperature and smoke attenuation. (It

should be remarked that the recording lag between the radiometer and temperature measurements is within 8 seconds.) The

smoke measurement lags behind these other data by about 5 to 10

seconds, the time for gas to flow from the 10 ft station to

the window. This indicates that, at least at 300 s, radiant

transfer to the floor is primarily due to combustion product

radiation rather than ceiling radiation. This is further

confirmed by comparing the ratio of floor radiation at 300 and

360 s with the fourth power of the gas temperature ratio at

these times.

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whereas the ratio of corresponding ceiling temperatures is

essentially one. This implies that the gas is the primary

source of radiation since the energy radiated is proportional

to the fourth power of the temperature of the radiator. In

the following analysis this will be examined further by determining the emissivity and absorptivity of the combustion products .

3. ANALYSIS

An attempt will be made to use the smoke and gas data to

calculate the emissivity of the combustion products and their

absorptivity with respect to ceiling emitted radiation. In

order to do this, the gas compositions, the nature of the particulate matter in the smoke, and the temperature of gas mixture

all must be determined. This information is limited in these

fire experiments. However, with some reasonable estimates and

assumptions, calculations can be made to yield realistic results

In general, the spectral absorptivity of a combustion

product layer of mean beam length, L, is given by

:^ a = l-exp(K , + K ,)L (1)

where K , is the absorption coefficient due to molecular gas

g , A

, radiation,

and K , is the absorption coefficient due to particulate

- . P r A

; radiation.

The spectral absorption coefficient associated with gas specie

radiation depends on gas temperature, specie concentration, and

pressure. For particle absorption, K , depends on the particle

p , A complex index of refraction [m = n(l - kI)], size, shape, and

distribution. If scattering also occurs, then eq (1) must be

modified to account for transmittance and reflectance due^ to

scattering [4] . When scattering is negligible, eq (1) can be

used along with a knowledge of the spectral variation of K

and K to obtain the total absorptivity • ^'

« = —1- / a.e^ (T^)dA (2)

^S /o

^ b,A ' S

where e, is the spectral blackbody emissive power and T_ is

D , A 13 the source temperature.

8
The total emissivity of the mixture is determined from eq (2)

by replacing the source temperature with the mixture temperature (T) , i.e.

e = ^ /"a^e^ (T)dX (3)

aT o

It has been implicit in these formulations for emissivity

and absorptivity that an isothermal gas of temperature T is

being considered. In order to apply this to the corridor

experiments, some idealizations have been made. The combustion

product layer will be represented by an isothermal (T) infinite

slab bounded by a hot surface (T^) representative of the ceiling

and a cold surface (T^) representative of the cooler lower half

of the corridor. It is assumed that the gas in the lower half

space and floor are at the same temperature, and that this gas

is totally transparent. Uniform composition is also assumed

for the slab. The thickness of the slab is estimated by the

visible smoke layer and the temperature distribution. This

thickness, D, is indicated in figure 2 for all of the cases to

be analyzed. It is obvious that its selection is somewhat

arbitrary. Visual inspection of photographs of the corridor

suggests that its thickness is about 3 ft. Figure 4 illustrates the idealized model describing the radiative transfer

process in the corridor. If the floor and ceiling surfaces are

taken as blackbodies, then it can be shown [5] that the net

heat flux to the floor is given by

qj = a [1-a (T,T^) ] T^^ + e (T) aT^ - aT^"^ (4)

where a and e are evaluated at the mean beam length L = 1.8D

(for an infinite slab) . The first term on the left represents

the energy transmitted by the ceiling through the gas layer

to the floor, the second ''term represents the energy emitted

4 from the gas to floor, and oT^ represents the energy emitted

by the floor. It will be useful to employ the ratio

q" (l-a)T^

q" r- 4

^

' ^g,f eT

in order to assess the relative importance of the energy radiated from the gas to the floor compared with that received

from the ceiling.

9

In order to calculate for the mixture it is convenient

to consider

N

1-a = (1-a ) . n (1-a. . ) (6)

which follows from eq (1). In eq (6), a is the spectral

A , p

absorptivity of the particulate matter and a .is the spectral

A , 1

absorptivity of the ith gas specie. The important wavelength

range for fire situations can be assessed from figure 5 which

shows the locus of wavelengths above and below which 10 percent

of blackbody radiation is distributed. Particulate matter

attenuates and emits radiation as a smoothly continuous function

of wavelength. On the other hand, the gases radiate over discrete wavelength bands. For example, the important combustion

products have major emission bands at 2.7 and 6.3pm for H2O,

2.7, 4.3, and 15um for f and 4.7ym for CO.

The work of Edwards and Balakrishnan [6] has been used to

determine the spectral absorptivities and emissivities of a mixture of gases. They use a wide band absorption model in

their analysis and describe a computer routine (TOTAL) for

calculating total absorptivity and emissivity. This computer

program was used in this present study, and it is described

in the Appendix.

In order to determine the contribution of the particulate

matter, it is necessary to digress to the theory of attenuation

by particles [4,5,7]. For simplicity, spherical particles of

uniform size and distribution will be considered. In the large

particle limit, i.e., l-^r/x > 5 (r = particle radius):

K = I e ^

(7)

a 4 r

is the absorption coefficient, and

K^ = |p^ (8)

is the scattering coefficient with

e = particle emissivity,

p = particle reflectivity,

and f^ = volume concentration of particles. (The p and wavelength, A, subscripts have been dropped here for convenience.)

11
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In the small particle limit, i.e., l-nr/X < 0.6;

K

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with

m = n (1-Ki) (11)

The terms containing m can be evaluated if the nature of the

particle is known. If k = 0, only scattering can occur for

the particles. Since smoke can vary in particulate composition, it is difficult to predict accurately the attenuation

by smoke without measuring the refractive index (n) and the

absorption index (nic) for the smoke. For example, Foster found

that wood smoke generated from heated sawdust was found to be

tarry spherical droplets with m = 1.5 - 0.0015 i (A = O.Sym)

which indicates nearly pure scattering [8]. Yet, King found

that wood smoke from flaming combustion consists of both

liquid and solid particles, implying the possibility of

attenuation by both scattering and absorption [9] . Carbon

particles (soot) are mainly responsible for radiation from

flames and will also be present in smoke. For soot, n = 1.57

and ic = 0. 348 at A = 0.55 m, and n = 2.04 and k = 0.56 at

A = 2.5ym [5]. In general, smokes of obvious color suggest

that absorption becomes important [10] . In the fire experiments examined in this study, the smoke varies in color from

grey to black.

Equations (7) and (9) will be examined together with

the smoke data in table 1 in order to develop an empirical relationship for the absorption coefficient for smoke in these corridor experiments. The transmission of smoke recorded in table

1 is given by

at 0.52um where K (= K + K ) is the extinction coefficient.

e a s As a representative case, test 348 at 300-360 s is examined.

This yields = 0.074 cm""*". If the large particle limit is

assumed to be applicable, an average particle radius can be

determined from eq (7) . If the particles are characterized

3

as soot with a density of 2 g/cm and an emissivity of 1,

(12)

13
""6 2 TTir then f = 0.8x10 and r = 0.08y and correspondingly, —r

= 0.97. The large particle limit is not applicable because

2 7T r It requires that > 5. Hence, eq (9) would appear more

suitable. In this case, eq (9) becomes

K = 4.64 f /X(cm ^) (13)

cX V

where X is in cm.

It will be useful to compare the measured value of the

extinction coefficient: K = 0.074 cm~l at X = 0.52 m, with

^ -1

the value predicted by eq (13) at 0.52)jm: K = .07/cm . This

a

implies that scattering is negligible for the case of test 348

at 300-350 s. On the other hand, calculations based on the

wood flooring test (349) for time 370-420 s yield a value of

K = 0.014 cm""'' and a value of K = 0.009 cm""*". This implies

e a that scattering is significant for this case. Observations of

the fire development indicated the presence of grey smoke within

the corridor, which suggests a scattering medium. Yet, at a

later time (550-610 s) , observations show a black smoke layer,

suggesting the dominance of absorption. Similar calculations,

for this time, yield K = 0.012 cm and K = 0.013 cm which

e a

indicates negligible scattering.

The assumption of smoke composed of soot particulates

coupled with the small particle limit as expressed in eq (13)

appears to give a reasonable prediction of K in the visible.

This is implied from the fact that the above calculations indicate that K is approximately equal to or less than the measured

a

extinction coefficient, K^. The apparent lack of a scattering

medium also makes eq (13) a good estimate of K^. However, the

implication from the theory that the scattering component may

be small is subject to question, since the theory relies on the

physical nature of the particulate matter and the absence of

liquid aerosols in the smoke.

Nevertheless, it is still reasonable to assume that

^a >> Kg in the infrared region. Since K ig proportional to

4 ^ 1/X and K is proportional to 1/a , K becomes completely

insignificant in the infrared, the wavelength range of interest

in fires (see fig. 5) . Thus, eq (9) represents all the attenuation in the infrared region.

14
For X = 2.5y (the infrared) eq (9) becomes

K = 5.85 f /A (14) d V

which is only about 25% higher than eq (13) . The variation is

due to the change of n and k with wavelength. As a result of

the above discussion, it is reasonable to use

K = k p f /A (15)

p, A o p v'

(p is the particle density)

as an empirical relationship for the coefficient of absorption

due to particles. This expression is consistent with eqs (13)

and (14) above. The selection of the quantity K was based

on the data from the corridor fire experiments.

A more complete analysis for carbon smokes has been

reported by Tien, et al [11] . They develop approximate analytical expressions for K based on Mie scattering theory.

Unfortunately, the lack of measurements of particle size distribution and refractive index of smokes precludes the use of

such exact expressions for K . In fact, they point out that

a particle size can vary from 0.005|im for soot in flames to lOOym

for oil flames in industrial furnaces. Also, the agglomeration

of particles in smoke will increase particle size after combustion. For soot in flames, various investigators report

experimental correlations of the form

K = k,f /A^ (16)

a 1 v'

where a is dependent on A and can vary from 0.45 to 1.75ym [11],

but generally is nearly 1 over the range, 1 to 7ym [5] . It

should be noted that eq (15) , used in the program TOTAL, is

really eq (16) , with a = 1, and k^^ = k^Pp*

Combining eq (15) with eq (12) and using the smoke data

in table 1 (where p f is the mass concentration of the solids)

,

p V

k^ can be determined (for A 0.52ym). Since there is no information in regard to any possible wavelength-dependence of k , it was assumed to be constant. Values of k are tabulated

in table 1. As discussed above, scattering*^is suspected to be

significant in test 349 (370-420 s) and consequently its

value of k^ ig overestimated for use in eq (15). In fact,

this value of k^ is greater than the other values where absorption is believed to be the dominant mechanism of attenuation

in the visible.

15
Ideally, the procedure should be to determine which portion

of the attenuation in the visible was due to absorption in

order to calculate the value of k . This value of k would be

the most appropriate for the determination of k i in the

p , A infrared regions. In practice, however, it was not feasible

to isolate the scattering component, and, therefore, it was

assumed to be zero (based on the previous observations) . Therefore, the average value of all the k^ values was employed.

Equation (15) was used to modify the computer program

TOTAL [6] given in the Appendix. TOTAL calculates a and e by

use of eqs (1,2,3 and 6).

4. RESULTS AND DISCUSSIONS

Table 2 represents a compilation of data necessary to

make the calculations for a, e, and q^. Only times before

flameover are considered. A mean time is used and average

values are used for gas concentration and temperatures over

the sampling times given in table 1. Where possible, H2O

concentration was determined by assuming 90 percent of the

condensables to be water. Where the condensable data was not

available, the H2O concentration was estimated by calculation.

This was done by using an approximate pyrolysis model for

wood [12]

,

^"1.5%. 5 • ^«2^ " ^"2^ O.7CH2O -h O.SCHq 33

where x was taken as 0.13 which is representative of the

approximately 10% moisture content of the wood cribs burned

in these fire experiments. Combustion of the volatiles CH2O

result in

Combustion Products ^ WO2 + yCO + ZCO2 + O.83H2O

+ 3. 76 (z + w + y/2)N2

It can be shown that the volume concentrations ix^) of the

measured components are related to H2O by

The constant k^ of eq (15) was determined from the data

(table 1) with an average value of

k^ = 0.024ym(cm)"-'- (mg/^)"-*-

16
which is within 30 percent of all values. In table 2 one

value of particulate concentration was interpolated between

two measured values, while another value was estimated by

using eqs (12) and (15) and the value of k . For a particle

3 ° density of 2g/cm (soot) , this k^ corresponds to a k^ [eq

(16)] of 4.8, which compares favorably to that coefficient

given in eq (13) for carbon smoke.

With the program TOTAL, a and e were calculated in the

manner previously described. Using eqs (4) and (5), q^, the

net flux to the floor and q" ^/q" -r, the ratio of the ceiling

flux to the gas flux, were calculated. These values are presented in table 3.

Figure 6 shows the spectral emission of the particles

and gas during test 349 at t = 468 seconds. The continuous

emission due to particles alone is represented by the dotted

line labeled 0.25mg/il. The emissivity of this particulate

cloud alone (neglecting the molecular gas contribution) is

0.15. If the concentration is increased by a factor of 10

the emissivity rises to 0.74. For illustration, the spectral

emission from a 2.5 mg/liter particulate cloud is also shown

in figure 6. The significant gas bands consist of and

and are located at 2.7ym, 4.3ym and 6.3ym. The widths (cal

culated by TOTAL) are nearly directly proportional to the gas

volume fractions. With the addition of the gas absorption

to the particulate absorption (Ppf^ = 0.24mg/il), the total

emissivity for the mixture is 0.48. Thus, in this case of low

particulate concentration, the gas contributes more than the

particles to the total emissivity.

An examination of figure 7 shows the dependence of total

emissivity on particulate concentration for three different

cases. Curve 1 employs the gas and temperature data from test

348, t = 330 seconds and varies the particulate concentration.

The modified program TOTAL was used to generate curve 1. Three

basic regions are discerned: low, intermediate and high concentration. For the low concentrations, as seen before in test

349, the gas contributes primarily, while at high concentration

the particulate matter is the primary source of emissivity. In

the intermediate range, the total emissivity has significant

contributions from both.

Curves 2 and 3 employ the same gas and temperature data,

but are generated by two different procedures. Curve 2 is

derived from the results of Felske and Tien [13] for emissivity

as a function of soot volume concentration. A soot density of

3

2 g/cm was assumed to convert their volume concentration to

mass concentration. Curve 3 was generated by TOTAL.

17
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20
Figure 8 shows how the radiant heat fluxes in the corridor vary with particulate concentration based on a fixed gas

composition. As expected, the ratio is a strong function of

soot density. The gas radiation is predominant for pariticulate concentrations above 0.8 mg/liter. However, at the same

time, the net flux to the floor is a fairly weak function of

the concentration. This results since the hot combustion

products which heat the ceiling are slightly higher in temperature than the ceiling. Hence, if the gas is totally transparent, the floor receives ceiling emitted radiation oT ; yet,

^ 4 if the gas is opaque (e = 1), it radiates to the floor as oT . Moreover, the view factor between the floor and the ceiling

and upper walls is nearly identical to the view factor

between the floor and the hot combustion products. Unless one

could spectrally discriminate, a radiometer measurement of the

floor flux would not necessarily reveal the source of radiation

5. CONCLUSIONS

^ The role of combustion products on radiative transfer has

been examined by analysis of data from corridor fire experiments. Although the data were not necessarily complete,

reasonable assumptions were introduced in order to permit the

determination of emissivity and absorptivity of the hot combustion products. Measurements (fig. 3) have shown that under

some circumstances radiation due to particulates in the

combustion products can be significant. Analysis suggested

that attenuation of radiation by the particulates in these

experiments was due to absorption, with scattering as a

negligible factor. Based on this and on the theory of

radiative attenuation by particles, an empirical model was

introduced to describe the attenuation by the particulates.

The results of these calculations displayed the relative

contribution of both molecular gas radiation and particulate

emission in these corridor fire experiments. The assumptions

used in these calculations have been to simplify the analysis

and were necessary because more detailed data were not

available. The effect of non-uniform temperature and concentrations on radiative heat transfer in the combustion

products can have a substantial influence on the results.

Moreover, the effect of scattering has not really been dealt

with to any conclusive end in this paper. In the least, this

paper demonstrates that one can not ignore the radiative transfer effects of the combustion products in compartment fires.

6. ACKNOWLEDGEMENTS

The data from the corridor experiments 348 and 349 on

light transmission and particulate and condensable concentrations were provided by Tom Lee. The authors are grateful for

his cooperation. In addition, the authors are grateful to

21
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D. K. Edwards and A. Balakrishnan for sending us a copy of

their program, TOTAL.

7. REFERENCES

[1] Fung, F. C. W. , Suchomel, M. R. and Oglesby, P. L.

,

Fire J., Vol. 67, 41 (1973).

[2] Quintiere, J. and Huggett, C. , An Evaluation of Flame

Spread Test Methods for Flooring Materials, Fire Safety

Research, Proceedings of a Symposium held at the

National Bureau of Standards, August 22, 1973, Nat. Bur.

Stand. Special Pub., SP-411 (Nov. 1974).

[3] Birky, M. M. , Am. Chem. Soc, Polymer Preprints, Vol.

14, 1,011 (1973) .

[4] Hottel, H. C. and Sarofim, A. F., Radiative Heat Transfer,

McGraw-Hill, N.Y. (1967).

[5] Siegel, R. and Howell, J. R. , Thermal Radiation Heat

Transfer, Vol. 16, 25 (1973).

[6] Edwards, D. K. and Balakrishnan, A., Int. J. Heat Mass

Transfer, Vol. 16, 25 (1973).

[7] Kerker, M. , The Scattering of Light and Other Electromagnetic Radiation, Academic Press, N.Y. (1969)

.

[8] Foster, W. W. , British J. Appl. Phys . , Vol. 10, 416

(1959)

.

[9] King, T. , Fundamentals of Smoke and Carbon Monoxide

Generation From Burning Selected Plastics and Red Oak,

Fire Safety Research, Proceedings of a Symposium held

at the National Bureau of Standards, August 22, 1973,

Nat. Bur. Stand. Special Pub., SP-411 (Nov. 1974).

[10] Stern, A. C. , ed.. Air Pollution, Academic Press, N.Y.

362 (1968).

[11] Tien, C. L. , Doormink, D. G. and Rafferty, D. A., Comb.

Sci. Tech., Vol. 6, 55 (1972).

[12] Harmathy, T. Z., Fire Tech., Vol. 10, 196 (1972).

[13] Felske, J. D. and Tien, C. L. , Comb. Sci. Tech., Vol. 7,

25 (1973)

.

23
Appendix

Emissivity and absorptivity of a multicomponent gas

mixture can be calculated by using the wide band absorption

model of Edwards and Balakrishnan [6] . They formulate a

computer program TOTAL to compute the above values. In order

to do the calculation for a gas-soot mixture, an additional

term for the soot transmissivity is necessary. From TOTAL,

the spectral gas transmissivity is given by

M N

exp(-Kg^,L) = .n^ .n^ ^l-%,i,j^ ^^-^^

where a . .is the absorptivity of the ith gas specie and jth

wavelength band. Substitution of eq (A-1) into eq (1) yields

the spectral mixture absorptivity,

M N

% = i-exp(-Kp^,L)..n^ .n^ (l-"x,i,j)-

K , is given by eq (15) and the a . . are determined by the

p , A A , 1 , 3 procedure presented in reference 6 and executed in TOTAL. The

total absorptivity is calculated by a spectral integration of

-1

eq (A-"2) over the wave-number range of 0 to 8,500 cm using

the trapezoidal rule.

/oo

a. (T,x. /L,p)e, , (T )dX (A-3)

" - aT^ o

^ b,A s

e, = spectral blackbody emissive power

Q = Stefan-Boltzmann constant

= mole fraction of ith gas species

T = gas temperature

Tg = surface temperature (ceiling in this case)

p = total pressure of mixture

Emissivity is calculated by replacing T with T

/oo

e^(T,Xi,L,p)ej^ ^(T)dX (A-4)

a-r o

24
Nomenclature

a constant

D thickness of combustion product layer

ej^ ^ spectral blackbody emissive power

volume concentration of particles

k ,k, constants

o 1

K absorption coefficient (particle)

3, K extinction coefficient

e K , gas spectral absorption coefficient

g , A K , particulate spectral absorption coefficient

p , A

Kg scattering coefficient (particle)

2. photometer path length

L mean beam length

m complex index of refraction, n(l-Ki)

n real part of index of refraction

p total pressure of gas mixture

q" ^ flux from ceiling to floor

c , r net flux to the floor '

q" _ flux from gas to floor g,f

r particle radius

T temperature of the gas

temperature of the ceiling

temperature of the floor

T temperature of the source

25
gas volume concentration

a total absorptivity

spectral absorptivity

a spectral absorptivity of the particulate matter

A , p

^ spectral absorptivity of the ith gas specie

e total emissivity, or particle emissivity

ic absorption index/n

X wavelength

p particle reflectivity

Pp particle density

a Stefan-Boltzmann constant

T transmissivity , or transmission

Subscripts

b blackbody

c ceiling

f floor

g gas mixture

i gas specie

j gas band

A spectral

USC0MM-NH8-0C

26
NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLIC ATION OR REPORT NO.

NBSIR 74-596

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLF AND SUBTITLIRadiative Heat Transfer From Products of

Combustion in Building Corridor Fires

5. Publication Date February 1975

6. Performing Organization Code

7. AUTHOR(S) . , ^ , ^ • j_ • is.evin orornxjery ana. ijaineo v^uxritxtix t; 8. Performing Organ. Report No. NBSIR 74-596

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 4915676

n. 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

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.)

The contribution of radiative lioat transfer from hot combustion

products to corridor floors is examined. Data from full-scale corridor

fire experiments is used to calculate emissivity and absorptivity of

the combustion products. An empirical model based on attenuation by

absorptipn is used to specify the absorption coefficient due to particulates in the products. In these experiments it is shown that

radiation from the combustion products is just as significant as

radiation from convectively heated walls and ceiling of the corridor.

Calculations show that the ratio of radiant heat transfer to the floor

due to ceiling emission to that by combustion product emission ranges

from about 0.2 to 0.7. Also, molecular gas radiation and particulate

radiation can both be significant for the combustion products. Calculations show that the emissivity of the gaseous combustion products

alone would be about 0.3, but the inclusion of soot particles yields

an emissivity for the total combustion product mixture of as high as

0.73, based on the experimental data considered.

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

)

Combustion products; full-scale fire; radiative heat transfer.

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