NBSIR 75-794

HEAT TRANSFER IN FURNACES FOR CIB

COOPERATIVE PROGRAM AND HEAT

BALANCE ANALYSIS OF WALL

FURNACE

J. B. Fang and J. T. Scott

Center for Fire Research

Institute for Applied Technology

National Bureau of Standards

Washington, D. C. 20234

November 1975

Final Report

U.S. DEPARTMENT OF COMMERCE, Rogers C.B. Morton, Secretary

James A. Baker, III, Under Secretary

Dr. Betsy Ancker-Johnson. Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Acting Director

CONTENTS

Page

LIST OF TABLES iv

LIST OF FIGURES v

LIST OF NOMENCLATURE . . . vii

1. INTRODUCTION 1

2. TEST EQUIPMENT 2

3. TEST METHOD 3

3.1. Comparison of Furnaces 3

3.2. Heat Balance in Furnace 4

4. TEST RESULTS AND DISCUSSIONS 4

4.1. Comparison of Furnaces 4

4.2. Heat Balance in Furnace 5

5. REFERENCES 6

APPENDIX A. HEAT BALANCE IN FURNACE 36

APPENDIX B. A LIST OF ASSUMED PROPERTIES FOR TEST FURNACE ... 39

iii
LIST OF TABLES

Page

Table 1. General Test Information 8

Table 2. Average Heat Contribution for Test No. 1 9

Table 3. Measured Data for Test 1 10

Table 4. Measured Data for Test 2 11

Table 5. Measured Data for Test 3 12

iv
LIST OF FIGURES

Page

Figure 1. Location of Radiometers and TNO Heat Flux Meters in

Test Wall 13

Figure 2. TNO Heat Flux Meter With Thermocouple Locations .... 14

Figure 3. Test Wall Thermocouple Locations 15

Figure 4. Details of Wall-Testing Furnace 16

Figure 5. Upper TNO Heat Flux Meter Readings 17

Figure 6. Lower TNO Heat Flux Meter Readings in Test No. 1. . . . 18

Figure 7. Upper TNO Heat Flux Meter Readings in Test No. 2. . . . 19

Figure 8. Lower TNO Heat Flux Meter Readings in Test No. 2. . . . 20

Figure 9. Upper TNO Heat Flux Meter Readings in Test No. 3. . . . 21

Figure 10. Lower TNO Heat Flux Meter Readings in Test No. 3. . . , 22

Figure 11. Furnace Temperatures in Test No. 1 23

Figure 12. Furnace Temperatures in Test No. 2 24

Figure 13. Furnace Temperatures in Test No. 3 25

Figure 14. Stack and Wall Temperatures in Test No. 1 26

Figure 15. Stack and Wall Temperatures in Test No. 2 27

Figure 16. Stack and Wall Temperatures in Test No. 3 28

Figure 17. Radiometer Readings in Test No. 1 29

Figure 18. Radiometer Readings in Test No. 2 30

Figure 19. Radiometer Readings in Test No. 3 31

Figure 20. Inlet Air and Exhaust Gas Velocities in Test No. 1. . . 32

Figure 21. Calculated Heat Input and Output Curves for NBS Wall

Furnace Using a Lightweight Masonry Block Test Wall

(Test No. 1) 33

v
LIST OF FIGURES, (cont'd)

Page

Figure 22. Comparison of Calculated Radiant Heat Flux Incident

at Furnace Walls and Radiant Flux Measurement (R-2) on Test Wall for Test No. 1 34

Figure 23. Schematic Diagram of Furnace and Heat Transfer ... 35

vi
LIST OF NOMENCLATURE

A. Interior surface area of furnace including test specimen

a A„ Cross-sectional area of the exhaust stack

E

A„ Interior surface area of the test specimen

A Surface area of the furnace walls w

C^ Heat capacity at constant pressure for air

C^ Heat capacity at constant pressure for the i-th species

Cy Heat capacity at constant volume for furnace gas mixture

E Total energy contained in furnace gases

h Convective heat transfer coefficient

H^ Enthalpy of the inlet air at the datum temperature T

q

H,, Radiative heat flux incident at the gray surface element

H^, Enthalpy of fuel gas at the datum temperature T

q

H. Enthalpy of the i-th species at temperature T

H? Enthalpy of the i-th species at the datum temperature

M^ Molecular weight of the i-th species

Q Heat loss to both test specimen and furnace walls

D

Q Heat loss to both test specimen and furnace walls by convection

Qp Heat supplied by fuel combustion

Q Heat loss to the bounding surfaces

Xj

Q Heat loss to both test specimen and furnace walls by radiation

Qg Heat loss to test specimen

QTT Heat loss to furnace walls

w

T Absolute temperature

T^, Temperature of exposed walls including test specimen

T- Temperature of exhaust gases

vii
LIST OF NOMENCLATURE, (cont'd)

T-j. Temperature of inlet air

T^ Temperature of furnace gases

T

q

Datum temperature

Tq Surface temperature of the test specimen

t Time variable

U„ Velocity of exhaust gases

L

V Volume of furnace

w, Mass flow rate of the inlet air

A

w Mass flow rate of fuel gas

r

w. Mass flow rate of the i-th species

1

X. Mole fraction of the i-th species

1

cig Absorptivity of gaseous mixture at T^ for radiation emitted from

interior walls at T

D dg Total absorptivity of the furnace gases to be evaluated at the

surface temperature of the test specimen

Total absorptivity of the furnace gases to be evaluated at the

surface temperature of the furnace walls

e Effective surface emissivity of furnace walls including test

specimen

Surface emissivity of furnace walls including test specimen

Emissivity of gaseous mixture

Eg Surface emissivity of the test specimen

Density of gaseous mixture

o Stefan-Boltzmann constant

viii
HEAT TRANSFER IN FURNACES FOR CIB COOPERATIVE PROGRAM

AND HEAT BALANCE ANALYSIS OF WALL FURNACE

J. B . Fang and J. T. Scott

Tests were conducted in the NBS wall panel furnace as part

of a CIB international cooperative program to measure and com- pare heat transfer in fire endurance furnaces. Additionally,

a heat balance analysis showed that a cellular concrete block

wall specimen absorbed more heat by convection than by radiation. The rate of radiant heat transfer was found to decrease

slowly, while the furnace exhaust heat loss increased during

the test from 42 to 58 percent of the heat output. The calculated radiant heat fluxes incident at furnace walls was found

to be somewhat lower than the experimental values measured at

the test wall.

Key words: Fire resistance ratings; fire test furnace; heat

balance; heat transfer; temperature-time curve.

1. INTRODUCTION

These preliminary tests were performed as part of a cooperative

effort to correlate the fire resistance of reference specimens obtained

by various testing laboratories. This project was initiated following

the ninth meeting of CIB (Conseil International du Batiment) Commission

W. 14 in Paris in May 1970 where it was decided to continue the work on

the comparison of the performances of fire test furnaces.

Previous efforts to compare furnaces had shown wide variability

among laboratories in fire resistance determinations for ratings up to 90

minutes. [1]^- Recently, Castle [2] made radiant and total heat flux

measurements in several test furnaces operated in accordance with ASTM E119 method, and reported a wide variation in the radiation and convection

levels to the specimen determined in these furnace environments. The

primary reasons for these differences were that fuel properties and its

input rate, amount of air introduced, furnace geometry, thermal properties of furnace walls and test specimen, the operating pressure, and

the positions of burners and the exhaust stack, were varied among the

furnaces, even though the same prescribed temperature- time curve was followed

.

A method for measuring the heat transfer rate and comparing the performance of various furnaces was described by van Keulen in his report on "Comparison of Heat Transfer in Furnaces ."[ 3] The report provided testing

Numbers in brackets refer to the literature references listed at the

end of this paper.

1
and measurement details for determining heat transfer rate along with

the theory for correlating test results between furnaces. Three tests were conducted at NBS to measure the rates of heat transfer by radiation and convection using two TNO heat flux meters [3] set in

a cellular concrete block wall. In these tests, measurements were

restricted to heat flux into the elements separating the heated furnace

from the outside. The application of an overall heat balance concept to a wall panel furnace was first introduced by Harmathy. [4] He studied the effect of thermal properties of a test specimen on the fuel consumption in a temperature-programmed fire test furnace. Therefore, additional measurements were taken to provide information for a heat balance analysis of the wall panel furnace. The intent of the thermal analysis was to provide relative indications of the level and mode of heat transfer processes taking place in the furnace, and to obtain a better understanding of the various pheno- mena involved in the determining of the fire endurance rating of a panel

assembly.

2. TEST EQUIPMENT A 4.9 x 3.0 m (16 x 10 ft) high test wall was constructed of precast cellular concrete blocks. The blocks were 22.9 x 45.7 x 15.2 cm (9 x 18 x 6 in) in size, had a density of 0.50 g/cm 3 (31 lbs/ft 3

) and a thermal conductivity of 0.117 W/m-°K (0.0675 Btu/hr-f t-°F) . The test wall had

two TNO heat flux meters and two radiometers built into it as shown in figure 1. The radiometers were commercial water-cooled 150 degree

viewing angle instruments of the Gardon circular foil type with a saphire

window to measure the radiant heat flux component. The TNO heat flux meters were constructed of refractory sillimanite. Two identical slabs were joined to form a 19.5 x 30 x 3 cm thick (7.7 x 11.8 x 1.2 in) heat flux meter. The exposed surface of the meter was enameled and one-half of it treated with a gold paste in order to provide

a difference in emissivity between the two halves. Three thermocouples were imbedded in each half of the meter while additional thermocouples

monitored the temperature 5 cm in front of the exposed surface and 5 cm behind the unexposed side of the heat flux meter. All thermocouples were

of 0.5 mm diameter chromel-alumel wires. A diagram of thermocouple locations is shown in figure 2. The furnace temperature was measured by 12 metallic sheathed mineral

insulated fast response thermocouples symmetrically arranged within the furnace and 10 cm from the test specimen to provide an approximation of

its average temperature. These thermocouples comprised 1 mm diameter

chromel and alumel wires insulated with magnesium oxide from a closed

end 6.4 mm (1/4 in) OD stainless steel (type 310) sheathed tube. For comparison purposes the furnace temperature was also monitored using 12

2
ASTM thermocouples mounted within heavy iron pipes and symmetrically

distributed 10 cm from the test wall. The time constants of the sheathed

and the ASTM thermocouples were found to be approximately 1.2 and 6.2 minutes respectively, using a gas fired furnace maintained at a constant temperature of 900 °C. Specimen surface temperatures were measured using eight thermocouples

arranged as shown in figure 3. Other temperatures monitored during the

test were the furnace wall, the exhaust gas and the room temperature.

Inlet air and exhaust gas velocities were measured by means of pitot

tubes in conjunction with a differential pressure transducer. Furnace gas concentrations of O2, CO2 and CO were measured during

the tests. Exhaust gas samples were taken using a stainless steel tube positioned in the exhaust stack. The gas was drawn through a trap filled with glass wool and was cooled with dry ice to remove smoke particles and water vapor. The gas was divided into three streams which passed through

individual instruments of the following types: non-dispersive infrared

analyzers for CO and CO2, and a magnetic susceptibility analyzer for O2. Details of the wall test furnace including principal dimensions, are given in figure 4. The furnace is of the natural updraft type. The fuel was natural gas containing approximately 95% methane and having a specific

gravity of 0.595 and a higher heating value of 38.5 J/cm3 (1,033 Btu/ft 3 ). The gas composition and its thermochemical data are tabulated in table 1 along with some information on furnace walls and test specimen. This natural gas was supplied through 92 air-aspirating burners mounted in the wall opposite the specimen. The gas flow rate was measured every

5 minutes during Test No. 1.

3. TEST METHOD

3.1. Comparison of Furnaces

To promote uniform test conditions the test wall was dried during

Test No. 1. The ISO R-834 standard time-temperature curve was followed

for one hour. The furnace was left closed until it cooled down in order

to avoid water uptake in the test wall. Two tests were then conducted in the wall panel furnace with Test

No. 2 being of 60-minute duration and Test No. 3 being a 90-minute test. A constant pressure of 1.5 mm of water column was maintained at a height

of 2.3 m above the bottom of the test wall during both tests. Periodic

recordings were made of various instruments on a data logger and later processed and plotted by computer.

3
3.2. Heat Balance in Furnace

A description of the method and equations used for the heat balance

calculations are given in appendix A. Determination of the terms in the

heat balance equation were made by experimental measurements and by calculations using developed heat transfer formulae. The results of the

fully instrumented first test were used for the heat balance analysis.

4. TEST RESULTS AND DISCUSSIONS

4.1. Comparison of Furnaces

The variations of temperature readings of TNO heat flux meters with

time for each test are shown in figures 5 to 10. It can be seen that the

temperature of furnace gases near the meters was considerably higher than

the exposed surface temperature throughout the test. Figures 11 to 13

illustrate time sequence of average furnace gas temperature measured

during the tests along with the ISO R-834 standard curve plotted for

comparison. An inspection of these figures show a significant difference

in the temperatures measured using sheathed versus ASTM thermocouples.

The results indicate over a 100 °C difference between the temperatures

measured after 20 minutes during Test No. 1 with similar results obtained

in the other tests. This temperature difference was attributed to high

thermal capacitance of the iron protection tubes utilized in ASTM thermocouples and significant radiation loss from the tubes to the cooler furnace walls.

The average surface temperatures of furnace walls and the test

specimen, and the flue gas in the exhaust stack for the three tests are shown in figures 14 to 16 as a function of time. It is important to note

that the surface temperature of the test specimen was approximately equal

to that of furnace walls. Figures 17 to 19 show plots of radiation flux

densities determined at two locations of the test specimen versus time.

As shown in the figures, there was little variation in the measured

radiant fluxes between tests 1 and 2. The reason for the higher irradi- ance observed at the lower portion (radiometer No. 2) of the test wall

than that at its upper part (radiometer No. 1) as shown in figure 19 was

not known.

Time variations of the velocities of air entering into the furnace

through the inlet ports, and combustion gases flowing inside the exhaust

stack of Test No. 1 are given in figure 20. The results of gas analysis

demonstrated that a process of complete combustion of fuel gas occurred

in the test furnace since no CO was detected in flue gas. The concentrations of CO2 and O2 in the exhaust stream were found to be relatively

constant after approximately 10 minutes after the start of the test. The

flue gas composition averaged over the last 50 minutes of the test was

8.7% C02 , 8.4% 02 and 82.9% N2 (dry basis).

The test results tabulated in tables 3 through 5 were forwarded to

van Keulen for data analysis with the other participating laboratories.

Summary data of the test series were given in his report along with

4
construction details of TNO heat flux meter, and the procedure for furnace

performance evaluation. [5] He compared the performance of each test

furnace based on the amount of heat accumulated in the standardized wall

test material versus time curve, and concluded that a correction factor

to reduce differences between furnaces was not presented due to wide

scattering of test results, and insufficient data for justification. The

determination of separate contributions of radiation and convection

components to the heating of the test specimen was unsuccessful because

of evaporation of the gold coating on TNO heat flux meters.

4.2. Heat Balance in Furnace

Using the equations developed in appendix A, determinations were

made of the heat input and output terms. Figure 21 provides a graph of

each term in the heat balance equation. Inspection of the curves showed

a decreasing rate of heat supply from the fuel while there was a slight

increase in heat loss through the exhaust stack. Convective and radiative

heat losses decreased during the test. The sensible energy supplied by

the inlet air and the heat stored in the furnace gases were very small

and were neglected.

The determined convective heat transfer coefficient, h, ranged from

89 to 180 W/m2 -°C (16 to 32 Btu/hr-f

t

2 -°F) . These h values seem to be

comparable with values determined by other experiments. [6] A check of

the convective and radiant heat transfer throughout the test with the

calculated h values, assumed thermal properties of furnace wall material

as given in appendix B, and measured furnace gas temperatures using a method described in reference 7 showed that the deviation between the

estimated average surface temperature of the furnace walls and the actual

measured value varied from 0.2 to 11.3% with an average of 3.7%.

Since there were some difficulties in calibration of the oxygen

analyzer, the composition and mass flow rate of combustion products were

calculated based on the measured gas composition and mass rate of the

fuel gas, and the concentration of C0 2 in the exhaust stream. It was

found that the flue gas consisted of 7.3% C02 , 14.9% H2 0, 5.1% 0 2 and

72.7% N2 , and the fuel burned with approximately 36% in excess of the air

required for complete combustion. The total emissivity and absorptivity

for furnace gases were derived from H2 0 and C0 2 emissivity charts developed by Hottel and his coworkers [8] with a correction to account for

spectral overlap of emission bands. The gas emissivity was found to

range from 0.30 to 0.22, decreasing with an increase in gas temperature,

and the absorptivity varied between 0.33 and 0.22.

Listed in table 2 are the average heat transfer contributions for

each of the terms in the heat balance equation along with their percentage

contribution to heat input or output. For this furnace, the largest heat

loss was due to the flow of hot combustion products through the exhaust

stack, and this increased from 42% at 10 minutes to 58% at 60 minutes.

Convective heat loss to the furnace walls was found to decrease with time

from 42 to 34% of the total heat input, and the rate of radiant heat

5
transferred into furnace walls was also seen to decrease gradually with

increasing wall surface temperature during the test.

Figure 22 shows a comparison plot of time variation of calculated

radiant heat flux incident at the furnace walls and the measured radiant

flux obtained at the test wall for Test No. 1. The calculated values

were computed on the basis of the rate of radiant heat loss shown in

figure 21, and the average interior wall temperature using a surface

emissivity of 0.8 for all furnace walls. It can be seen from the figure

that the calculated values were approximately 15% less than those determined experimentally. This discrepancy in radiative heat transfer to the

surface element may be due to non-uniformity of the temperature and

composition of furnace gases. Also there might have been introduced some errors with higher readings on the radiometer as a result of reradiation

from the heated sapphire window attachment to the foil sensing element.

The fire resistance rating of a structural element depends upon its

physical and thermal properties and the heat flux incident at its bounding

surfaces from the surrounding furnace walls and the furnace gas. The

magnitude of the incident heat flux is determined by the furnace geometry,

the surface emissivity and thermal properties of the furnace walls, the

radiative properties, the gas flow and turbulence characteristics of the

furnace gas as well as its temperature. The incident heat flux to the

test wall appears to be a more appropriate parameter to be measured during

the test than the gas temperature for characterizing and monitoring the

furnace fire intensity.

The results of this study are limited to the single test which

involved one material and one set of test conditions. Future testing

with additional instrumentation by including water-cooled total heat

fluxmeters and gas purged radiometers will make possible a verification

of the results obtained. Extension to other materials of different

thermal properties will provide data for better comprehension of the fire

endurance testing since thermal properties determine the temperature

level of the exposed surface, and the amount of heat absorbed by the test

wall.

5 . REFERENCES

[1] Correlation Tests on Furnaces for Separating Elements, Bundesantalt

fer Materialprufung (BAM) Laboratory for Fire Protection, West

Germany, (Jan. 1970).

[2] Castle, G. K. , The Nature of Various Fire Environments and the

Application of Modern Material Approaches for Fire Protection of

Exterior Structural Steel in Them, AVCO Systems Division, A paper

presented at A.I.Ch.E. Loss Prevention Symposium, Nov. 14, 1973,

Philadelphia.

6
[3] van Keulen, J., Comparison of Heat Transfer in Furnaces, paper for

CIB Commission W.14, Group 1, Fire Endurance (Nov. 1971).

[4] Harmathy, T. Z., Design of Fire Test Furnaces, Fire Technology,

Vol. 15, No. 2, 140-150 (May 1969).

[5] van Keulen, J., Comparison of Heat Transfer in Several Wall Furnaces,

Report of CIB Commission W.14, No. BVI-74-17 (Feb. 1974).

[6] Seigel, L. G. , Effect of Furnace Design on Fire Endurance Test

Results, Fire Test Performance, ASTM STP 464, 57-67 (1970).

[7] Hill, P. R. , A Method of Computing the Transient Temperature of

Thick Walls from Arbitrary Variation of Adiabatic-Wall Temperature

and Heat-Transfer Coefficient, Nat. Advisory Committee for Aeronautics,

(U.S.) Tech Note 4105 (Oct. 1957).

[8] Hottel, H. C. and Sarofim, A. F., Radiative Transfer (McGraw-Hill,

New York, 1967)

.

7
Table 1. General Test Information

INd UUL al uao

Gas Composition: 95.1% CH^, 3.0% C 2 H 6

, 0. 76% C 3 H 8 0.29% C 4 H 10 , 0.14% C 5 H 12 , 0.70% C0 2

0 (117 No

Specific Gravity: 0.595

Heating Value

(corrected to 14.2

°C (60 °F), 762 mm

(30 in) Hg dry): 38.5 J/cm3 (1,033 Btu/ft 3

) (Gross)

j't. / j / cm \?jx i5uu/rt ^ viNet )

Furnace Walls: Fire Brick

IcoL Wall

.

r^l V> C J 1LVJ.J_C3.-L ill P\jU11_J. nn p C f~LC RDXUL.t.0 1 r.p Density = 0.50 g/cm3 (31

Thermal Conductivity = 0

VU.UD/J DLU/ 1 L HI J7 ^

lbs/ft 3

) .117 W/m-°K

Gas Flow Data: 226 m

3 (8,000 ft 3

) for 1 hour test

Note: For additional information see figures 1-4.

8
Table 2. Average Heat Contribution for Test No. 1

Term

Rate of Heat Flow Percent

Kw (10 s I»tu/hr) Avera^;e Range

Energy- In 2,180 7. 45 1UU

Energy Out 1,155 o

j

.

y j 53 42-58

243 0. 83 11 7-16

782 2. 67 36 34-42

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Figure 4.

LONGITUDINAL SECTION HALF ELEVATION

'ii. ,? f e J„ i„ •? 10 SCALE

Details of Wall-Testing Furnace.

A, Furnace Chamber; B, Burners; C, Thermocouple Protection

Tubes; D, Pit for Debris; E, Observation Windows; F, Air

Inlets; G, Flue Outlets and Dampers; H, Firebrick Furnace

Lining; I, Reinforced Concrete Furnace-Shell; K, Gas Cocks;

L, Control Valve; M, Ladders and Platforms to Observation

Windows; N, Movable Fireproofed Test Frame; 0, Loading Beam;

P, Hydraulic Jacks; Q, Test Wall; R, Asbestos Felted Pads

Covering Thermocouples on Unexposed Surface of Test Wall.

16
TN8 HEAT FLUX METER (TOP J

To Eo 5

TIME (HIN)

Figure 5. Upper TNO Heat Flux Meter Readings

17

TiriE (niN)

igure 7. Upper TNO Heat Flux Meter Readings

19

o To £o So 40 io 6~o ^

So So ih

TIflE (fllN)

Figure 9. Upper TNO Heat Flux Meter Readings in Test No. 3.

21
Figure 10. Lower TNO Heat Flux Meter Readings in Test No. 3.

22
o ~~to Fo~ To 40 So ko &o So ih

ti he (hin)

Figure 11. Furnace Temperatures in Test No. 1.
100CI

0 10 20 -30 40 So 60 I70 80 5o K30

ti he iniN)

Figure 12. Furnace Temperatures in Test No. 2.

24
0 "To !>0 S 4Q Eo 60 ^70 ElO So iko

TIME tHIN)

Figure 13. Furnace Temperatures in Test No. 3. 25
iOOO

© EXPOSED WRLL SURFACE CflVGJ A EXHRUST STRCK

+ FURNRCE WRLL

(

! o "To S 40 So ko ^o So [io i~b TI ME iniN)

Figure 14. Stack and Wall Temperatures in Test No. 1.
T I HE IHINJ

Figure 15. Stack and Wall Temperatures in Test No. 2.

27
1 1 100 _

[I

o To Eg- ~~40 Eo Eo ^o &o So iho

TIME ( MIN

)

Figure 16. Stack and Wall Temperatures in Test No. 3.

28
Figure 17. Radiometer Readings in Test No. 1.

29
15

© RRDIOnCTER NO. 1 A RROI OflETER HQ. 2

40

TIME (tllN)

Figure 18. Radiometer Readings in Test No. 2,

30
Figure 19. Radiometer Readings in Test No. 3.

31
3500

3400

3300

J200

3100

3000

2900

2600

2700

2600

2500

2400

2300

2200

2100

2000

1900_

1800_

1 700 « 1600_

1500_

1400

1300_

I200_

:. : : 1000_

900.

800_

700_

£ 00 _ 500_

400_

300-

200

_

100_

0

EXHAUST

INLET

To £o 5( 40

HUE

"To-

(hin)

To 7~o 8~o S

Figure 20. Inlet Air and Exhaust Gas Velocities in Test No.

32
TIME (min ]

Figure 21. Calculated Heat Input and Output Curves for NBS

Wall Furnace Using a Lightweight Masonry Block Test Wall

(Test No. 1).

33
14

0 10 20 30 40 50 60

TIME (min]

Figure 22. Comparison of Calculated Radiant

Heat Flux Incident at Furnace Walls and

Radiant Flux Measurement (R-2) on Test Wall

for Test No. 1.

34
BURNERS

1

Vm1 1 FURNACE

WA TEST WALL

QA

-'HEAT SUPPLIED BY INLET AIR

Q

c -.HEATLOSS BY CONVECTION

Q^HEAT VIA EXHAUST GASES

Q

F

: HEAT SUPPLIED BY FUEL COMBUSTION

Q6

: HEAT STORED IN FURNACE GASES

(VHEATLOSS BY RADIATION

Figure 23. Schematic Diagram of Furnace and Heat Transfer.

35
APPENDIX A. HEAT BALANCE IN FURNACE

The law of conservation of energy applied to the test furnace, which

is considered as a control volume, expresses the fact that the rate of

increase of total energy contained in the furnace gases will equal the ' sum of (a) the net rate of energy transport into the system associated

with the mass flow and (b) the rate of heat generation by fuel combustion,

minus the rate of energy removal across the bounding surfaces. Accordingly a macroscopic energy balance equation for the test furnace illustrated in figure 23 can be written in the form:

dE

dt t-4 x x xn ^ x x out F

XL

In order to make the analysis mathematically feasible, the following

assumptions were made:

1. There is no temperature variation in the furnace gases.

2. A stoichiometric complete combustion process occurs in the

furnace.

3. The heat loss by radiation through openings can be neglected.

4. The furnace walls and test specimen are gray-bodies, and the

entire furnace walls have substantially uniform surface temperatures and can be assigned a single mean temperature.

The total energy accumulated within the furnace gases comprises

internal, kinetic and potential energy, the last two of which may be

neglected in comparison with the remaining one. The rate of energy

stored in the furnace gases and the sensible heat supplied by inlet air

and fuel were calculated from the following expressions:

dE d < T

M-V

ST = %cv^ (2 > /T fl 1 C

F

dT) + w

A

( H; + /

1

CAdT) (3)

T T

o o

The velocity and temperature of the inlet air and the volumetric

flow rate of fuel into the furnace were measured throughout the test.

The contributions of these two terms, which were evaluated in reference

to standard conditions at a datum temperature of 15 °C (60 °F) , were

found to amount to less than one percent of the total heat transfer

supplied. Since these quantities were of negligible impact and were on opposite sides of the heat balance equation, equation 1 reduced to:

36
Qt, X = y^w.H.) + QT (4) F Z-T 1 i'out XL

v '

The rate of heat provided by the fuel combustion was equal to the

rate of fuel consumed multiplied by its net heating value. The composition of the exhaust gases can be determined either by direct experimental

measurement or by calculation from air overall material balance for each

chemical species present, based on the measured fuel gas composition and

concentration of one of the component gases in the exhaust stream along

with the assumption of complete combustion for the fuel gas reacted with

air. The heat loss due to the venting of the exhaust gases was calculated

from:

V(w.H.) _ = yV(H? + f

E

C.dT) (5) Z-i i x out Z_-i i l l

o

/ xi

M

i \ where w

i = ( PmueV ) .

Heat loss to the bounding surfaces consisting of the test specimen

and the walls of the test furnace occurred mainly by convection and radiation from the hot furnace gases. The radiation incident at the test

specimen consisted of direct emission from the furnace gases, and radiative contribution from surrounding furnace walls through the gases. The

net rates of radiation and convection losses to the test specimen can be

expressed by

0 = OA e' (e I - a T ^ + oa e £ Kl- a )T lf -(l-a)T lf W l S S S

v M M S S

' S S W

LK W

; W

v S; S

J

+ hAo (T - T_) (6)

s M S

where a^ and <* are the total absorptivities of the furnace gases, to be

evaluated at the furnace wall and test specimen temperatures, respectively,

[8] Ag, e* and Tg are the surface area, effective surface emissivity,

surface emissivity, and absolute surface temperature of the test specimen,

respectively.

Similarly, the net rates of radiative and convective exchange for

the furnace walls with furnace gases and the test specimen are % ' °v; ca* - Vw"> + aA

s

E sEw

i (1 -

a

s> h" - (1 " aw>

Tw"l + "» (TM

" V (7 >

37
where A^ and are the surface area and surface temperature of the fur- nace walls, respectively. £^ and £^ denote the surface emissivlty and

effective surface emissivity of the furnace walls, respectively.

A review of figure 14 showed that there was little variation between

the surface temperatures of furnace walls and test specimen. Incorporating this information, the test specimen and furnace walls were treated

as a single zone. Defining to be the sum of Qg and Q^, and combining

equations 6 and 7 yields

A simplified equation describing the overall heat balance for the

test furnace can be obtained by introducing the above relationship into

equation 4. Thus,

% • S <w

i

H

i>out

+ «R + V (9)

Both the total emissivity and absorptivity for the furnace gases were

determined in accordance with the procedures recommended in the text [8]

taking into account the concentrations of CC^ and 1^0 vapor, gas temperature, furnace geometry and size, and surface temperatures of furnace walls.

A value of (1 + £ T) )/2 was used for the effective surface emissivity, £,

of the entire boundary walls. [8] The geometric beam length used in gas

radiation calculation was equivalent to 4 times of the furnace volume

divided by its internal surface area.

All parameters in equations 8 and 9 were either known or measured

except for the convective heat transfer coefficient (h) . By calculating

all the other quantities, it was possible to determine the convective

heat transfer coefficient. The above equations were solved at 10 minute

time intervals from 10 to 60 minutes. A plot of the heat input and output

terms in the overall heat balance equation is shown in figure 21.

The net radiant heat flux density at a gray surface element of total

emissivity and at temperature T due to incidence of radiative heat

flux H_ coming from the surroundings was expressed by

a r '

eB % - 'V> < 10 > o Evaluation of the radiant flux incident at furnace walls at any time was possible using the above, equation along with known or measured values

for all the other parameters. Figure 22 was derived from these results.

38
APPENDIX B. A LIST OF ASSUMED PROPERTIES FOR TEST FURNACE

Furnace Walls:

Heat Capacity: 0.84 J/g-°K (0.2 Btu/lb-°F)

Thermal Conductivity: 0.52 W/m-°K (0.3 Btu/hr-f t-°F)

Density: 1.25 g/cm 3 (78 lb/ft 3

)

Surface Emissivity (£„) : 0.8

D Effective Surface Emissivity (e): 0.9

Furnace:

Total Volume (V): 14.2 m

3 (492 ft 3

)

Total Internal Surface Area (AD ) : 55.7 m

2 (600 ft 2

)

USCOMMNBS-DC

39
NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 75-7942. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Heat Transfer in Furnaces for CIB Cooperative

Program and Heat Balance Analysis of Wall

Furnace

5. Publication Date November 1975

6. Performing Organization Code

7. AUTHOR(S)

J. B. Fang and J. T. Scott

8. Performing Organ. Repo' No. NBSIR 75-794

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 4926389

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

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

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

bibliography or literature survey, mention it here.) Tests were conducted in the NBS wall panel furnace as

part of a CIB international cooperative program to measure

and compare heat transfer in fire endurance furnaces. Additionally, a heat balance analysis showed that a cellular concrete block wall specimen absorbed more heat by convection

than by radiation. The rate of radiant heat transfer was

found to decrease slowly, while the furnace exhaust heat loss

increased during the test from 42 to 58 percent of the heat

output. The calculated radiant heat fluxes incident at furnace walls was found to be somewhat lower than the experimental

values measured at the test wall.

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) Fire resistance ratings ; fire test furnace; heat

balance; heat transfer; temperature-time curve.

18. AVAILABILITY (^Unlimited

1 1 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. C13

|3C | Order From National Technical Information Service (NTIS)

Springfield, Virginia 22151

19. SECURITY CLASS

(THIS REPORT)

UNCL ASSIFIED

21. NO. OF PAGES

47

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

22. Price $3-75

USCOMM.DC 29042-P74