USDA Forest Service 

Research Paper INT -69 

1969 

HEAT TRANSFER AND FIRE SPREAD 

Hal E. Anderson 

INTERMOUNTAIN FOREST AND RANGE EXPERIMENT STATION 

Ogden, Utah 84401 

This file was created by scanning the printed publication.

Errors identified by the software have been corrected;

however, some errors may remain.

HEAT TRANSFER AND FIRE SPREAD 

Hal E. Anderson 

Research partially supported by the 

Advanced Research Projects Agency 1 

Department of Defense 1 under ARPA 

Order 818. This report has been 

cleared for open publication. 

USDA Forest Service 

Research Paper INT-69 

1969 

INTERMOUNTAIN FOREST AND RANGE EXPERIMENT STATION 

Forest Service 

U.S. Department of Agriculture 

Ogden 1 Utah 844 01 

Joseph F. Pechanec 1 Director 
THE AUTHOR 

HALE. ANDERSON has been Project Leader of the 

Fuel Science Research Work Unit since 1966. 

He joined the staff of Intermountain Station's 

Northern Forest Fire Laboratory at Missoula, 

Montana, in 1961 and served as Project Leader 

of the Fire Physics Project from 1962 to 1966. 

Prior to employment with the Forest Service he 

was with the General Electric Company and 

worked on thermal and nuclear instrumentation 

from 1952 to 1961. His B.S. degree in physics 

was obtained at Central Washington State 

College in 1952. 
CONTENTS 

GENERAL PROBLEM .............•... 

DEVELOPMENT OF MATHEMATICAL DESCRIPTION 

Moisture Content . 

Radiant Heat .. 

Convective Heat 

Bulk Density of Fuel Bed 

Flame and Burning Characteristics 

TEST PROCEDURES ..••••.•• 

TEST RESULTS AND DISCUSSION . 

Role of Fuel Descriptors 

Radiant Heat . . • . 

Convective Heat 

Fire Response to cr and I. . 

CONCLUSIONS .. 

LITERATURE CITED . 

APPENDIX 

. . 

. . . 

. . . . 

. . . 

. . 

Page 

1 

1 

1 

2 

4 

5 

5 

6 

8 

8 

9 

13 

15 

17 

17 

19 

~ .. 

GENERAL PROBLEM 

Research in fire physics and fuel science at the Northern Forest Fire Laboratory 

(Missoula, Montana) is directed toward understanding and describing fire propagation 

through forest fuels and determining how the rate of fire spread is influenced by 

atmospheric, topographic, and fuel variables. Considerable qualitative information 

has been collected over the years; but quantitative data have become available only 

recently. An increase in this information has raised new questions and posed new 

problems. One fundamental question is: What are the relative roles of the several 

mechanisms of heat transfer (radiation, convection, conduction, and mass transport) in 

activating and sustaining the spread of fire? 

Test fires in mat-type fuel beds of pine needles burned in still air and with 

controlled wind conditions demonstrated that radiation significantly influenced fire 

spread in still air (Rothermel and Anderson 1966). Several mathematical models of fire 

spread by the various heat transfer mechanisms have been developed and tested to some 

degree (Fons 1946; Emmons 1963; Hottel et al. 1965; Thomas and Law 1965). From this 

research and from results of our own experiments, we have developed and tested a 

mathematical description of fire spread (under no-wind condition) based on radiant 

heat transfer. This paper presents the development of the mathematical description, 

and the test procedures and results, and compares data from these tests with those 

from other fire research. 

DEVELOPMENT OF MATHEMATICAL DESCRIPTION 

MOISTURE CONTENT 

Fuel moisture content has long been recognized as a major influence on ignition 

and fire spread (Gisborne 1928); therefore, any mathematical description of fire ~pread 

must include the influence of moisture. My approach to this task is to estimate the 

total heat required to remove the moisture and subsequently raise the fuel to ignition 

temperature. Various earlier researchers (Fons 1950; Martin 1964; Simms 1960, 1961, 

1963) indicate a temperature of 300° to 380°C. typifies the pilot ignition point. 

Research at the Northern Forest Fire Laboratory (Mutch 1964) showed that a temperature 

of 320°C. (608°F.) would·produce pilot ignitions in ground forest fuels. This temperature agrees with results of other research and was selected to represent pilot ignition 

temperature. 

The energy required to remove the water contained in a pound of wet fuel and then 

to ignite it was determined from data published by Byram et al. (1952). These data 

were developed into an equation that estimates the energy input per pound of fuel at 

any moisture content up to 20 percent of ovendry weight. The equation takes into account 

the heat required to raise the fuel to ignition, the heat required to raise the moisture 

to boiling temperature, the heat of desorption, the latent heat of vaporization, and 

the variation in boiling temperature with moisture content. Until now, no consideration 

had been given to the endothermic heat of pyrolysis that leads to the ignition of fuel. 

M0.83 M 

Qig CF(Ti- T1) + Cw[M(T2- T1) + [71(~)] 0 (1) 

0 169 T -5.92 T2 - M(71M- • )] + Lt[(?f) ]Tl + H(M)Tl 

where: 

Qig B.t.u./lb. (cal./g.) 

CF 0.327, specific heat of fuel 

C 1.0, specific heat of water 

w 

T1 ambient temperature 
Figure 1.--Heat required 

to bring 1 pound of fue Z 

to ignition as a function 

of fuel moisture content. 

T2 boiling temperature 

..ci 

....... 

::i 

..,; 

cri 

:::l 

Q. 

.!: 

c 

Q) 

..r::. 

c: 300 

~ ·c 

~ 

T. ignition temperature 608°F. (320°C.) 1 

Lt latent heat of vaporization 

M moisture content, lb./lb. (g./g.) 

heat of desorption (16 cal./g.). 

Fuel moisture content (percent) 

Using this equation, we developed a curve (figure 1) to show the relation of energy 

input to moisture content of the fuel (in percent). 

Additional definitions are listed in the Appendix. 

RADIANT HEAT 

We knew how much heat was required to raise the moist fuel to ignition and the 

temperature at ignition. Our next step was to develop an equation that would describe 

the change in rate of spread. Research by Thomas (1963) and Emmons (1963) indicated 

that the heat flux from the fire to unburned fuel can be related to rate of spread. 

Assuming that the energy requir~d to cause ignition remains constant and that the 

emissive power of the fire remains constant--just high enough to cause ignition when 

the fire reaches the unburned fuel--we can write: 

Q (2) 

where: 

Q heat per vertical cross section of the fuel bed to cause ignition, B.t.u./ft. 2 

E emissive power of the fire, B.t.u./ft. 2 - hr. 

a attenuation constant 

x distance from the fire front to the fuel particle or elemental volume in 

question, ft. 

t time, hr. 

This can be modified by: 

dx dt =-R 

2 

· .......... : 
where: 

R = steady rate of spread, ft./hr. 

Substituting and integrating equation (2): 

E R = - (3) aQ 

The quantity, Q = B.t.u./ft. 2 , must be modified so Q. , B.t.u./lb. can be used. This 

is accomplished by: lg 

where: 

fuel particle density, lb./ft.3 (g./cm.3) 

fuel particle projected surface area to volume ratio, ft.2/ft.3 (cm. 2/cm.3). 

The attenuation factor "a" must be put into some measurable form. It is assumed to be 

proportional to the total projected area of fuel in a unit volume of space (Committee 

on Fire Research, 1961, p. 126). 

1 

a = 4.f 

where: 

A void volume per total surface area 

1/4 = projected portion of surface area. 

Equations 4 and 5 are substituted in equation 3, which takes the form: 

a AE 

R = a 

PfQ. lg 

(5) 

(6) 

This mathematical description states that the rate of spread is dependent on the 

emissive power of the fire and will be modified by the size of the fuel particles, oa; 

porosity of the fuel bed, A; density of the fuel particles, pf; and the amount of 

energy required for ignition (primarily a function of the amount of moisture in the 

fuel), Qig· The emissive power of the fire is made up of two components: (1) the 

combustion zone within the fuel bed; (2) the flame plume above the fuel bed. Both 

components contribute to radiant heating. However, convective heating takes place 

only in the fuel bed and in the region of the fuel bed-fire plume interface. In the 

study reported herein we are concerned with describing rate of spread in absence 

of wind with the assumption that radiation was the primary source of heat. 

The fuel descriptors are independent of the two source components. However, 

the contributions of heat to the fuel are dependent on the relative weight and influence 

of each mode of heat transfer. The radiant heat from each component is defined thus: 

E oE T 4 (combustion zone emissive power) c c c 

Ef OEfTf4 (flame emissive power). 

The impact of the flame's emissive power on the fuel ahead of the fire is a function of 

distance and shape of the flame; these must be taken into account. This modification 

3 
describes the irradiance of the element. By integrating the configuration factor, F12 , 

over the distance of influence and dividing by the configuration factor for an infinite 

plane source integrated over 1 foot for the two components transferring radiant heat, 

a numerical value, F12', is obtained; it describes the magnitude of the heat impact of 

each component. The absorptivity of the fuel element is considered equal to unity; 

however, the radiant heat loss of the element to its surroundings is regarded as 

negligible. 

Equation 6 was modified to show these considerations: 

a A 

R = __ a___ [crs T 4 F12 ' 

pfQ. c c lg 

(7) 

An earlier report (Anderson 1968) showed that the variation in flame irradiance 

can be important. The configuration factor for the combustion zone was determined prior 

to testing. However, the flame configuration factor had to be determined later from 

photographs of the flame shape. A form of equation 7 was tested against data collected 

from earlier testing (Anderson and Rothermel 1965) and was found to agree with rates 

of spread previously observed. We designed a study program to investigate unknowns in 

equation 7 and to determine whether radiant heat could account for rate of spread under 

the no-wind condition. 

CONVECTIVE HEAT 

We recognized that radiant heat might not account for all the heat; so we had to 

determine a convective heat transfer coefficient for the needles. For this, some 

measure of the gas velocity in the fuel bed had to be derived. Also, the Reynolds and 

Nusselt numbers were essential for calculating the convective heat transfer coeff\4ient 

h . The research previously reviewed by Hottel (Blinov and Khudiakov 1959) and presgnted by Thomas (1963) showed two expressions for Reynolds number: 

where: 

VL regression rate of liquid burning surface 

d characteristic dimension, pan diameter or flame depth 

v = kinematic viscosity = ~/p g 

~ dynamic viscosity 

pg gas density 

m1 rate of weight loss. 

Equation 9 can be put into the same form as equation 8 by rearranging terms: 

4 

m1 pbAVF' lb./sec. 

A d 2 

~ = vp g 

(8) 

(9) 
VF linear regression rate of fuel surface, ft./sec. 

bulk density of fuel bed 

2 ml pbd VF VFd p 

NRE = ]ld = vp d 

g \) 

( __l). 

Pg (10) 

The quantity V (Pb) represents the gas velocity, V , at the surface of the fuel, and F- g p 

VF is the same as,gthe VL used by Hottel. Multiplying the regression rate of the 

surface by the ratio of fuel density to gas density provides the value of the gas 

velocity at the surface. This means that liquid-pool fires and solid-fuel fi~es should 

correlate. 

BULK DENSITY OF FUEL BED 

We noted a similarity between equation 6 and the equation published by Thomas and 

Law (1965). The equations are equivalent in concept except that a A/Pf is replaced by 

1/pb (bulk density of the fuel bed). These two quantities are app¥oximately equal; 

the exact relation can be determined by considering the properties of the fuel particle 

and fuel bed. The porosity of a fuel bed, A, is defined as: 

(11) 

where: A= porosity, ft.~/ft.2· 

cr fuel particle surface area-to-volume ratio, ft. 2/ft.3 

a 

vl fuel bed volume, ft. 3 

v2 fuel particles volume, ft.3 

Rearranging this equation we have: 

(12) 

The volumes of the fuel bed, v1 , and the fuel particles, V2, are proportional to the 

respective densities: 

where_Wb is the weight of the fuel. Combining these terms and substituting into 

equat1on 12, the result is: 

(13) 

This relation exists for fuel beds made up of a single size of fuel. In more complex 

fuel beds, the bulk density provides a gross estimate; whereas appraising by size 

classes, variation of particle density, and proportion of each size class provides a 

more accurate estimate. For the present, we are considering only homogeneous beds of 

a single fuel. 

FLAME AND BURNING CHARACTERISTICS 

Information that would enable us to predict flame size or burning rates from a 

given fuel complex is not yet available; hence, it is difficult to estimate rates of 

5 
fi r·c spread accurately. Factors that affect flame size and burning rate include: 

(1) physical properties of the fuel bed and of the fuel particles; and (2) chemical 

properties of the fuel elements (e.g., crude fat content, silica-free ash content, 

and the amount of cellulose and/or hemicellulose in the fuel. Investigations are being 

conducted at the Northern Forest Fire Laboratory to determine how much the chemical 

properties of the fuel influence flammability--discussion of such investigations is 

outside the scope of this paper. 

The physical properties of fuels are also under study at the Laboratory and include 

fuel particle size, thermal properties, fuel bed porosity and continuity, and several 

other factors. These are of importance to the spread equation since some enter the 

fuel descriptor set, crA/pfQ. . Frequently it has been observed that the residence time 

of flame at a given point i~ga fuel bed is related to diameter of the fuel particle. 

A review of fire research literature and unpublished tests here at the Laboratory 

indicate that residence time is a function of particle diameter (Fons et al. 1962; 

Byram et al. 1966; McCarter and Broido 1965; Wooliscroft and Law 1967). 

TEST PROCEDURES 

The measurements necessary to evaluate the rate of spread according to equation 7 

were determined from the unknowns in the equation. These are the emissivities of the 

combustion and flame zones, the temperature of each zone, and the flame shape mean 

configuration factor for each zone. By comparing the calculated rate of spread to the 

observed rate we obtain a means of determining the relative importance of the role of 

radiant heat transfer in the propagation of fire. This does not give us any information 

about the generation of radiant energy. However, we gain some insight into the 

generation phase through measurements of weight loss, flame residence time, and radiant 

heat fluxes to the fuel. 

Many of the methods mentioned above except for two have been described in previous 

publications (Anderson and Rothermel 1965; Anderson 1968). Two measurements not used 

in previous work are: determination of the configuration factor; and the radiant heat 

fltuc passing through a fuel element. Configuration factor determinations were made 

using the techniques described in "Flame Shape and Fire Spread" (Anderson 1968). A 

sequence of at least 10 photographs (1 second exposure at f:ll on Plus X film) in an 

overlay was used to determine average flame shape and length. 

Radiant heat fluxes from the flame and the combustion zone were measured with 

Gardon-type heat rate sensors. These sensors were water cooled and shielded with 

sapphire windows so that only radiant heat was measured. The recorded millivolt signal 

from these sensors was corrected for transmissivity, percent radiation below the 

wavelength cutoff of the window, configuration factor, and view area enclosed. Besides 

indicating the heat flux passing through a particular point, the resulting values 

could be compared with the combustion and flame zone temperature measurements for 

calculation of the emissivity of each zone. 

The heat rate sensors in the fuel bed were placed with the sensing element 0.5 

inch. below the surface of the fuel bed. Each sensor faced the oncoming fire front and 

was positioned to view all of the fire in the fuel bed. Thermocouples were located at 

the surface of the fuel bed and 0.5 inch below it to provide data on temperatures as 

the fire front approached and passed. The peak values represented the fire front's 

arrival and were used to calculate the blackbody emissive power of the combustion 

zone's fire front. The emissivity of the zone was determined by dividing the heat 

rate sensor value of heat flux by the calculated blackbody value. 

The heat flux of the flame was measured in nearly the same manner as were the heat 

rate sensors in the fuel bed except the sensors were positioned so that one edge of 

their view angle coincided with the surface of the fuel bed. The sensor then viewed 

the space above the bed. Thermocouples, 5 mil chromel/alumel, were placed 2, 11, and 

6 
22 inches above the fuel bed surface to measure flame temperature. Analysis of the 

flame size for each test set (consisting of 3 or more fires) indicated which 

thermocouples were in the flame envelope. From these thermocouples an average flame 

temperature was determined. This was used to determine an average blackbody emissive 

power. The average emissive power of the flame was also determined by considering 

the heat rate sensor value at discrete distances from the flame. The emissivity of 

the flame was determined as described for the combustion zone. 

A preliminary series of tests was made with ponderosa pine needle beds to assess 

the magnitude of the influence of porosity. Fuel beds of 0.5 and 1.0 ft. 2 load area 

and constant loadings were burned as stationary fires with surface ignition. The fuel 

depth was varied to provide various porosities and measurements of weight loss and 

flame length were made. 

The radiant heat fire tests were conducted with three replications in three pine 

needle fuels--ponderosa pine (Pinus ponderosa Laws.); western white pine (Pinus 

monticola Dougl.); and lodgepole pine (Pinus contorta Dougl.). The fuels wereconditioned to moisture contents varying from 2.5 to 23 percent of ovendry weight. 

Ambient conditions were maintained at 90° F. with relative humidities of 7 to 92 

percent; ambient conditions were matched to fuel moisture contents. Fuel beds were 

prepared according to established technique (Schuette 1965) . A summary of the test 

conditions and fuel characteristics is given in table 1. 

Table 1.--Ambient conditions and fuel characteristics for each test set 

(A set constitutes three or more fires) 

~' 

Fuel type Particle Heat to Fuel heat 

& moisture Air Relative density ignition content 

content temperature humidity a a pf Qig H 

% oF. %RH ft. 2jft. 3 lb./ft. 3 ft. 31ft. 2 B.t.u./lb. B.t.u.!.J~ 

pp - 2.6 90.5 7.0 1,741 31.8 9.1 X 10- 3 213 8,744 

pp - 4.2 90.5 13.2 1,741 31.8 8.8 X 10- 3 237 8,744 

pp - 5.3 90.5 22.2 1,741 31.8 9.1 X 10- 3 254 8,744 

pp - 5.9 90.7 30.7 1,741 31. 8 8.5 X 10- 3 262 8, 744 

pp - 8.6 90.8 51.3 1,741 31.8 8.5 X 10-3 300 8,744 

pp - 14.0 90.3 75.3 1,741 31.8 8.5 X 10- 3 347 8,744 

pp - 20.5 90.5 92.2 1,741 31.8 8.4 X 10- 3 377 8,744 

WP - 3.4 90.6 6.1 2,790 33.5 5.9 X 10- 3 227 8,457 

WP - 6.7 91.1 21.6 2,790 33.5 5.6 X 10- 3 275 8,457 

WP - 7.4 90.5 30.9 2,790 33.5 5.5 X 10- 3 283 8,457 

WP - 10.1 90.8 51.2 2,790 33.5 5.6 X 10- 3 317 8,457 

WP - 15.3 90.4 75.8 2,790 33.5 5.6 X 10- 3 353 8,457 

WP - 21.6 90.5 91.3 2,790 33.5 5.6 X 10- 3 388 8,457 

LPP - 3.6 92.2 6.2 2,188 35.4 4.6 X 10- 3 230 8,748 

LPP - 5.4 90.8 21.9 2,188 35.4 4.8 X 10-3 260 8,748 

LPP - 6.5 90.8 31.0 2,188 35.4 4.3 X 10- 3 270 8,748 

LPP - 8.8 90.8 51.1 2,188 35.4 4.5 X 10- 3 301 8,748 

LPP - 13.4 90.7 75.8 2,188 35.4 4.9 X 10- 3 345 8,748 

LPP - 23.2 90.1 91.0 2,188 35.4 5.0 X 10- 3 402 8,748 

PP is ponderosa pine 

WP is western white pine 

LPP is lodgepole pine 

7 
TEST RESULTS AND DISCUSSION 

ROLE OF FUEL DESCRIPTORS 

During the development of the equation to describe fire spread in terms of radiant 

heat transfer, a group of fuel descriptors was established. This group, OaA/PfQig, can 

be determined prior to a test fire; by correlating it to the rate of spread, a best 

estimate of the heat flux can be obtained. Figure 2 shows the results of 3 or more 

test fires averaged at each condition. Taking an increment along the linear portion 

of the curve, the maximum heat flux into the fuel is found to be 40 X 103 B.t.u./ft. 2 -

hr.(3.0 cal./cm.2 -sec.). Low fuel moisture contents resulted in the high rates of 

spread and as moisture content increased a point was reached where a departure from a 

linear relation occurred. Following the departure to zero rate of spread; the intercept represents the point where moisture content prevents fire spread. By determining 

Q. and referring to figure 1, the moisture contents for no spread were found: J.g 

MC = 24.2 percent 

MC = 24.2 percent 

412 B.t.u. 

lb. 

-3 1.13 X 10 , Q. J.g 

412 B.t.u. 

lb. 

Lodgepole pine: I -3 cr A pfQ. = 0.81 X 10 , Q. a J.g J.g 

359 B.t.u. 

lb 0 

~ 

..c 

;::: ' 

:0 

0 

~ 

a. 

Ul 

'+-

0 

(I) 

0 

0::: 

80 

70 

60 

50 

40 

30 

20 

10 

• Ponderosa pine 

o White pine 

4> Lodgepole pine 

/ . • .• .. lD 

l •• : 

~ .•1 

••• ··1 ! 

.+" : .:: •••• ! .. . 0 ~· .. ~·· : ______ _. .: ________________ ._ __ _. ____ ~--~----~ 

0 0.5 .6 .8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 

Figure 2.--A near linear relation is exhibited between the experimental rate of spread and 

the fuel descriptor's set. Note the rolloff a~ the low end. 

8 
Fuel type 

& moisture 

content 

Table 2.--Calculated maximum heat fluxes associated with 

rate of spread and the fuel descriptors 

cr A Experimental a rate of spread Heat flux 

PfQ. 1g RE qT/A 

% ft 0 

3 I B 0 t 0 u 0 ft./hr. B.t.u./ft. 2 - hr. Cal. /em. 2 - sec. 

pp 2.6 2.34 X 10- 3 76.1 3.26 X 104 2.46 

pp 4.2 2.02 x lo- 3 61.8 3.06 X 104 2.30 

pp 5.3 1.96 X 10- 3 57.0 2.90 X 104 2.18 

pp 5.9 1. 78 X 10- 3 51.6 2.90 X 104 2.18 

pp 8.6 1. 55 X 10- 3 39.6 2.56 X 104 1. 93 

pp - 14.0 1.34 X lo-3 33.0 2.46 X 104 1. 85 

pp - 20.5 1. 22 X lo-3 21.0 1. 74 X 104 1.31 

WP 3.4 2.17 X 10- 3 58.8 2.71 X 104 2.04 

WP 6.7 1. 70 X lo- 3 50.4 2.96 X 10 4 2.23 

WP 7.4 1.62 X lo-3 42.6 2.63 X 104 1.98 

WP - 10.1 1.47 X 10- 3 36.6 2.49 X 10 4 1. 88 

WP - 15.3 1. 32 X lo-3 26.4 2.00 X 104 1. 51 

WP - 21.6 1. 20 X 10- 3 17.4 1.45 X 104 1. 09 

LPP - 3.6 1. 24 X 10- 3 30.6 2.47 X 104 1. 86 

LPP - 5.4 1.14 X 10- 3 25.8 2.26 X 104 1 :irJ 

LPP - 6.5 .98 X 10- 3 21.6 2.21 X 104 1.66 

LPP - 8.8 .93 X 10-3 18.0 1.94 X 104 1.46 

LPP - 13.4 .88 X lo- 3 12.0 1.36 X 104 1. 02 

LPP - 23.2 .77 X 10- 3 

PP is ponderosa pine 

WP is western white pine 

LPP is lodgepole pine 

The values for ponderosa and western white pine are in agreement with previous laboratory 

findings. Fires in lodgepole pine needle beds at 23.2 percent MC would not spread even 

with repeated ignition of the fuel bed leading edge substantiating the above cutoff 

value. The porosity of this fuel appears to be the factor responsible but additional 

work with variations in porosity is needed to substantiate this. 

RADIANT HEAT 

The total heat flux related to fire spread was calculated for each set of test 

fires. These values are tabulated in table 2. The radiant heat fluxes reported by 

Thomas and Law (1965) are of the same magnitude where cr and/or A were varied. This 

general agreement indicates radiant heat does contribute to rate of spread, but in the 

present case the energy is the combined sum of the heat transfer components. The next 

step was to determine how much heat was being supplied by the flame and how much by 

the combustion zone. Analysis of all the tests showed a nearly constant combustion 

zone temperature with no significant correlation to fuel moisture content. 

9 
10 

Table 3.--Test results for each fuel type and moisture condition 

(Values are average of three or more fires in each set.) 

Fuel type 

& moisture I I 

content R tR D L B T Tf Ef F12 F12 Ef* c 

% ft. /hr. min. ft. ft. lb./min. oF. oF. Flame Comb. zone B.t.u./ft.- hr. 

pp - pp - pp -

pp - pp - pp -

pp -

WP -

WP -

WP -

WP -

WP -

WP -

LPPLPPLPPLPPLPP2.6 76.1 1. 27 1. 61 5.5 

4.2 61.8 1. 27 1. 31 5.0 

5.3 57.0 1. 27 1. 20 4.7 

5.~ 51.6 1. 27 1. 09 4.3 

8.6 39.6 1. 27 .84 3.5 

14.0 33.0 1. 27 .70 2.9 

20.5 21.0 1. 27 .44 2.0 

3.4 58.8 . 92 .90 2.2 

6. 7 50.4 .92 .78 2.0 

7.4 42.6 .92 .65 1.9 

10.2 36.6 .92 .56 1.5 

15.3 26.4 .92 .40 1.1 

21.6 17.4 .92 .27 . 9 

3.6 30.6 1. 06 .54 1.5 

5.4 25.8 1. 06 .46 1.5 

6.5 21.6 1. 06 .38 1.1 

8.8 18.0 1. 06 .32 .9 

13.4 12.0 1. 06 .21 . 7 

*Average of heat flux sensor signal. 

PP is ponderosa pine 

WP is western white pine 

LPP is lodgepole pine 

6.0 

u 

Q) 

IJ) 

I c.\1:: 5.0 -..... 

::i 

+--' 

a:i 4.0 Q) 

u 

c 

§ 

.E 3.0 Q) 

Q) 

E 

0 

li: 

0.98 1591 1680 0.28 

.77 1591 1627 .28 

.81 1591 1570 .28 

.70 1591 1509 .28 

.57 1591 1507 .28 

. 35 1591 1392 .28 

.17 1591 1254 .28 

. 35 1434 1321 .16 

.31 1434 1380 .16 

.31 1434 1531 .16 

.27 1434 1450 .16 

.26 1434 1311 .16 

.20 1434 1229 .16 

.21 1492 1548 .16 

.19 1492 1548 .16 

.13 1492 1303 .16 

.14 1492 1358 .16 

.12 1492 1135 .16 

1.18 

1.19 

1.11 

1. 07 

.95 

.85 

. 71 

.60 

.58 

.57 

.46 

.40 

.35 

.43 

.42 

.36 

.33 

.20 

0.08 6.22 X 

.08 9.46 X 

.08 8.7Q X 

.08 8.88 X 

.08 6.58 X 

.08 6.33 X 

.08 1.97 X 

.08 4.03 X 

. 08 3.31 X 

.08 4.28 X 

.08 3.64 X 

.08 2.88 X 

.08 1. 73 X 

.08 3.20 X 

.08 4.50 X 

.08 4.7 X 

.08 -3.9 X 

.08 

• Ponderosa pine 

o White pine 

~ Lodgepole pine 

oL-~~--~------~------~------~------~-----

-.25 0 .5 2 3 4 5 

Distance from fire (ft.) 

Figure 3.--FZame emittance caZcuZations from heat rate sensors for fires 

in fueZ beds at 6-percent moisture content. 

10 3 

10 3 

10 3 

10 3 

10 3 

10 3 

10 3 

10 3 

10 3 

10 3 

10 3 

10 3 

10 3 

10 3 

10 3 

10 3 

10 3 

~~ 
The different fuel types produced a slight difference in the average temperature 

of the combustion zone, as follows: 

Fuel type 

Ponderosa pine 

Western white pine 

Lodgepole pine 

Average temperature 

15 91° F. ( 86 7 ° C • ) 

1434° F. (779° C.) 

1492° F. ( 811° C.) 

These combustion zone temperatures are not unusual if moisture is removed from the fuel 

before the fire front or combustion zone reaches it. The irradiance of the fuel could 

change with moisture content changes because emissivity varied or the absorptivity of 

the intervening gases varied. The heat rate sensors for the combustion zone were 

placed too close to the surface of the fuel and were not sufficiently collimated. As a 

result, poor repeatability was obtained. However, these measurements did indicate a 

rather constant heat flux from the combustion zone. We found no decrease in heat flux 

with increases in fuel moisture content; this tended to support the thermocouple data 

but due to the lack of repeatability no reliable estimate of combustion zone emissivity 

could be made. The equation was evaluated for rate of spread by using a value of 1.0 

for the combustion zone. 

The thermocouples located above the fuel bed showed that the average flame 

temperature decreased as fuel moisture content increased: 

Fuel type 

Ponderosa pine 

Western white pine 

Lodgepole pine 

Temperature range 

(oF •) 

1680 1254 

1531 - 1229 

1548 - 1135 

Rate of change 

(°F./percent MC) 

24 

24 

42 

Also, the burning rate, flame length, and flame depth were found to decrease in this 

same manner,as shown in table 3. These three parameters along with flame temperature 

govern the emissive power of the flame. The values obtained from the heat rate sensors 

do show a decrease with moisture increase but not as rapidly as the above variables of 

burning rate, flame length and depth. The emissive power values derived from the heat 

rate sensors at various distances from the flame agreed very closely with the values 

determined after the sensors had entered the flame (figure 3). The average emissive 

power was obtained from these values and compared with the blackbody emissive power 

determined by the thermocouple readings to calculate the emissivity of each test set 

(figure 4) . Ponderosa pine fuel beds produced taller and thicker flames than the other 

fuels which generated flames with smaller dimensions; the calculated emissivities are 

substantiated by these physical characteristics of the flames. 

By using the data of the emissive powers we can estimate the total radiant heat flux 

that has an impact on the fuel ahead of the fire. The values of heat flux can be calculated according to equation 7 and summed for comparison with the total heat flux found 

to be necessary to produce the measured rate of spread (see table 2). The results of 

this analysis are shown in figure 5 with the summed radiant heat flux as a percentage of 

the total heat flux and plotted against fuel moisture content. The radiant heat fluxes 

were determined by using a combustion zone emissivity of 1.00 and flame emissivities of 

0.28 for ponderosa pine fires and 0.16 for lodgepole and western white pine fires. 

This analysis shows that radiant heat can account for 40 percent or less of the 

total heat flux necessary for the fire spread observed in these fuel beds. The rest 

of the heat flux must come from some other heat transfer mechanism. Conduction appears 

to be insignificant; a brief analysis indicated only 1/50 of the necessary energy 

would be available through this mechanism. This means convective heat transfer must be 

the primary source through some horizontal transport mechanism. 

11 

. ' .., .. 
1-

if 

~ ~ 

12 

.4 

~ > 

:.;= 

'iii • . !!? 

E 

w . 2 

.I 

0 

0 2 

• 

• • 0 

• 

• 

. ........ . .. ···-... 

EF • Ponderosa pine 0.28 

o White pine } 0 16 ~ Lodgepole pine · 

····· ---..P.-.... ~--'EII.-o---------[]······ ······· <t> ••••••••••••••• -:• 

···••..0 

4 6 8 10 12 14 16 18 20 22 

Fuel moisture content (percent) 

Figure 4.--FZame emissivities for fires in three fueZs at the same environmental 

conditions were determined from heat fZux sensor measurements. 

1.0 • Ponderosa pine 

o White pine ~ ~ 

.9 ~ Lodgepole pine 

.8 

.7 

.6 

.5 

.4 -· • 

• 

• -· 

. 3 • • 

. 2 ~ ~ ~ [] 

[] $ Q [] a 

. I [] 

0 

0 2 4 6 8 10 12 14 16 18 20 22 

F ue I moisture content ( percent) 

Figure 5.--Portion of totaZ heat fZux contributabZe to radiant heat fZux. 

:,,, .,,,,-
CONVECTIVE HEAT 

As mentioned earlier, it was necessary to determine a convective heat transfer 

coefficient. In addition, both the Reynolds and the Nusselt numbers had to be computed. 

Using the procedures outlined previously, a gas velocity and Reynolds number were 

calculated for each test set. If solid fuel fires respond in a manner similar to 

liquid pool fires, then nearly equal values of Reynolds numbers should occur for fires 

of similar dimensions. Figure 6 shows how the solid fuel fires grouped near the curve 

for gasoline pool fires. The same forces seem to apply to the various fires resulting 

in turbulent, transitional, and laminar regimes. Fires in ponderosa pine beds with 

less than 9 percent moisture content were turbulent and in the transitional regime fo~ 

moisture contents above 9 percent. All fires in western white pine and lodgepole pine 

were in the transitional or laminar regimes. 

Values for the gas velocity in each test set were determined and were used with 

the diameter of the fuel particle to determine the Reynolds number. The Nusselt number 

for cylinders was used to calculate the convective heat transfer coefficient. This 

combined with the temperature difference between the combustion zone and the ambient 

air provided a measure of the convective heat transfer component. 

In all tests the calculated convective heat flux exceeded the net heat flux which 

is obtained by subtracting the radiant heat flux from the total heat flux values in 

table 2. This means that a horizontal transfer efficiency coefficient does exist. 

This horizontal transfer coefficient was calculated for each fuel: 

Ponderosa pine: n 

Western white pine: n 

Lodgepole pine: n 

(0.90 

(1.00 

(1. 00 

0.014 MC*) 

0.028 MC) 

0.036 MC) 

*MC is the fuel moisture content in percent. 

These coefficients infer less heat transfer in ponderosa fuel of low moisture contents 

and a more rapid decrease in heat transfer for western white pine and lodgepole pine 

fuels because their burning regimes are transitional or laminar. 

Incorporating the horizontal transfer coefficients into equation 7 the new description of fire spread by heat transfer becomes: 

+ + nh (T -TI)] c c (14) 

where: 

T combustion zone temperature c 

T1 ambient air temperature. 

Values for each component of the equation were obtained for the experimental data. The 

resulting rates of spread are compared to the experimental values in figure 7. The 

equation was found to describe rate of spread quite accurately but does point out the 

following areas where additional research is needed: 

1. Estimation prior to a fire of how much flame will be generated. 

2. Is there a physical limitation to fire spread caused by maximum heat flux into 

the fuel bed? 

3. What is the relation between fuel bed characteristics and convective heat 

transfer? 

13 
1.0 

- Gasoline 

·-· Ponderosa pine 

White pine 

.5 Lodgepole pine 

u 

Q,) 

~ 

;:::: 

.... .2 0"1 

> 

0.1 

.05 

.04~----~------_.----~~----~~--~~----~~----~~--~--~----~ 10-2 2 5 2 5 2 5 

Flame depth or diameter (ft.) 

Figure 6.--Burning regimes of various fuels based on cold vapor density and viscosity. 

Figure ?.--Comparison of 

experimentar rates of 

spread to theoretical 

curve of fire spread 

showing end points for 

fuel moisture content. 

14 

-~ 

.c 

........ 

---

"0 

0 

~ 

a. 

(/) 

0 

Q) 

0 

0:: 

150 

140 

130 

120 

110 

100 

90 

80 

70 

• Ponderosa pine 

c White pine 

~ Lodgepole pine 

Fuel moisture content (percent) 
50 

Figure 8.--ReZation of 20 

residence time to particle In 

thickness determined from ~ :::J 10 

measurements made during c .E 

test fires. Q) 5.0 E 

+= 

Q) 

0 

c 

Q) 2.0 'tJ 

·u; 

Q) 

0::: 1.0 0 

.5 

.2 

.I 

10-2 2 

Particle thickness {inches) 

4. Over what range of particle sizes and bed porosities does the fuel descriptor 

set apply? 

Values for the combustion zone and flame temperatures determined experimentally 

were used to test equation 14 against fires in beds of different widths. This was done 

for the fires described in "Fire Spread and Flame Shape" (Anderson 1968). The equation 

yielded a rate of spread that was within: 99 percent of the experimental rate of spread 

for a 1.5-foot-wide ponderosa pine bed; 77 percent to 89 percent for 5.0-foot beds; 103 

percent for a 1.5-foot-wide bed of western white pine; and 89 percent for 5.0-foot-wide 

beds. Rate of spread was overestimated at 136 percent of the experimental value for 

5-foot-wide beds of lodgepole pine primarily because the flame depth measurements differed by a factor of three. In addition, the flame-shielded test (Rothermel and 

Anderson 1966) was used and the value from the equation was 97 percent of the experimental spread assuming no radiant heat from the flame. These evaluations support the 

credibility of the equation and further work will determine whether this approach is 

applicable to a variety of fuels. 

FIRE RESPONSE TO cr AND A 

In fuel beds where the particles are loosely arranged, each particle will burn in 

a manner predominantly controlled by its own thermal properties. The energy feedback 

to the particle from surrounding fuel elements and their pyrolysis products will influence the burning characteristics but may be a nearly constant value until the particles 

are very far apart or very close together. This idea was checked by plotting research 

data for a variety of particle sizes ranging from 1.75 X l0- 2 to 4.00 inches against the 

residence time or duration of active flaming. The results shown in figure 8 suggest that 

in porous fuel beds, residence time in minutes is equal to 8 times the particle diameter 

or thickness in inches. At the low end of the curve the residence time for a single 

15 
needle falls on the line. Those points above the line are residence times for the test 

fuel beds and have porosities from 4.3 to 9.1 X lo-3 ft.3/ft.2. Much of the other data 

were for fuel beds with porosities between 2.45 and 6.04 X lo-2 ft.3/ft.2. It would 

appear porosity has an important influence on the residence time and the burning rate 

of a fuel bed and rather small changes can make major changes in a fuel bed's burning 

characteristics. 

The tests of stationary fires in fuel beds of fixed area and loading revealed the 

influence of porosity on burning rate and flame length. It was found that an optimum 

porosity exists where the fuel burning rate is maximum (figure 9). This occurs with 

loading held constant but as loading is increased, the maximum burning rate occurs at 

a different porosity. It is possible that as loading increases the burning rate will 

reach a nearly constant level over a large range of porosities. Additional work is in 

progress to fully evaluate porosity, area of combustion, and loading. The values of 

a A. for the three fuel types used in the main test series ranged from 10 for lodgepole 

t~ 18.9 for western white pine with ponderosa pine at 16. These values are on the low 

side of optimum porosity and any variation will have a significant effect on the fire's 

behavior. Comparing these results to porosities measured in the field, we found even 

lower porosities for the needle layer under a pure stand of ponderosa pine. Any 

disturbance to the forest floor litter layer increasing the spacing between needles 

can cause an increase in burning rate and more flaming activity. It appears the 

dimensionless group a A., may be a good indicator of potential fire spread in a fuel. 

a 

The influence of fuel particle density seems quite straightforward and follows 

the results presented by Fans et al. (1962). He shows that as the specific gravity of 

the fuel decreases the rate of spread increases. The location of pf in the denominator 

of equation 14 reflects this behavior. 

0.7 

0 0. 5 ft.2

, .125 lb./ft.2 ~' 

• I .0 ft.~ .125 lb./ft.2 

D 0.5 ft.~ .25Qib./ft. 2 

0.6 

• I .0 ft.~ .2501b./ ft. 2 

0.5 . ...._, I . • ~ c .E 

0.4 

..0 ' 

cu 

'§ 0.3 0"1 

c • • 

·c: 

"-:J I 

CD 

0.2 

0.1 • 

0 0 ~----~----*-----*-----------------~----~-------- 20 40 60 80 100 120 140 160 

6?\ (Dimensionless) a 

Figure 9.--Injtuence of porosit~~ A.~ on burning rate for fires in ponderosa pine needles 

with a a of 1~740 ft. /ft. 3• Each data point is average of three fires. a 

16 
CONCLUSIONS 

The work conducted to date indicates that radiant heat 

only 40 percent of the total heat flux necessary to sustain 

Convective heat transfer at the interface of the combustion 

probably accounts for the rest. Burning characteristics and 

controlled by the fuel particle size and the porosity of the 

residence time of a fire is controlled by the particle size. 

seems to exist between residence time and particle size. 

transfer can account for 

a spreading fire. 

zone and the new fuel 

flame depth are strongly 

bed. In porous beds the 

A direct relationship 

Fuel beds of solid fuel elements can be correlated to liquid pool fires by using 

the ratio· of fuel bed density to cold vapor gas density. Three burning regimes, 

turbulent, transitional, and laminar, exist in solid fuels and may contribute to 

discrepancies found among various sets of experimental fires. 

A group of selected fuel descriptors consolidates the more important parameters 

into a measure of the bulk heat requirement, B.t.u./ft.3, and, with the experimental 

rates of spread, indicates the maximum heat flux is near 40 X 103 B.t.u./ft. 2 - hr. 

(3 cal./cm.2 - sec.). 

The tallest flames and highest burning rates occur where an optimum porosity 

exists. Natural litter fuel beds appear to have low porosities and small changes can 

cause large shifts in burning rate. 

LITERATURE· CITED 

Anderson, Hal E. 

1968. Flame shape and fire spread. Fire Technol. 1968 (Feb.): 51-58, illus. ~-

and R. C. Rothermel. ----~-1965. Influence of moisture and wind upon the characteristics of free-burning 

fires. Tenth Symp. (Int.) on Combust., pp. 1009-10-19, illus. 

Pittsburgh: The Combustion Institute. 

Blinov, V. I., and G. N. Khudiakov. 

1959. Certain laws governing diffusive burning of liquids. Reviewed by H. C. 

Hottel. Fire Res. Abstr. and Rev. 1(2): 41-44. 

Byram, G. M., H. B. Clements, M. E. Bishop, and R. M. Nelson, Jr. 

1966. An experimental study of model fires. Project Fire Model final report. 

U.S. Forest Serv., Southeastern Forest Exp. Sta., 51 pp., illus. 

----~-' F. M. Sauer, W. L. Pons, and R. K. Arnold. 

1952. Thermal properties of forest fuels. U.S. Forest Serv., Fire Research, 

34 pp., illus. 

Committee on Fire Research. 

1961. A study of fire problems. Nat. Acad. Sci., Nat. Res. Counc. Pub. 949, 

174 pp., illus. 

Emmons, Howard. 

1963. Fire in the forest. Fire Res. Abstr. and Rev. 5(3): 163-178, illus. 

Pons, Wallace L. 

1946. Analysis of fire spread in light forest fuels. J. Agr. Res. 72: 93-121, 

illus. 

17 
Fons, Wallace L. 

1950. Heating and ignition of small wood cylinders. Ind. and Eng. Chern. 42(10): 

2130-2133, illus. 

, H. B. Clements, E. R. Elliott, and P. M. George. ----~~ 1962. Project Fire Model summary progress report II. U.S. Forest Serv., 

Southeastern Forest Exp. Sta., 55 pp., illus. 

Gisborne, H. T. 

1928. Measuring forest fire danger in northern Idaho. U.S. Dep. Agr. Misc. Pub. 

29, 64 pp., illus. 

Hottel, H. C., C. G. Williams, and F. R. Steward. . 

1965. The modeling of fire spread through a fuel bed. Tenth Symp. (Int.) on 

Combust., pp. 997-1007, illus. Pittsburgh: The Combustion Institute. 

Martin, S. 

1964. Ignition of organic materials by radiation. Fire Res. Abstr. and Rev. 

6(2): 85-98, illus. 

McCarter, R. J., and A. Broido. 

1965. Radiative and convective energy from wood crib fires. Pyrodynamics 2: 

65-85, illus. 

Mutch, R. W. 

1964. Ignition delay of ponderosa pine needles and sphagnum moss. J. Appl. Chern. 

14: 271-275. 

Rothermel, Richard C., and Hal E. Anderson. ~~ 

196E. Fire spread characteristics determined in the laboratory. U.S. Forest 

Serv. Res. Pap. INT-30, 34 pp., illus. 

Schuette, Robert D. 

1965. Preparing reproducible pine needle fuel beds. U.S. Forest Serv. Res. Note 

INT-36, 7 pp., illus. 

Simms, D. L. 

1960. Ignition of cellulosic materials by radiation. Combust. and Flame 4(4): 

293-300, illus. 

1961. Experiments on the ignition of cellulosic materials by thermal radiation. 

Combust. and Flame 5(4): 369-375, illus. 

1963. On the pilot ignition of wood by radiation. Combust. and Flame 7(3): 

253-261, illus. 

Thomas, P. H. 

1963. The size of flames from natural fires. Ninth Symp. (Int.) on Combust., 

pp. 844-859. New York: Academic Press, Inc. 

and Margaret Law. -------1965. Experiments on the spread of fire. Rep. on Forest Res. 1965: 124-130, illus. 

Wooliscroft, M. J., and Margaret Law. 

18 

1967. A report on forest fire fieldwork. Joint Fire Res. Organ., Fire Res. Note 

647, 14 pp., illus. 
Symbol 

A 

cf 

c 

D 

E 

E 

w 

c 

L 

Lt 

M 

MC 

NRE 

Q 

Qig 

R 

Tl 

T2 

TF 

TI 

T c 

vl 

v2 

VF 

VL 

Definition 

area 

specific heat of fuel 

specific heat of water 

flame depth 

APPENDIX 

emissive power of fire 

combustion zone emissive power 

flame emissive power 

configuration factor 

fuel heat content 

heat of desorption 

flame length 

latent heat of vaporization 

moisture content 

fuel moisture content, ovendry 

Reynolds number 

heat per vertical cross section of bed 

heat to raise 1 lb. fuel to ignition 

rate of spread 

ambient temperature 

boiling temperature 

temperature of flame zone 

ignition temperature 

temperature of combustion zone 

void volume per unit of load area 

fuel volume per unit of load area 

fuel bed regression burning rate 

liquid burning velocity 

Measure 

ft. 2 

0.327 

1.000 

ft. 

B . t . u. I ft .. 2 

B • t . u. I ft . 2 

B. t. u. I ft. 2 

B.t.u./lb. 

B.t.u./lb. 

ft. 

B.t.u. 

lb./lb. 

percent 

B. t. u. I ft. 2 

B.t.u./lb. 

ft. /hr. 

ft. 3jft. 2 

ft. 3jft. 2 

ft./sec. 

ft./sec. 

hr. 

hr. 

hr. 

19 
Symbol 

a 

d 

h c 

m 

(J 

a 

(J 

20 

Definition 

attenuation constant 

characteristic dimension 

convective heat transfer coefficient 

weight loss rate 

total heat flux 

time 

fuel bed depth 

weight of fuel per unit of load area 

separation distance 

emissivity of combustion zone 

emissivity of flame zone 

horizontal convective heat transfer coefficient 

bed void volume-to-surface area ratio 

dynamic viscosity 

kinematic viscosity 

bulk density of fuel bed 

fuel particle density 

gas density 

particle surface area-to-volume ratio 

Stefan-Boltzman constant 

Measure 

ft. -l 

ft. 

B.t.u./ft. 2 - hr. - 0 

lb./sec. 

B.t.u./ft. - hr. 

hr. 

ft. 

lb./ft. 2 

ft. 

ft. 3 /ft. 2 

~~ 

ft. 2 /sec. 

lb./ft. 3 

lb./ft. 3 

lb./ft. 3 

ft. 2 /ft. 3 

B. t. u./ft. - hr. 0 

-

AFLC/HAFB, Ogden 
Anderson, Hal E. 

1969. Heat transfer and fire spread. U.S. Dep. Agr., Forest Serv., 

Intermountain Forest and Range Exp. Sta., Ogden, Utah 84401. 

20 pp., illus. (USDA Forest Serv. Res. Pap. INT-69) 

Experimental testing of a mathematical model showed that radiant heat 

transfer accounted for no more than 40% of total heat flux required to 

maintain rate of spread. A reasonable prediction of spread was possible 

by assuming a horizontal convective heat transfer coefficient when certain 

fuel and flame characteristics were known. Fuel particle size had a linear 

relation to residence time of the flame while fuel bed porosity influenced 

burning rate. Burning regimes of liquid pool fires (turbulent, transitional, 

and laminar) appeared to also apply to moving fires in solid fuels. 

Key words: fire research; rate of spread; heat transfer; radiation; 

convection; heat flux; burning rates. 

Ander son, Hal E. 

1969. Heat transfer and fire spread. U.S. Dep. Agr., Forest Serv., 

Intermountain Forest and Range Exp. Sta., Ogden, Utah 84401. 

20 pp., illus. (USDA Forest Serv. Res. Pap. INT-69) 

Experimental testing of a mathematical model showed that radiant heat 

transfer accounted for no more than 40% of total heat flux required to 

maintain rate of spread. A reasonable prediction of spread was possible 

by assuming a horizontal convective heat transfer coefficient when certain 

fuel and flame characteristics were known. Fuel particle size had a linear 

relation to residence time of the flame while fuel bed porosity influenced 

burning rate. Burning regimes of liquid pool fires (turbulent, transitional, 

and laminar) appeared to also apply to moving fires in solid fuels. 

Key words: fire research; rate of spread; heat transfer; radiation; 

convection; heat flux; burning rates. 

Anderson, Hal E. 

1969. Heat transfer and fire spread. U.

Intermountain Forest and Range Exp

20 pp., illus. (USDA Forest Serv. Res

Experimental testing of a mathematical mod

transfer accounted for no more than 40% of 

maintain rate of spread. A reasonable predi

by assuming a horizontal convective heat tran

fuel and flame characteristics were known. F

relation to residence time of the flame while 

burning rate. Burning regimes of liquid pool 

and laminar) appeared to also apply to moving 

Key words: fire research; rate of spread

convection; heat flux; burning rates. 

Anderson, Hal E. 

1969. Heat transfer and fire spread. U.

Intermountain Forest and Range Exp

20 pp., illus. (USDA Forest Serv. Res

Experimental testing of a mathematical mo

transfer accounted for no more than 40% o

maintain rate of spread. A reasonable predi

by assuming a horizontal convective heat tran

fuel and flame characteristics were known. F

relation to residence time of the flame while 

burnip.g rate. Burning regimes of liquid pool 

and l~inar) appeared to also apply to moving 

Key words: fire research; rate of spread

convection; heat flux; burning rates. 
Headquarters for the Intermountain Forest and 

Range Experiment Station are in Ogden, Utah. 

Field Research Work Units are maintained in: 

Boise, Idaho 

Bozeman, Montana (in cooperation with 

Montana State University) 

Logan, Utah (in cooperation with Utah 

State University) 

Missoula, Montana (in cooperation with 

University of Montana) 

Moscow, Idaho (in cooperation with the 

University of Idaho) 

Provo, Utah (i n c o o p era t i on with 

Brigham Young University) 
FOREST SERVICE CREED 

The Forest Service of the U. S. Department of 

Agriculture is dedicated to the principle of 

multiple use management of the Nation's forest resources for sustained yields of wood, 

water, forage, wildlife, and recreation. 

Through forestry research, cooperation with 

the States and private forest owners, and management of the National Forests and National 

Grasslands, it strives -as directed by Congress - to provide increasingly greater service 

to a growing nation.