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: 



f Ig 



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 coefficient 

 h . The research previously reviewed by Hottel (Blinov and Khudiakov 1959) and pre- 

 sented by Thomas (1963) showed two expressions for Reynolds number: 



N 



V (8) 



RE V ' 

 m 



where : 



Vj^ = regression rate of liquid burning surface 

 d = characteristic dimension, pan diameter or flame depth 

 V = kinematic viscosity = y/p 

 y = dynamic viscosity 



p = gas density 



mi = rate of weight loss. 

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



mi = p, AV„, lb. /sec. 



^ D t 



A = d^ 



y = 



4 



