To employ the concept of the unit fuel cell, the individual particle view must be 

 extended to the array within the unit cell. The unit cell then replaces the particle 

 as the heat absorber. Consequently, attention is focused on the heat absorbed per 

 unit volume, P D Qig> rather than on the heat absorbed per unit mass by the individual 

 particle where is the bulk density and is the heat of preignition. 



In the unit volume concept the distribution of heat within the particle is less 

 important; so the assumption that all heat is uniformly absorbed to a given depth in 

 the fuel particle (Thomas 1967) is an equally useful concept. Frandsen (1971") 

 extended the individual particle concept to the fuel array by introducing effective 

 bulk density. The problem is now resolved to the efficiency of heating the unit fuel 

 cell to ignition. The heat per unit volume, P^Qigj is necessary to bring the unit 

 cell uniformly to ignition. Therefore, the heat per unit volume for ignition at non- 

 uniform heating is ep^Q^gj where e, the effective heating number, is the efficiency. 

 The unit fuel cell is not restricted to regular arrays. In field conditions where 

 irregular arrays exist, the unit fuel cell must be described by statistical methods. 



The following brief exposition serves to show how e is related to the fire spread 

 model developed by Rothermel (1972) . 



The rate of fire spread through a fuel array depends on the static fuel parameters, 

 6, p , and Q^g> an d the dynamic source function, 1^, (Rothermel 1972). The static 



parameters are related to the absorption of energy in the preignition phase, whereas 

 the dynamic source function is related to the combustion zone. Their ratio leads to 

 the rate of fire spread through the array: 



a, 



e$P Q. 

 P ig 



(1) 



where £ is the efficiency of converting total reaction intensity, I , to propagating 

 intensity, I --the portion of intensity driving the fire (Rothermel 1972) . 



e = Effective heating number 



3 = p b //p p = P ac -ki- n g ra tio = volume occupied/total bulk volume 



= Ovendry bulk density 

 Pp = Ovendry particle density 



Q. = Heat of preignition, the heat per unit ovendry mass necessary to 

 1 ^ ignite the fuel. 



In this study, the effective heating number was related to the size (surface area-to- 

 volume ratio) of the particles making up a regular fuel array of similarly shaped 

 particles. All other variables were held constant. For convenience, the subscript p 

 has been dropped from p for the remainder of the paper. Henceforth, the particle 

 density will be denoted simply as p. 



3 



