Introduction 



A spreading fire is a series of particle-to-particle ignitions where the energy 

 necessary for propagation has its source within the combustion zone where particles 

 are undergoing a measurable weight loss through pyrolysis (Fons 1946) . These 

 consecutive ignitions do not depend on uniformly heated fuel. Frandsen (1971) 

 accounted for nonuniform heating ahead of the fire by defining the effective heating 

 number. 



Fuel particles ahead of a spreading fire (fig. 1) receive heat from the combustion 

 zone, which increases their internal energy. The distribution of heat within similarly 

 shaped fuel particles at ignition is dependent on the following factors: location 

 of the heat source and heat flow through the surface; surface area-to-volume ratio 

 and thermal diffusivity of the fuel. A moisture gradient can also play a major role. 

 Assuming that the net heat flux and diffusivity are fairly constant and that the 

 moisture gradient is zero, then the surface area-to-volume ratio becomes the signifi- 

 cant independent variable. Only in fine fuels (diameter <1 mm.) is heating uniform. 

 Larger fuels do not achieve uniform internal temperatures because heat impinging on 

 the particle cannot diffuse from the surface at a rate comparable to the influx of 

 heat. The result is a thermal gradient within the particle that may leave the tempera- 

 ture of the central portion, or of one side, relatively unchanged, depending on 

 whether the flow of heat is uniform over the surface or unidirectional. 



Although fire spread is attributed to particle-to-particle ignition, the interval 

 between ignitions must be averaged over a long time to obtain a rate of spread 

 representative of the bulk array. The average rate of spread can then be related to 

 the average fuel bed properties. If a constant rate of spread is achieved, the quasi- 

 steady state exists. The fuel bed can then be represented by a minimum unit fuel cell 

 that has all the characteristics of the fuel array and retains its usefulness as an 

 elemental unit volume in applying the conservation of energy (Frandsen 1971) . 



