Ignition of Wood (3) Thermal Theory of Ignition of Wood by High Temperature Air

Abstract

In this report, mathematical theory of ignition of wood is developed and as a special case, an equation determining the time lag in ignition, under the conditions that the wood board is heated one-dimensionally at constant temperature, is introduced by this theory.
Obtained equation is as follows :
τ=2/3ln{Hφ/2(1-ε)(ΣN_i)}
+2/3ln{(1+θ₀/Θ)(1-λ)F(Θ)/√1_τκ(1-F)⁴}
-2/3ln{1-4(RΘ/E)(1-F(Θ))/F(Θ)}
+3/4ln{E/RΘ+2E/3R_Θ (1-F(Θ))}
τ : time lag in ignition, φ : a limit volume of producted gases in space which has height H, and unit area, Θ : heating temperature (fluid temp.), κ : heat diffusibility of wood, E : activation energy of decomposition of wood, F (Θ) : a function of Θ, x₀ : reduced thickness of heat transfer coefficient at wood surface, N_i : a coefficient of decomposition of wood on i component gas product, Σ : summation on all the component of produced gases, R,ε : constant.
Results of experiment in the last report [Bull. Fire Prev. Soc. japan, Vol. 3 No. 1, 2, (1953)] may be explained well by this equation.