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=2/3
ln{H
φ/2(1-ε)(
ΣNi)}
+2/3
ln{(1+
θ0/Θ)(1-λ)
F(Θ)/√1
τκ(1-
F)
4}
-2/3
ln{1-4(
RΘ/
E)(1-
F(Θ))/
F(Θ)}
+3/4
ln{
E/
RΘ+2
E/3
RΘ (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, x
0 : reduced thickness of heat transfer coefficient at wood surface,
Ni : 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.
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