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Critical values for some non-class A geometries in thermal ignition theory. (English) Zbl 0880.35123
Summary: In a previous paper, the authors used a path-following method for the two point boundary value problem governing the ignition of a solid reactant undergoing slow oxidation for symmetric class A geometries and showed the occurrence of multiplicity of steady states. In this paper, the problem is solved in some non-class A geometries (infinite square rod and cube), making use of finite difference discretization of the boundary value problem. It is shown that the multiplicity of steady states changes and that the critical parameters are also different from those found from the shape factor approach.
MSC:
35Q80Appl. of PDE in areas other than physics (MSC2000)
80A25Combustion, interior ballistics