Thermal explosion theory with Arrhenius kinetics: homogeneous and inhomogeneous media

Abstract

The classical thermal explosion problem for a reactive slab with Arrhenius kinetics and small activation energy parameter is considered. Perturbation series expansions are obtained that give an expression for the critical Frank-Kamenetskii parameter. We verify that the often used ‘Frank-Kamenetskii approximation’ is the first-order problem in such an expansion procedure. The analysis is extended to a reactive slab with a random distribution of reactant. The statistical properties are incorporated in an effective thermal diffusivity that may be expressed as a function of its mean and the variance about the mean. Some other expressions are also considered. It is shown that a random distribution decreases the thermal stability when compared with criticality with mean properties.