Effect of domain perturbations on the critical condition for steady-state thermal explosions

A region heated by a temperature-dependent source is said to be stable if the heat conducted to the surroundings can balance the heat generated in the region. The critical value of the Frank-Kamenetskii number gives the limit of stability, the point at which a steady temperature field is no longer possible. Assuming that the critical Frank-Kamenetskii number can be obtained for a symmetric region where the problem is one-dimensional, we present a method for determining how it changes as the region is displaced into a less-symmetric region. We find that the displacement can be either stabilizing or destabilizing. The case of exponential heat generation is fairly well-predicted by the case of linear heat generation.