Criteria for thermal explosions with and without reactant consumption

Abstract

Thermal explosions occur when reactions evolve heat too rapidly for a stable balance between heat production and heat loss to be preserved. Even when reactions are kinetically simple, and obey the Arrhenius equation, the differential equations for heat balance and reactant consumption cannot be solved explicitly to express temperatures and concentrations as functions of time unless strong simplifications are made. This difficulty exists for the spatially uniform (Semenov) as well as for the distributed temperature (Frank-Kamenetskii) case. Solutions become possible if strong simplifications are made (no reactant consumption; approximations to the Arrhenius term). Ignition is then represented by the threshold at which stationary states disappear. A single parameter (see appendix for definitions and symbols) summarizes the criteria for ignition. In the spatially uniform case, the Semenov parameter has the critical value e_1. In the distributed temperature case, the Frank-Kamenetskii parameter has critical values that depend on the geometry.