The transitional points of thermal explosion theory

Abstract

Thermal explosions occur when reactions generate heat too rapidly for a stable balance between heat production and heat loss to be maintained. The differential equation associated with this physical behaviour cannot be solved explicitly unless strong simplifications are made : these cases have been well-studied. For the classical problem, it is well-known that ignition phenomena continue up to a value εtr = RT a/E = 0.25. This upper bound is sharply defined, and is known as the transition point. Having developed a criterion characterising the transitional state, exact values are obtained for εtr for the three class A geometries and a range of Biot numbers using an implicit finite difference scheme. From these, an unusual relationship between εtr and reactant geometry for low Biot numbers is detected. Several approximate methods of obtaining these transition points are also described. The variational principle idea was found to give experimentally sound results with relatively little computational effort.