The Thermal Explosion Confined by a Constant Temperature Boundary: II— The Extremely Rapid Transient

Abstract

The extremely rapid transient phase of a thermal explosion in a vessel with constant wall temperature is described. The solution is developed in terms of a nearly-inert, cool, reactant-rich conduction-controlled zone and a highly localized veritable fireball controlled by chemical reaction rates, which are separated by a distinct zone of time-invariant spatial structure. In the first region the temperature is only slightly different from the initial value. In contrast, the variation in temperature in the fireball is large, ranging almost to the adiabatic explosion value. The rise in temperature is accompanied by significant fuel consumption. When the fireball formation is nearly complete, the fuel available therein is vanishingly small. The theoretical formulation provides a specific time scale for the rapid transient process, which is extremely short in comparison to that in the induction period which precedes the explosive event. The fireball size, found to depend on the material properties of the combustible, is extremely sensitive to the activation energy of the one-step reaction model.