Accounting for reactant consumption in the thermal explosion problem. part IV. numerical solution of the arrhenius problem

Abstract

The Marching Taylor expansion method is used to determine the critical conditions for the thermal explosion problem with the reaction governed by the Arrhenius reaction kinetic equation. The contrast between the behavior with high θ ad and high θ a, low θ ad and low θ a as well as high θ ad and low θ a is demonstrated. The effect of the degree of reaction is examined. The criticality boundaries with different degrees of reaction are established as a function of the ambient temperature. Comparison with results existing in the literature is shown. Finally an approximate method for determining the critical state is presented. This reduces the computation time needed for establishing accurately the critical states.