Hermite-Padé approximation approach to exothermic explosions with heat loss

Abstract

We consider in this study the steady-state solutions for the exothermic chemical reaction in a slab, taking into account the heat loss to the ambient and assuming an Arrhenius-type temperature dependence. Analytical solutions are obtained for the governing nonlinear boundary value problem using the homotopy analysis method. A special type of Hermite-Padé approximation is used to extract numerical estimations of the critical Frank-Kamenetskii parameters and the critical temperatures. The consequences of heat loss are explored within the framework of a one dimensional, steady state model.