Thermal explosion with convection in porous media: a mathematical approach

Abstract

This paper studies the interaction between natural convection and thermal explosion in porous media. The model consists of the heat equation with a nonlinear source term describing heat production due to an exothermic chemical reaction coupled with the Darcy law. The conditions for the existence of unique solutions of the energy equation are established by the Lipschitz continuity approach. The analytical solution is obtained via Olayiwola's generalized polynomial approximation method (OGPAM), which shows the influence of the parameters involved on the system. The effect of changes in values of parameters such as the Frank-Kamenetskii number, Rayleigh number, and inverse of Vadasz number are presented graphically and discussed. The results revealed that convection can change the conditions of thermal explosion.