Combustion Fronts in Porous Media: Modeling and Analytical Simulation

Abstract

In this paper, a mathematical model for forward propagation of a combustion front with Arrhenius kinetics through a porous medium is presented. The reaction involves oxygen and a solid fuel We assume that this solid fuel depends on the space variable. Under an incompressible assumption, we obtain a simple model whose variables are temperature, oxygen mass fraction, fuel concentration, seepage velocity and pressure. We also assume that the amount of gas produced by the reaction is equal to the amount of gas consumed by it. By actual solution, we prove the existence and uniqueness of solution of the model. We examine the properties of solution under certain conditions. Using large activation energy asymptotics, the analytical solution of the model was provided via Homotopy perturbation method (HPM) and the results are presented graphically. It is discovered that the influence of Frank-Kamenetskii number on the heat transfer and species consumption is quite significant.