Modeling and simulation of combustion fronts in porous media

We study a model for forward propagation of a combustion front through a porous medium. The reaction involves oxygen and a solid fuel. We assume that this solid fuel depends on the space variable. We also assume that the amount of gas produced by the reaction is equal to the amount of gas consumed by it. By actual solutions, we prove the existence and uniqueness of solution of the model. We show that temperature is non-decreasing function of time. We use the similarity variable to transform the system of partial differential equations, describing the problem under consideration, into a boundary value problem of coupled ordinary differential equations and an efficient numerical technique is implemented to solve the reduced system. The results are presented graphically and discussed. It is discovered that the heat transfer and species consumption are significantly influenced by the Frank–Kamenetskii number.