Combustion waves with reactant depletion

A simple model for the propagation of a combustion wave is proposed and the speed of propagation is predicted. It is assumed that the reactant ignites at a specified temperature and then burns until depleted with reaction rat e dependent on temperature and reactant concentration. The exact solution a nd linear stability are determined in the case of constant heat generation and a numerical scheme is developed to generate traveling wave solutions in the more general case. This numerical method is applied to the case where the temperature dependence of the reaction rate is modeled by the Arrhenius function.