Combustion pseudo-waves in a system with reactant consumption and heat loss

A model for the combustion of a reactant with heat loss in an infinite two-dimensional layer or an infinitely long circular cylinder is derived. Using center manifold techniques the model is shown to reduce to a one-dimensional model on an infinite region for both geometries. For an exothermic first-order reaction with Arrhenius temperature dependence, a numerical method is used to calculate solutions and comparisons are made with the no-reactant consumption case. Traveling pseudo-waves are shown to exist and their speeds determined. A first-order estimate of the reaction zone thickness, obtained by perturbation methods, is shown to be in excellent agreement with the full numerical solution.