The effect of wind on combustion waves with reactant depletion

A simple model for the propagation of an exothermic reaction is proposed accounting for reactant depletion and for heat transport via advection (wind). To study travelling-wave solutions, we assume that the reactant ignites at a specified temperature. The speed of propagation of the resulting combustion wave depends on ambient wind conditions. This dependence on wind conditions is determined explicitly for simple reaction dependence on temperature, and stability is examined. An existence criterion is determined for general reaction dependence on temperature. It is shown that no travelling wave can exist if there is too great a headwind and that tailwinds do not cause such extinction. We also determine conditions on the reaction rate term for which only a single temperature maximum is allowed. Numerically obtained temperature profiles are included to demonstrate these results.