On Nonadiabatic Condensed Phase Combustion

We analyze the effects of melting and volumetric heat losses on the propagation of a reaction front in condensed phase combustion. Considering both homogeneous and heterogeneous models for the reaction rate, we calculate the propagation velocity for steady, planar burning as a function of the parameters in the problem. In particular, we show that this quantity is a multi-valued function of the heat loss parameter. We interpret the critical value of this parameter at which the propagation velocity has a vertical tangent, and which varies with the melting parameter, as an extinction limit beyond which a steady, planar combustion wave cannot sustain itself. We also present a model for nonsteady, nonplanar burning and consider the linear stability of the steady, planar solution. As in the adiabatic case, this basic solution is unstable to pulsating disturbances for sufficiently large values of a modified activation energy parameter. We show, in agreement with experimental results, that the effects of heat loss, as well as melting, are destabilizing in the sense that the neutral stability boundary becomes more accessible when these phenomena are taken into account.