Deflagration of gasifying condensates with distributed heat loss

This paper examines steady linear deflagration of condensates that undergo surface gasification followed by a one-step Arrhenius type gas phase reaction. A distributed heat loss proportional to the temperature excess above the ambient is postulated. (Adiabatic deflagration and deflagration with a radiative heat loss from the condensate-gas interface were treated in an earlier paper.) A distinguished limit asymptotic analysis for large gas-phase activation energy E' and an 0(1/ E') heat loss yields an analytical relation between the pressure p and the burning rate m. In general heat loss is found to lower m from its adiabatic value at a given p. The results for pyrolyzing condensates show that the m- p curve, which was monotonic in the absence of heat loss, is now either C-shaped (exothermic pyrolysis) or S-shaped (endothermic pyrolysis), thereby exhibiting ignition and extinction characteristics. Furthermore, extinction is now "true" (a sudden disappearance of the gas-phase reaction zone at a finite distance from the interface) rather than "effective" (recession of the reaction zone far away from the interface so that the gasification products pass away effectively unburnt). For vaporizing condensates, nonadiabaticity leaves the response qualitatively unaltered.