A free boundary problem related to the combustion of a solid

The purpose of this paper is to take direct account of the physics associated with a surface that regresses dynamically during the ignition transient. Since the depletion rate of the surface is expected to be most heavily influenced by oxidation reactions occurring directly at the surface of the solid, we will neglect any external gas-phase and internal solid-phase reactions. Hence, we assume a system in which there is a vigorous Arrhenius surface reaction which drives the depletion of the boundary. In addition, we will assume an impervious solid and neglect the transport of heat by conduction inside the solid. Neglect of solid-phase energy transport by conduction limits the practical appeal of this modelling effort since it is equivalent to assuming small conductivity in the solid compared to the gas-phase. Therefore, we treat the case where heat is conducted toward the solid surface where it supports the exothermic surface reactions; the rest of the heat is lost to the surroundings by conductive flow away from the surface. We also neglect exchange of heat with the surroundings by radiation.