Theory for Endothermic Gasification of a Solid by a Constant Energy Flux

Abstract

By asymptotic methods, which treat the ratio of the thermal energy to the activation energy for gasification as a small parameter, the entire temperature-time history is derived for a semi-infinite solid, whose surface is subjected to a constant energy flux. It is found that an initial stage of inert heat-conduction is separated from a final stage of transport-controlled gasification by a short transition stage, which contains reactive-diffusive and transient-diffusive zones if distributed gasification occurs. The time to onset of gasification is obtained from an analysis of the transition stage. The manner of approach to quasisteady regression is described by the perturbation analysis. The results are of interest in connection with ignition of reactive solids which experience exothermic reactions only in the gas phase. In particular, it is shown that within the accuracy to which experiments can be performed, the dependence of ignition time on heat flux for such materials is identical with the dependence for materials which exhibit condensed-phase or interfacial ignition reactions, provided that the gas-phase reaction time is small compared with the time to onset of gasification.