Numerical Solution of a Gasification Problem

Abstract

A problem of gasification and heating of a solid due to the action of an external energy source is discussed. The problem involves a moving boundary when the solid gasifies. At parts of the boundary where gasification is taking place, a model problem looks very much like the one-phase Stefan problem with an energy source at the moving boundary. However, any gas produced is assumed to blow away immediately, and there is no conduction to the solid from the outside, even when the surface temperature of the solid is below the gasification temperature. Accordingly, if the temperature is extended to a function defined over all space by setting it equal to the gasification temperature outside, the temperature will not necessarily be continuous at the boundary, and instead a Neumann condition may be satisfied there. Also, no resolidification is possible, so that the region occupied by the solid cannot increase. Thus, one has the possibility of a situation in which the boundary may alternately move and be stationary.