Diffusion-controlled smoulder propagation in a composite slab

The steady propagation of a thin smouldering front parallel to the faces of a composite reactive slab has been considered. The slab consists of a doub le layer of solid with differing densities. As the smouldering front progre sses into the solid it leaves behind an inert porous medium through which o xidizer is able to diffuse to the front. It is assumed that the reactive so lid is sufficiently dense for no oxidizer to be present. The oxidizer conce ntration on one face of the slab is specified, the other being impervious t o the transport of reactants. Dimensionless equations and boundary conditio ns are obtained for the concentration of oxidizer in the porous medium. The se are solved to first order by use of a complex-variable method and a hodo graph transformation giving the shape of the smouldering front for various parameter combinations. The analysis is extended to the case where the laye rs are of unequal thickness. Simple expressions for the shape of the front and the oxidizer concentration are obtained when one layer thickness is lar ge. The model here considered is a first step in a more comprehensive analy sis of smouldering in a non-uniform medium.