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 double layer of solid with differing densities. As the smouldering front progresses into the solid it leaves behind an inert porous medium through which oxidizer is able to diffuse to the front. It is assumed that the reactive solid is sufficiently dense for no oxidizer to be present. The oxidizer concentration on one face of the slab is specified, the other being impervious to the transport of reactants. Dimensionless equations and boundary conditions are obtained for the concentration of oxidizer in the porous medium. These are solved to first order by use of a complex-variable method and a hodograph transformation giving the shape of the smouldering front for various parameter combinations. The analysis is extended to the case where the layers are of unequal thickness. Simple expressions for the shape of the front and the oxidizer concentration are obtained when one layer thickness is large. The model here considered is a first step in a more comprehensive analysis of smouldering in a non-uniform medium.