Non-planar smoulder propagation governed by diffusion

The steady propagation of a thin smouldering front in a half-space has been considered. A suitable coordinate transformation has allowed the region near the leading edge of the front to be examined for both a maintained planar surface and with surface collapse due to material shrinkage. The change in the oxidizer concentration for a small increment in the propagation speed for large time and surface collapse has been determined. The influence of two types of nonlinear diffusion on the shape of the smouldering front has been found; other cases can be dealt with in a similar manner.