Perturbation analysis of the heat transfer in porous media with small thermal conductivity

An approximate analytical solution for the one-dimensional problem of heat transfer between an inert gas and a porous semi-infinite medium is presented. Perturbation methods based on Laplace transforms have been applied using the solid thermal conductivity as small parameter. The leading order approximation is the solution of Nusselt (or Schumann) problem. Such solution is corrected by means of an outer approximation. The boundary condition at the origin has been taking into account using an inner approximation for a boundary layer. The gas temperature presents a discontinuous front (due to the incompatibility between initial and boundary conditions) which propagates at constant velocity. The solid temperature at the front has been smoothed out using an internal layer asymptotic approximation. The good accuracy of the resulting asymptotic expansion shows its usefulness in several engineering problems such as heat transfer in porous media, in exhausted chemical reactions, mass transfer in packed beds, or in the analysis of capillary electrochromatography techniques.