The free-convection boundary-layer flow on a vertical surface embedded in a porous media driven by an exothermic catalytic chemical reaction on the surface is considered. The governing equations of this how are reduced to a pair of coupled, parabolic partial differential equations for the temperature and the concentration of the fluid reactant. These equations are governed by the,dimensionless chemical parameters lambda and epsilon, which are measures of the reactant consumption and the activation energy, respectively, as well as the Lewis number. Similarity solutions are obtained which are valid near the leading edge of the surface. Asymptotic solutions, which are valid at large distances downstream from the leading edge, are obtained for the two independent situations when lambda = 0 and lambda not equal 0. A numerical solution to the partial differential equations is then obtained. The numerical solution is investigated for a range of the chemical parameters lambda and epsilon, and was found to exhibit localized rapid increases in temperature when lambda and epsilon are small. Comparisons between the numerical solution and the similarity and asymptotic solutions are made and are found to be in good agreement. (C) 1997 Elsevier Science Ltd.