The free convection, boundary-layer flow in a fluid-saturated porous medium near a general, three-dimensional stagnation point when heat is released by an exothermic catalytic reaction on the surface, converting a reactive component within the convective fluid to an inert product, is considered. The reaction is modelled by first-order kinetics with an Arrhenius temperature dependence. First, the flow behaviour for the initial, small time solution (unsteady flow) and certain ranges of parameter values is considered, and this is followed by the discussion of the possible steady-state solutions (large time) of the governing equations. The transition range between these two analytical solutions is performed numerically using a very efficient finite-difference scheme. It is shown that the analytical and numerical solutions are in very good agreement over appropriate time intervals and the influence of the reactant parameters lambda, delta and epsilon on the flow, heat transfer and concentration characteristics is discussed. Copyright (C) 2003 John Wiley Sons, Ltd.