In this paper the two-dimensional conjugate free convection in a porous medium is investigated from a vertical plate fin. Both physically and mathematically it is important to consider a smooth profile for the tip of the fin, such as a rounded tip of an arbitrary shape. Such fin shapes approximate well the rectangular fin, and their study allows a more accurate prediction of the heat transfer quantities, since no restrictive conditions have to be imposed, such as an insulated tip, and there are no singularities appearing in the mathematical formulation. The governing equations of the convective flow in the porous medium are coupled to the governing equation for the heat flow in the fin by the conditions of continuity of the temperature and the heat flux at the solid/porous media interface. The governing non-dimensional parameters are the convection-conduction parameter, N-cc, and the aspect ratio of the fin, lambda. (C) 2004 Elsevier Ltd. All rights reserved.