Conjugate free convection from vertical fins embedded in a porous medium

The problem of conjugate free convection in a porous medium from a vertical plate and a vertical cylindrical fin is considered. The governing equations for 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 interface. The heat flow in the fin is taken to be either two-dimensional or one-dimensional, in order to compare the results provided by both approaches. The nondimensional parameters that appear are the convection-conduction parameter, N-cc , and the aspect ratio of the fin, lambda(p) for the plate fin and lambda(c) for the cylindrical fin. The surface curvature parameter lambda(C) appears as a parameter which is directly dependent on lambda(c) in the case of the cylindrical fin. Considering two-dimensional conduction in the solid fin is a more realistic approach from a practical standpoint, but the shortcoming of specifying zero heat flux at the tip of the fin is discussed.