Mixed convection boundary-layer flow over a vertical surface embedded in a porous medium

Abstract

In this paper we have numerically investigated the existence and uniqueness of a vertically flowing fluid passed a model of a thin vertical fin in a saturated porous media. We have assumed the two-dimensional mixed convection from a fin, which is modelled as a fixed, semi-infinite vertical surface, embedded in a fluid-saturated porous media under the boundary-layer approximation. We have taken the temperature, in excess of the constant temperature in the ambient fluid on the fin, to vary as x ̄ λ , where x ̄ is measured from the leading edge of the plate and λ is a fixed constant. The Rayleigh number is assumed to be large so that the boundary-layer approximation may be made and the fluid velocity at the edge of the boundary-layer is assumed to vary as x ̄ λ . The problem then depends on two parameters, namely λ and ε, the ratio of the Rayleigh to Péclet numbers. It is found that when λ>0 (<0) there are (is) dual (unique) solution(s) when ε is grater than some negative values of ε (which depends on λ). When λ<0 there is a range of negative value of ε (which depends on λ) for which dual solutions exist and for both λ>0 and λ<0 there is a negative value of ε (which depends on λ) for which there is no solution. Finally, solutions for 0< ε⪡1 and ε⪢1 have been obtained.