Similarity Solutions for Free Convection Between Two Parallel Porous Walls at Different Temperatures

Abstract

Problem statement: A two dimensional steady laminar free convective flow of viscous incompressible fluid between two parallel porous walls is considered. Approach: Using the similarity variable, the partial differential equations were reduced to ordinary differential equations. The coupled ordinary differential equations were solved numerically using shooting method. The effect of various physical parameters, such as the Prandtl number, Grashof number, permeability parameter and ratio of the free stream velocity to parallel wall parameter on the boundary layer velocity and skin-friction coefficient were investigated. Results: Some of the several important findings of the results were (i) the fluid velocity increased as either of the Grashof number, permeability parameter, ratio of free stream velocity parameter to parallel wall parameter was increased. (ii) The fluid temperature decreased as either of the Grashof number, ratio of free stream velocity parameter to parallel wall parameter increased and increased as permeability parameter was increased. (iii) Skin friction increase owing to an increase in Grashof number, ratio of free stream velocity parameter to parallel wall parameter and decrease with increasing permeability parameter. In this study, a similarity solution for free convective flow between two parameter porous walls situated a distance L apart was considered. Numerical results were presented to illustrate the details of the flow, skin-friction characteristics and their dependence on the flow conditions and fluid properties. Conclusion: In particular, we found that, the fluid velocity increased as either of the Grashof number, permeability parameter, ratio of free stream velocity parameter to parallel wall parameter was increased.