Natural convection from an isothermal vertical surface embedded in a thermally stratified high-porosity medium

Abstract

Non-Darcy effects including convective, boundary and inertia effect on the natural convection boundary layer flow along an isothermal vertical surface embedded in a thermally stratified high-porosity medium are considered and solved. The ambient temperature (less than the vertical surface temperature) increases linearly with the height measured from the leading edge and its slope is proportional to the stratification parameter S. Positive values of S implies a stable, stratified ambient fluid. A flow reversal is observed for S < 1. But it becomes very weak and insignificant when the Darcy and inertia resistances on the flowing fluids in high-porosity medium increase. For S < 1, the flow reversal is evident. Such flow regime, in fact, is modelled by the elliptic type partial differential equations and this situation is not the scope of the present paper. In this study, only S < 1 is considered because the governing boundary layer equations are of parabolic type. It is found that as S increases, a plume flow arises at the end of heating part of the vertical surface where minimum temperature difference (or thermal buoyancy) occurs. For small values of S, the plume flow is not obvious and the flow regime behaves like that of S = 0.