Mixed Convection Boundary-Layer Flow Over a Vertical Surface Embedded in a Porous Material Subject to a Convective Boundary Condition

Abstract

The mixed convection boundary-layer flow on one face of a semi-infinite vertical surface embedded in a fluid-saturated porous medium is considered when the other face is taken to be in contact with a hot or cooled fluid maintaining that surface at a constant temperature $T_\mathrm{{f}}$. The governing system of partial differential equations is transformed into a system of ordinary differential equations through an appropriate similarity transformation. These equations are solved numerically in terms of a dimensionless mixed convection parameter $\epsilon$ and a surface heat transfer parameter $\gamma$. The results indicate that dual solutions exist for opposing flow, $\epsilon <0$, with the dependence of the critical values $\epsilon _\mathrm{{c}}$ on $\gamma$ being determined, whereas for the assisting flow $\epsilon >0$, the solution is unique. Limiting asymptotic forms for both $\gamma$ small and large and $\epsilon$ large are also discussed.