Variable Permeability Effect on Vortex Instability of Non-Darcian Mixed Convection Flow Over a Horizontal Permeable Surface Embedded in a Saturated Porous Medium

A linear stability theory is used to analyze the vortex instability of a horizontal mixed convection boundary layer flow in a saturated porous medium. The non-Darcian effects, which include the inertia force and surface mass flux are examined. The variation of permeability in the vicinity of the solid boundary is approximated by an exponential function. The variation rate itself depends slowly on the streamwise coordinate, such as to allow the problem to possess a set of solutions, invariant under a group of transformations. Velocity and temperature profiles as well as local Nusselt number for the base flow are presented for the uniform permeability (UP) and variable permeability (VP) cases. An implicit finite difference method is used to solve the base flow and the resulting eigenvalue problems are solved numerically. The critical Peclet number and the associated wave number are obtained for both UP and VP cases. The results indicate that, the inertial coefficient reduces the heat transfer rate and destabilizes the flow to the vortex mode of disturbance. The effect of variable permeability tends to increase the heat transfer rate and destabilize the flow to the vortex mode of disturbance. Further, for blowing, the Nusselt numbers are lower than those for an impermeable surface and the flow is more susceptible to the vortex instability, while the opposite trend is true for suction.