Variable porosity effect on vortex instability of a horizontal mixed convection flow in a saturated porous medium

A numerical analysis is made to analyze the variable porosity effect on the vortex mode of instability of a horizontal mixed convection boundary layer flow with a uniform free stream velocity in a saturated porous medium. The porosity of the medium is assumed to vary exponentially with distance from the wall. In the base flow, similarity solutions are obtained for the case of constant heat flux boundary condition. The stability analysis is based on the linear stability theory and the resulting eigenvalue problem is solved by the local similarity method. It is found that the variable porosity effect tends to increase the heat transfer rale and destabilize the flow to the vortex mode of disturbance. The effects of fluid-solid thermal conductivity ratio on the heat transfer and vortex instability are more significant for a uniform porosity medium than for a variable porosity medium.