Variable porosity and thermal dispersion effects on vortex instability of a horizontal natural convection flow in a saturated porous medium

A numerical analysis is made to analyze the variable porosity and thermal dispersion effects on the vortex mode of instability of a horizontal natural convection boundary layer flow in a saturated porous medium. The porosity of the medium is assumed to vary exponentially with distance from the wall. In the base flow, the governing equations are solved by using a suitable variable transformation and employing an implicit finite difference Keller Box method. The stability analysis is based on the linear stability theory and the resulting eigenvalue problem is solved by the local similarity approximations. The results indicate that both effects increase the heat transfer rate. In addition, the thermal dispersion effect stabilizes the flow to the vortex mode of disturbance, while the variable porosity effect destabilizes it.