Non-Darcian effects on vortex instability of a horizontal natural convection flow in a porous medium

The non-Darcian effects, which include the inertia, boundary and convective effects, on the flow and vortex instability of a horizontal natural convection boundary flow in a high-porosity medium are examined. In the base flow, the governing conservation equations are solved by using a suitable variable transformation and employing an implicit finite-difference scheme developed by Keller. The stability analysis is based on the linear stability theory, and the resulting equations are solved on the basis of the local similarity approximations. The results indicate that all of these three effects reduce the heat transfer rate. In addition, the combined boundary and convective effects stabilize the flow to the vortex mode of disturbance, while the inertia effect destabilizes it.