Variable permeability effect on vortex instability of mixed convection flow in a semi-infinite porous medium bounded by a horizontal surface

Abstract

A linear stability analysis is performed for the study of the vortex instability of mixed convection flows in a semi-infinite porous medium adjacent to a horizontal impermeable surface. The permeability of the medium is assumed to vary exponentially with distance from the wall. Two different aiding flows are considered: (1) flow past a horizontal impermeable surface with zero angle of incidence, and (2) stagnation point flow about a horizontal surface. 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. The resulting variable coefficient eigenvalue problem is solved numerically. The critical Peclet numbers and the associated wave numbers as a function of the mixed convection parameter M= Ra x / Pe x 3/2 are obtained for both UP and VP cases. It is found that the stagnation point flow is more stable than the case of horizontal aiding flow for both UP and VP cases. Further, the variable permeability effect tends to increase the heat transfer rate and destabilize the flow to the vortex mode of disturbance.