The onset of longitudinal vortices in mixed convection flow over an inclined surface in a porous medium with variable permeability

摘要

The conditions marking the onset of vortex instability in mixed convection flow over an inclined surface in a saturated porous medium with variable permeability are investigated by means of a linear stability analysis. The permeability of the medium is assumed to vary exponentially with distance from the wall. Velocity and temperature profiles as well as local Nusselt number for the base flow are presented for both uniform permeability (UP) and variable permeability (VP) cases. The resulting equations for both base and disturbance flows are solved numerically for the cases of (1) an inclined surface at constant wall temperature with free stream velocity at zero angle of incidence with the inclined surface and (2) an inclined surface with constant heat flux with free stream velocity at 45° with respect to the inclined surface. The critical parameter Pex*tan2φ and the critical wave numbers k* are computed for both UP and VP cases. It is found that the variable permeability effect tends to increase the heat transfer rate and destabilize the flow to the vortex mode of disturbance.