Variable permeability and inertia effect on vortex instability of natural convection flow over horizontal permeable plates in porous media

In this paper, the effect of variable permeability, inertia, and surface mass flux on vortex instability of a horizontal free convection boundary layer flow in a saturated porous medium is examined by linear stability theory. Forchheimer extended-Darcy model is used. The variation of permeability in the vicinity of the solid boundary is approximated by an exponential function. Velocity and temperature profiles as well as dimensionless local heat transfer rates in the form of Nusselt number for the base flow are presented for the uniform permeability (UP) and variable permeability (VP) cases. The critical Rayleigh numbers and the associated wave numbers are obtained for both UP and VP cases for non-parallel (NP) and quasi-parallel (QP) flows. The results indicate that the inertia coefficient reduces the heat transfer rate and destabilizes the flow to the vortex mode of disturbance. The effect of variable permeability tends to increase the heat transfer rate and destabilize the flow to the vortex mode of disturbance. Further, for blowing, the Nusselt numbers are lower than those for an impermeable surface and the flow is more susceptible to the vortex instability, while the opposite trend is true for suction. It is demonstrated that the NP flow model predicts a more stable flow than the QP flow model.