The influence of variable permeability on vortex instability of a horizontal combined free and mixed convection flow in a saturated porous medium

A linear stability theory is used to analyze the vortex instability of combined free and mixed convection boundary layer flow in a saturated porous medium incorporating the variation of permeability and thermal conductivity due to paking particles with non-uniform temperature. Forchheimer's extended-Darcy model is used. Local Nusselt number for the base flow are presented for both uniform permeability (UP) and variable permeability (VP) cases. An implicit finite difference method is used to solve the base flow and the resulting eigenvalue problems are solved numerically. The critical Peclet and Rayleigh numbers and the associated wave numbers are obtained for both UP and VP cases. The results indicate that, the inertia coefficients 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. (c) 2007 WILEY-VCH Vertag GmbH & Co. KGaA, Weinheim.