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Variable permeability effect on vortex instability of a horizontal natural convection flow in a saturated porous medium with variable wall temperature

A linear stability theory is used to analyze the vortex instability of free convection boundary layer flow in a saturated porous medium adjacent to a horizontal surface where the wall temperature is a power function of the distance from the origin. The variation of permeability in the vicinity of the solid boundary is approximated by an exponential function. The variation rate itself depends slowly on the streamwise coordinate, such as to allow the problem to possess a set of solutions, invariant under a group of transformations. 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 critical Rayleigh numbers and the associated wave numbers are obtained 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.