The Onset of Longitudinal Vortices in Mixed Convective Flow over an Inclined Surface in a Porous Medium

Abstract

The conditions marking the onset of vortex instability in mixed convective flow over an inclined surface in a saturated porous medium are investigated by means of a linear stability analysis. The basic state is assumed to be the steady two-dimensional boundary layer flow. The three-dimensional perturbation equations are simplified on the basis of a scaling argument whereby most of the streamwise derivatives of the disturbances are found to be negligible. For vortex disturbances, the resulting simplified equations in terms of the amplitude are solved approximately by the local similarity method. The eigenvalue problem is 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 deg with respect to the inclined surface. Both aiding and opposing external flows are considered. The critical parameters and the critical wave numbers of disturbances for the two cases are obtained. It is found that the effect of the external flow is to suppress the growth of vortex disturbances in both aiding and opposing flows. At the same value of the mixed convection parameter, the opposing flow is found to be more unstable than the aiding flow.