Instabilities of the buoyancy layer for the Carreau fluid in thermally stratified medium

In this study, we consider the buoyancy-driven flow of a non-Newtonian fluid over an inclined flat plate immersed in a thermally stratified medium. Using the Carreau model, we determine the base flow profiles and associated linear stability results for both pseudo-plastic and dilatant fluids. For steady basic flow, the shear-thinning behavior enhances the convection and heat transfer characteristics while it is opposite for shear-thickening flow. Based on linear stability analysis, the effects of Prandtl number, tile angle, and power-law index on the transverse traveling Tolmien-Schlichting waves, the stationary longitudinal rolls and the oblique rolls are investigated. Different from the Newtonian fluids, under appropriate parameters, a new oblique rolls mode appears in dilatant fluids. Furthermore, it is shown that both the TS mode and OR mode are destabilized and stabilized for shear-thinning and shear-thickening fluids, respectively. However, non-Newtonian effects always stabilize the SL mode. These results reveal that the nature of the stability depends on the rheological properties significantly.