Stability of the shear-thinning boundary-layer flow over a flat inclined plate

In this study, we consider the boundary-layer flow of an inelastic non-Newtonian fluid over an inclined flat plate. Using two popular generalized Newtonian models, we determine base flow profiles and associated linear stability results for a range shearthinning fluids. In addition to neutral stability curves, we also present results concerning the linear growth of the Tollmien–Schlichting waves as they propagate downstream. Furthermore, to gain an insight into the underlying physical mechanisms affecting the destabilization of the disturbances, an integral energy equation is derived and energy calculations are presented. Results from all three analyses suggest that the effect of shear-thinning will act to stabilize the boundary-layer flow. Consequently, it can be argued that the addition of shear-thinning agents could act as a passive control mechanism for flows of this nature.