Incompressible boundary layer flow past a hump with temperature-dependent viscosity

Abstract

The problem of boundary layer flow past a hump placed on a flat surface, where viscosity is coupled with temperature, is investigated using triple-deck theory. The incompressible Navier–Stokes equations supplemented by the heat and viscosity equations are considered in the limit that the Reynolds number is large. The triple-deck scalings are adopted, and asymptotic expansions are used to obtain some novel triple-deck equations coupled with the thermal boundary layer. We have used the same viscosity–temperature dependence as in Jasmine and Gajjar [Int. J. Heat Mass Transfer 48, 1022–1037 (2005)], in which viscosity varies inversely proportional to the temperature. The linear analysis is performed, and the nonlinear equations are solved numerically. Our results show that increasing the characteristic constant of the viscosity leads to enhanced peaks and troughs in the pressure and in the skin friction over the hump, as compared to the constant viscosity case. This suggests that temperature-dependent viscosity is more likely to provoke separation.