Shear Flow Over a Wall With Variable Temperature

Abstract

The Leveque solution for forced convection due to shear flow over a plate is one of the basic solutions of convective heat transfer. The solution is exact if the fluid velocity is linear, such as that generated by the movement of parallel plates. The solution is asymptotic if the thermal boundary layer is much thinner than the velocity boundary layer, such that the local velocity profile is approximately linear. This occurs for developing thermal boundary layers. Although the author discussed the general case, Leveque originally considered shear flow over a plate with a sudden constant temperature change. The problem was subsequently extended to the constant heat flux case by Worsoe-Schmidt. In both instances exact similarity boundary layer solutions are obtained. In this note he considers the variable wall temperature case. Both analytic and numerical methods will be used.