A formulation of combined forced and free convection past horizontal and vertical surfaces

The boundary-layer flow over semi-infinite vertical and horizontal flat plates, heated to a constant temperature in a uniform free stream, is studied when the buoyancy forces either aid or oppose the development of the boundary layer. Different mixed-convection parameters are introduced in the formulation of the respective problems involving horizontal and vertical surfaces such that smooth transition from one convective limit to the other is possible; in particular the governing equations for the purely forced and free convection cases are respectively recovered from the zero values of the Grashoff and Reynolds numbers. An effective numerical scheme is developed to incorporate the integral boundary condition appearing in the governing equations of the flow over a horizontal flat plate, thereby rendering numerical convergence possible. Locally similar and locally nonsimilar solutions are also obtained. They show considerable deviation of the velocity profiles from the rigorous finite-difference solution in the region of intense mixed convection, although good agreement exists for the wall values, as represented by the friction factors and Nusselt numbers, which are of primary interest. Simple explicit expressions correlating local Nusselt numbers over the entire range of mixed convection intensity when Prandtl numbers vary from 0.1 to 10 are determined. The separation points in opposing flows are also obtained.