Mixed convection boundary-layer flow on a horizontal flat surface with a convective boundary condition

The steady mixed convection boundary-layer flow on an upward facing horizontal surface heated convectively is considered. The problem is reduced to similarity form, a necessary requirement for which is that the outer flow and surface heat transfer coefficient are spatially dependent. The resulting similarity equations involve, apart from the Prandtl number, two dimensionless parameters, a measure of the relative strength of the outer flow M and a heat transfer coefficient gamma. The free convection, M=0, case is considered with the asymptotic limits of large and small gamma being derived. Results for the general, M > 0, case are presented and the asymptotic limit of large M being treated.