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Mixed convection over a horizontal plate : connecting boundary layer flows

Consider a flat horizontal plate aligned parallel to a uniform flow with velocity U∞ and temperature T∞. It is assumed that a heat source (or sink) of strength Q is at the leading edge of the plate and that the plate is adiabatic everywhere else. In the limit of large Reynolds number Re (boundary layer approximation) a similarity solution exists. Besides the Prandtl number Pr a second dimensionless parameter K appears in the dimensionless equations which describes the strength of the buoyancy effects. In case of the flow above a plate cooled at its leading edge (K < 0) two solution branches exist for buoyancy parameters K between some critical value K c < 0 and K = 0. Both solution branches are connected at K c . For K small and negative, one solution can be viewed as a perturbation of the Blasisus solution, where the buoyancy effects do not influence the velocity profile significantly, while the other solution branch has a large region with reverse flow. The aim of the present work is to discuss which of the two solutions for K < 0 is of physical relevance and stable with respect to small perturbations. After presenting the basic equations steady flows are presented which connect both similarity solutions.