Two-Dimensional Mixed Convection Along a Flat Plate

Abstract

For a horizontal plate, the axial pressure gradient induced by the buoyancy force is 0(Gr/Re{sup 5/2}). Numerous solutions have been developed by considering the free-convection effect as a perturbation quantity. Again, forced convection exists as a limit for small Gr/Re{sup 5/2} and the free-convection limit can be reached as the parameter approaches infinity. The critical difference between the flow over a horizontal plate and a vertical plate has been pointed out by Cheng and his co-workers. The buoyancy force normal to the plate can induce a vortex instability. The governing parameter for the development of this instability is Gr/Re{sup 3/2}. In this paper, the authors re-examine this problem. For a vertical plate, they show that two limits can exists for {xi} {yields} {infinity}, depending on whether Re {yields} O, or Gr {yields} {infinity}. The mixed-convection, boundary-layer solution is valid for the limit Re {yields} {theta}. The solution for the limit, Re {yields} O, is the free-convection solution, but the forced-convection effect cannot be obtained by solving mixed-convection, boundary-layer equations alone. Also, they demonstrate by order-of-magnitude arguments that Cr/Re{sup 5/2} is not the governing parameter for mixed convection along a horizontal plate. For an inclined plate, as long as no vortexmore » instability develops, Gr/Re{sup 2} is the sole parameter for mixed-convection flows. This conclusion is confirmed by recent measurements (24). The physical model of the analysis is kept simple in order to point out the important physics; thus, the forced flow is assumed along the same direction as the free convection (assisting flow), and the value of the Prandtl number is set to one (Pr = 1).« less