Mixed convection on a vertical surface with a prescribed heat flux: the solution for small and large Prandtl numbers
Tóm tắt
The mixed convection boundary-layer flow over a vertical surface with a prescribed surface heat flux is considered for both large and small values of the Prandtl number. The similarity equations are treated first. It is shown that, for large values of the Prandtl number, the solution approaches the forced convection limit with the free convection effects having only a small perturbation on this. The opposite is seen to be the case for small values of the Prandtl number, now free convection becomes the dominant heat transfer mechanism. A consequence of this is seen to be that the range of negative buoyancy parameter (opposed flow) over which a solution can exist decreases to zero as the Prandtl number is decreased. The scalings worked out for the similarity equations are then applied to the general boundary-layer flow, with the particular example of a uniform stream over a flat plate with uniform surface heat flux being treated in detail. Again it is seen that, for large Prandtl numbers, the solution approaches the forced convection limit whereas, for small Prandtl numbers, free convection dominates the flow. The effect of this is seen, for opposed flow, to delay the onset of separation for large Prandtl numbers, and to bring the separation point closer to the leading edge as the Prandtl number is decreased. An estimate for this effect is obtained.
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