Similarity solutions in axisymmetric mixed-convection boundary-layer flow |
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Authors: | T Mahmood J H Merkin |
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Affiliation: | (1) Department of Applied Mathematical Studies, University of Leeds, LS2 9JT Leeds, UK |
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Abstract: | The similarity equations for mixed-convection axisymmetric boundary-layer flow are considered. The equations involve a buoyancy parameter and a curvature parameter . The equations are solved numerically and it is found that for large , and of O(1), an asymptotic solution is approached, the nature of which is discussed. When is also large, of O( 1/4), the problem, at leading order, becomes independent of the mainstream and the free-convection limit is obtained. This problem is also discussed, including the behaviour for large values of 0, the free-convection curvature parameter. For < 0 we find that the solution can be continued past the point where the wall heat transfer becomes zero (where previous mixed-convection similarity solutions in plane geometry were terminated) with the solution ending as 0–. The nature of this limit is also discussed. For < 0 it is also found that there are solutions only in
b
= < 0 with two branches of solution bifurcating out of =
b
, and values of
b
are computed for a range of . The behaviour of the solution for large values of the curvature parameter , and of O(1), is discussed where it is shown that the solution proceeds in inverse powers of log . |
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Keywords: | |
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