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Dual solutions in mixed convection

Published online by Cambridge University Press:  14 November 2011

G. Wilks  and
J. S. Bramley
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Synopsis

Dual similarity solutions in the context of mixed convection are presented. In contrast to the Falkner–Skan solutions the bifurcation point is found to be distinct from the point of vanishing skin friction. The eigenvalue problem arising out of a stability analysis of these solutions is examined numerically. The numerical evidence would seem to indicate that the margin of stability is associated with the onset of reverse flow as opposed to the bifurcation point, as conjectured by Banks and Drazin in 1973.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 87 , Issue 3-4 , 1981 , pp. 349 - 358
Copyright
Copyright © Royal Society of Edinburgh 1981

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References

1Merkin, J. H.. The effect of buoyancy forces on the boundary layer flow over a semi-infinite vertical plate in a uniform stream. J. Fluid. Mech. 35 (1969), 439–450.CrossRefGoogle Scholar
2Wilks, G.. A separated flow in mixed convection. J. Fluid. Mech. 62 (1974), 359–368.CrossRefGoogle Scholar
3Mocoglu, A. and Chen, T. S.. Analysis of combined forced and free convection across a horizontal cylinder. Canad. J. Chem. Eng. 55 (1977), 265–271.CrossRefGoogle Scholar
4Sparrow, E. M., Eichorn, E. and Gregg, J. L.. Combined forced and free convection in boundary layer flow. Phys. Fluids 2 (1959), 319–328.CrossRefGoogle Scholar
5Banks, W. H. H. and Drazin, P. G.. Perturbation methods in boundary layer theory. J. Fluid. Mech. 58 (1973), 763–775.CrossRefGoogle Scholar
6Cohen, C. B. and Reshotko, E.. NACA Report 1293 (1956).Google Scholar
7Serrin, J. B.. Asymptotic behaviour of velocity profiles in the Prandtl boundary layer theory. Proc. Roy. Soc. London Ser. A. 299 (1967), 491–507.Google Scholar
8Peletier, L. A.. On the asymptotic behaviour of velocity profiles in laminar boundary layers. Arch. Rational Mech. Anal. 45 (1972), 110–119.CrossRefGoogle Scholar
9Chen, K. K. and Libby, P. A.. Boundary layers with small departures from the Falkner-Skan profile. J. Fluid Mech. 33 (1968), 273–282.CrossRefGoogle Scholar
10Wilks, G.. Heat transfer coefficients for combined forced and free convection flow about a vertical semi-infinite isothermal plate. Internat. J. Heat Mass Transfer 19 (1976) 951–953.CrossRefGoogle Scholar
11Wilks, G. and Bramley, J. S.. On the computation of eigenvalues arising out of perturbations of the Blasius profile. J. Computational. Phys. 24 (1977), 303–319.CrossRefGoogle Scholar
12Bramley, J. S.. Calculation of eigenvalues of systems of ordinary differential equations using the Riccati transformation. Lecture notes in Computer Science, ‘Codes for boundary value problems’ (1979), 309–318.Google Scholar