Hostname: page-component-77c89778f8-9q27g Total loading time: 0 Render date: 2024-07-19T12:10:01.522Z Has data issue: false hasContentIssue false
  • English
  • Français

On the behaviour of the laminar boundary-layer equations of mixed convection near a point of zero skin friction

Published online by Cambridge University Press:  19 April 2006

Roland Hunt  and
Graham Wilks
Roland Hunt
Affiliation:
Department of Mathematics, University of Strathelyde, Glasgow G1 1XH
Graham Wilks
Affiliation:
Department of Mathematics, University of Strathelyde, Glasgow G1 1XH
Get access Rights & Permissions [Opens in a new window]

Abstract

The boundary-layer equations of mixed convection are examined in the vicinity of separation. The correlation between the uniform wall temperature case and that of compressible boundary layer flow is outlined. Goldstein–Stewartson–Buckmaster theory is thus appropriate and associated indeterminacies in the theory are evaluated from a numerical integration. The case of uniform heat flux at the wall is then examined theoretically. Significantly it is concluded that the original Goldstein–Stewartson theory is sufficient to describe the structure of the singularity at separation in this case. Indeterminacies associated with the theory are determined via a reconciliation between analytical and numerical representation of skin friction and heat transfer coefficients near separation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 101 , Issue 2 , 27 November 1980 , pp. 377 - 391
Copyright
© 1980 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Buckmaster, J. 1970 The behaviour of a laminar compressible boundary layer on a cold wall near a point of zero skin friction. J. Fluid Mech. 44, 237.Google Scholar
Davies, T. & Walker, G. 1977 On solutions of the compressible laminar boundary layer equations and their behaviour near separation. J. Fluid Mech. 80, 279.Google Scholar
Goldstein, S. 1930 Concerning some solutions of the boundary-layer equations in hydrodynamics. Proc. Camb. Phil. Soc. 26, 1.Google Scholar
Goldstein, S. 1948 On laminar boundary layer flow near a position of separation. Quart. J. Mech. Appl. Math. 1, 43.Google Scholar
Keller, H. B. 1978 Numerical methods in boundary-layer theory. Ann. Rev. Fluid Mech. 10, 417.Google Scholar
Keller, H. B. & Cebeci, T. 1971 Accurate numerical methods for boundary layer flows I. Two dimensional laminar flows. Proc. 2nd Int. Conf. Numer. Meth. Fluid Dyn., Berkeley, California.
Merkin, J. H. 1969 The effect of buoyancy forces on the boundary layer flow over a semiinfinite vertical flat plate in a uniform stream. J. Fluid Mech. 35, 439.Google Scholar
Stewartson, K. 1958 On Goldstein's theory of laminar separation. Quart. J. Mech. Appl. Math. 13, 57.Google Scholar
Stewartson, K. 1962 The behaviour of a laminar compressible boundary layer near a point of zero skin friction. J. Fluid Mech. 12, 117.Google Scholar
Terrill, R. M. 1960 Laminar boundary layer flow near separation with and without suction. Phil. Trans. Roy. Soc. A 235, 55.Google Scholar
Wilks, G. 1974 A separated flow in mixed convection. J. Fluid Mech. 62, 359.Google Scholar