Hostname: page-component-6bf8c574d5-b4m5d Total loading time: 0 Render date: 2025-02-21T06:20:43.086Z Has data issue: false hasContentIssue false
  • English
  • Français

The behaviour of similar solutions in a compressible boundary layer

Published online by Cambridge University Press:  28 March 2006

J. B. Mcleod  and
J. Serrin
J. B. Mcleod
Affiliation:
Wadham College, Oxford and University of Sussex
J. Serrin
Affiliation:
Wadham College, Oxford and University of Sussex
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper discusses the mathematical properties of similar solutions of the boundary-layer equations in a compressible model fluid, under assumptions first introduced by Stewartson and by Li & Nagamatsu. Assuming a favourable pressure gradient and that backflow is not present, our results include (among other things) a rigorous proof that velocity overshoot occurs in the boundary layer if the wall is heated, and that this is true whether or not suction, blowing or slipping occurs at the wall; while, conversely, velocity overshoot does not occur when the wall is cooled and the amount of slipping at the wall is suitably restricted.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 34 , Issue 2 , 12 November 1968 , pp. 337 - 342
Copyright
© 1968 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

Cohen, C. B. & Reshotko, E. 1956 Similar solutions for the compressible laminar boundary layer with heat transfer and pressure gradient. NACA Report 1293.Google Scholar
Ho, D. & Wilson, H. K. 1967 A boundary value problem arising in boundary layer theory Arch. Rational Mech. Analysis 27, 165–174.Google Scholar
Li, T. & Nagamatsu, H. 1955 Similar solutions of compressible boundary layer equations J. Aero. Sci. 22, 607–616.Google Scholar
Mcleod, J. B. & Serrin, J. (To appear.) The existence of similar solutions for some compressible boundary layer problems.
Rosenhead, L. (Ed.) 1963 Laminar Boundary Layers. Oxford University Press.
Schlichting, H. 1960 Boundary Layer Theory, 4th ed. New York: McGraw-Hill.
Stewartson, K. 1949 Correlated compressible and incompressible boundary layers. Proc. Roy. Soc A 200, 84–100.Google Scholar
Stewartson, K. 1964 The Theory of Laminar Boundary Layers in Compressible Fluids. Oxford University Press.