Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-09T12:30:45.512Z Has data issue: false hasContentIssue false
  • English
  • Français

Linearized slip flow past a semi-infinite flat plate

Published online by Cambridge University Press:  28 March 2006

J. A. Laurmann
J. A. Laurmann
Affiliation:
National Aeronautics and Space Administration, Ames Research Centre Moffett Field, California
Get access Rights & Permissions [Opens in a new window]

Abstract

Incompressible slip flow past a semi-infinite flat plat at zero incidence is treated in terms of the linearized viscous flow equations. A formal solution is obtained using Fourier transforms and the Wiener-Hopf technique. Explicit inversion of the transform is not possible, but asymptotic expansions are discussed. These reveal the inadequacy of boundary-layer theory in predicting the nature of the solution, even at the plate surface. For example, the local shear forces on the plate are significantly different from boundary-layer values, even far downstream, where slip effects are small. The boundary-layer limit is approached as the Reynolds number based on the mean free path or, equivalently, the free-stream Mach number tends to infinity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 11 , Issue 1 , August 1961 , pp. 82 - 96
Copyright
© 1961 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

Carslaw, H. S. & Jaeger, J. C. 1947 Operational Methods in Applied Mathematics. Oxford University Press.
Doetsch, G. 1937 Theorie und Anwendung der Laplace-Transformation. Berlin: Springer.
Donaldson, C. Du P. 1949 An approximate method of estimating the incompressible laminar boundary-layer characteristics in slipping flow. NACA RM no. L9602.
Kuo, Y. H. 1953 On the flow of an incompressible viscous fluid past a flat plate at moderate Reynolds numbers. J. Math. Phys. 32, 83.Google Scholar
Lagerstrom, P. A. & Cole, J. D. 1955 Examples illustrating expansion procedures for the Navier-Stokes equations. J. Rat. Mech. Anal. 4, 817.Google Scholar
Lagerstrom, P. A., Cole, J. D. & Trilling, L. 1949 Problems in the theory of viscous compressible fluids. GALCIT report.
Laurmann, J. A. 1958 Slip flow over a short flat plate. First International Symposium on Rarefied Gas Dynamics, Nice. (Published by Pergamon Press, 1960.)
Lewis, J. A. & Carrier, G. F. 1949 Some remarks on the flat plate boundary-layer. Quart. Appl. Math. 7, 228.Google Scholar
Mirels, H. 1952 Estimate of slip effects on compressible laminar boundary-layer skin friction. NACA TN 2609.
Noble, B. 1958 Methods Based on the Wiener-Hopf Technique. London: Pergamon Press.
Probstein, R. F. 1960 Shock-wave and flow field development in hypersonic re-entry. Amer. Rocket Soc. Semi-Annual Meeting, Los Angeles, May.
Schaaf, S. A. & Chambré, P. 1957 Flow of rarefied gases. High Speed Aerodynamics and Jet Propulsion, vol. III, sect. 8. Princeton University Press.
Sherman, F. S. 1952 Skin friction in subsonic low density gas flow. Univ. Calif. Inst. Engng Res. Rep. no. He-150-105 (1952). Also J. Aero. Sci. 21 (1954), 85.
Sherman, F. S. & Talbot, L. 1958 Experiment versus kinetic theory for rarefied gases. First International Symposium on Rarefied Gas Dynamics, Nice. (Published by Pergamon Press, 1960.)
Yang, H. & Lees, L. 1956 Rayleigh's problem at low Mach numbers according to the kinetic theory of gases. J. Math. Phys. 35, 195.Google Scholar