Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-25T13:23:43.976Z Has data issue: false hasContentIssue false
  • English
  • Français

Slip flow past a tangential flat plate at low Reynolds numbers

Published online by Cambridge University Press:  12 April 2006

Ko Tamada  and
Hiroyuki Miura
Ko Tamada
Affiliation:
Department of Aeronautical Engineering, Faculty of Engineering, Kyoto University, Kyoto, Japan
Hiroyuki Miura
Affiliation:
Department of Mathematical Sciences, College of Engineering, University of Osaka Prefecture, Sakai, Japan
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper the slip flow of viscous fluid at low Reynolds numbers past a flat plate aligned with the flow is studied theoretically on the basis of Oseen-Stokes equations of motion. An integral equation for the distribution of fundamental singularities representing the plate is derived and solved approximately in the vicinity of the edge and main portion of the plate. A formula for the local skin friction is obtained and discussed numerically. It is also shown that the slippage of the flow gives rise to reduction of the drag force on the plate by an amount O(K|ln K|), where K is the Knudsen number. The velocity change near the edge of the plate is of particular interest and is found to be logarithmically singular there.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 85 , Issue 4 , 27 April 1978 , pp. 731 - 742
Copyright
© 1978 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.
Carrier, G. F., Krook, M. & Pearson, C. E. 1966 Functions of a Complex Variable. McGraw-Hill.
Donaldson, C. 1949 N.A.C.A. Rep. L9C02.
Laurmann, J. A. 1961 J. Fluid Mech. 11, 82–96.
Piercy, N. A. V. & Winny, H. F. 1933 Proc. Roy. Soc. A 140, 543–561.
Rosenhead, L. 1963 Laminar Boundary Layers, p. 183. Oxford University Press.
Schaaf, S. A. & CHAMBRÉ, P. L. 1958 In High Speed Aerodynamics and Jet Propulsion, vol. 3 (ed. H. W. Emmons), pp. 687–739. Princeton University Press.
Tamada, K. & Inoue, Y. 1976 Trans. Japan Soc. Aero-Space Sci. 19, 140–148.
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. Academic Press.