Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-18T21:49:32.787Z Has data issue: false hasContentIssue false
  • English
  • Français

Magnetohydrodynamic flow in rectangular ducts. II

Published online by Cambridge University Press:  28 March 2006

J. C. R. Hunt  and
K. Stewartson
J. C. R. Hunt
Affiliation:
Central Electricity Research Laboratories, Leatherhead
Seconded to: School of Engineering Science, University of Warwick, Coventry.
K. Stewartson
Affiliation:
Department of Mathematics, University College London
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper is an extension of an earlier paper by Hunt (1965) on laminar motion of a conducting liquid in a rectangular duct under a uniform transverse magnetic field. The effect of the duct having conducting walls are further explored; in this case the duct considered has perfectly conducting walls parallel to the field and non-conducting walls perpendicular to the field. A solution is obtained for high Hartmann numbers by analysing the boundary layers on the walls. This solution involves an integral equation of a standard form.

It is found that in this case, unlike the cases studied in the earlier paper, the velocity profiles in the boundary layers are monotonically decreasing. The effect of an external electrical circuit is examined, although it is found that it does not influence the form of the velocity profiles.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 23 , Issue 3 , November 1965 , pp. 563 - 581
Copyright
© 1965 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

Chang, C. C. & Lundgren, T. S. 1961 Z. angew. Math. Phys. 12, 100.
Grinberg, G. A. 1961 Appl. Math. and Mech. (PMM), 25, 1536.
Grinberg, G. A. 1962 Appl. Math. and Mech. (PMM), 26, 106.
Hale, F. J. & Kerrebrock, J. L. 1964 AIAA J. 2, 461.
Hunt, J. C. R. 1965 J. Fluid Mech. 21, 577.
Kerrebrock, J. L. 1961 J. Aero/Space Sci. 28, 631.
Neuringer, J. L. & Migotsky, E. 1963 Phys. Fluids, 6, 1164.
Resler, E. J. & Sears, W. R. 1958 J. Aero. Sci. 25, 235.
Rott, N. & Cheng, H. K. 1954 J. Rat. Mech. and Anal. 3, 357.
Shercliff, J. A. 1962 The Theory of Electromagnetic Flow Measurement. Cambridge University Press.
Shercliff, J. A. 1965 A Textbook of Magnetohydrodynamics. Oxford: Pergamon Press.
Sutton, G. W. & Carlson, A. W. 1961 J. Fluid Mech. 11, 121.
Uflyand, Y. S. 1961 Sov. Phys. Tech. Phys. 5, 1194.