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Fluid flow induced by a rapidly alternating or rotating magnetic field

Published online by Cambridge University Press:  19 April 2006

A. D. Sneyd
A. D. Sneyd
Affiliation:
Department of Mathematics, University of Waikato, Hamilton, New Zealand
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Abstract

This paper studies the effect of alternating or rotating magnetic fields on containers of conducting fluid. The magnetic Reynolds number is assumed small. The frequency of alternation or rotation is rapid so the magnetic field is confined to a thin layer on the surface of the container. A boundary-layer analysis is used to find the rate of vorticity generation due to the Lorentz force. When the container is an infinitely long cylinder of uniform cross-section, alternating fields normal to the generators or fields rotating about an axis parallel to the generators generate vorticity at a constant rate. For containers of any other shape the rate of vorticity generation includes both constant and oscillatory terms. A perturbation analysis is used to study the flow induced in a slightly distorted circular cylinder by a rotating field. Complex flows develop in the viscous-magnetic boundary layer which may be unstable.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 92 , Issue 1 , 15 May 1979 , pp. 35 - 51
Copyright
© 1979 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions. Dover
Batchelor, G. K. 1956 On steady laminar flow with closed streamlines at large Reynolds numbers. J. Fluid Mech. 1, 177Google Scholar
Dahlberg, E. 1972 AB Atomenergi, Studsvik, Sweden, Rep. no. AE-447
Moffatt, H. K. 1965 On fluid flow induced by a rotating magnetic field. J. Fluid Mech. 22, 521Google Scholar
Moffatt, H. K. 1978 Some problems in the magnetohydrodynamics of liquid metals. Z. angew. Math. Mech. 58, 65Google Scholar
Nigam, G. D. 1969 Flow of a fluid in a spherical container in presence of rotating magnetic field. J. Math. Phys. Sci. 3, 205Google Scholar
Richardson, A. T. 1974 On the stability of a magnetically driven rotating fluid flow. J. Fluid Mech. 63, 593Google Scholar
Sneyd, A. D. 1971 Generation of fluid motion in a circular cylinder by an unsteady applied magnetic field. J. Fluid Mech. 49, 817Google Scholar
Spivak, M. 1970 A Comprehensive Introduction to Differential Geometry, vol. 3. Boston: Publish or Perish Inc
Wood, W. M. 1956 Boundary layers whose streamlines are closed. J. Fluid Mech. 2, 77Google Scholar