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Liquid-metal flow in a rectangular duct with a strong non-uniform magnetic field

Published online by Cambridge University Press:  20 April 2006

John C. Petrykowski  and
John S. Walker
John C. Petrykowski
Affiliation:
Department of Theoretical and Applied Mechanics, University of Illinois, Urbana, IL 61801 Present address: Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830.
John S. Walker
Affiliation:
Department of Theoretical and Applied Mechanics, University of Illinois, Urbana, IL 61801
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Abstract

Liquid-metal flows in rectangular ducts having electrically insulating tops and bottoms and perfectly conducting sides and in the presence of strong, polar, transverse magnetic fields are examined. Solutions are presented for the boundary layers adjacent to the sides that are parallel to the magnetic field. Overshoots in the radial velocity profiles show that the side layers have zero displacement thickness and do not perturb the inviscid core. Very weak secondary flows involve four significant vortices, as reflected in the polar velocity profiles.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 139 , February 1984 , pp. 309 - 324
Copyright
© 1984 Cambridge University Press

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References

Holroyd, R. J. 1979 An experimental study of the effects of wall conductivity, non-uniform magnetic fields and variable-area ducts on liquid metal flows at high Hartmann number. Part 1. Ducts with non-conducting walls J. Fluid Mech. 93, 609–630.CrossRefGoogle Scholar
Holroyd, R. J. 1980a MHD flow in a rectangular duct with pairs of conducting and non-conducting walls in the presence of a non-uniform magnetic field J. Fluid Mech. 96, 335–353.Google Scholar
Holroyd, R. J. 1980b An experimental study of the effects of wall conductivity, non-uniform magnetic fields and variable-area ducts on liquid metal flows at high Hartmann number. Part 2. Ducts with conducting walls J. Fluid Mech. 96, 355–374.Google Scholar
Holroyd, R. J. & Walker, J. S. 1978 A theoretical study of the effects of wall conductivity, non-uniform magnetic fields and variable-area ducts on liquid-metal flows at high Hartmann number J. Fluid Mech. 84, 471–495.CrossRefGoogle Scholar
Hunt, J. C. R. & Shercliff, J. A. 1971 Magnetohydrodynamics at high Hartmann number Ann. Rev. Fluid Mech. 3, 37–62.Google Scholar
Hunt, J. C. R. & Stewartson, K. 1965 Magnetohydrodynamic flow in rectangular ducts. Part 2 J. Fluid Mech. 23, 563–581.Google Scholar
Ludford, G. S. S. & Walker, J. S. 1976 On establishing fully developed duct flow in strong magnetic fields. In MHD-Flows and Turbulence (ed. H. Branover), pp. 7–15. Wiley: Israel Universities Press.
Ludford, G. S. S. & Walker, J. S. 1980 Current status of MHD duct flow. In MHD-Flows and Turbulence II (ed. H. Branover & A. Yakhot), pp. 83–95. Israel Universities Press.
Petrykowski, J. C. 1981 A three-dimensional magnetohydrodynamic duct flow in a non-uniform magnetic field. Ph.D. dissertation, University of Illinois at Urbana-Champaign.
Tabeling, P. & Chabrerie, J. P. 1981 Magnetohydrodynamic secondary flows at high Hartmann numbers J. Fluid Mech. 103, 225–239.Google Scholar
Walker, J. S. 1980 Large interaction parameter magnetohydrodynamics and applications in fusion reactor technology. In Fluid Mechanics and Energy Conversion, Proc. SIMS Conf., pp. 215–229. SIAM.
Walker, J. S. 1981 Magnetohydrodynamic flows in rectangular ducts with thin conducting walls. Part 1. Constant-area and variable-area ducts with strong uniform magnetic fields J. Méc. 20, 79–112.Google Scholar
Walker, J. S. & Ludford, G. S. S. 1975 Duct flow in strong magnetic fields Recent Adv. Engng Sci. 6, 329–335.Google Scholar
Walker, J. S., Ludford, G. S. S. & Hunt, J. C. R. 1971 Three-dimensional MHD duct flows with strong transverse magnetic fields. Part 2. Variable-area rectangular ducts with conducting sides J. Fluid Mech. 46, 657–684.Google Scholar
Walker, J. S., Ludford, G. S. S. & Hunt, J. C. R. 1972 Three-dimensional MHD duct flows with strong transverse magnetic fields. Part 3. Variable-area rectangular ducts with insulating walls J. Fluid Mech. 56, 121–141.Google Scholar