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MHD flow in a rectangular duct with pairs of conducting and non-conducting walls in the presence of a non-uniform magnetic field

Published online by Cambridge University Press:  19 April 2006

Richard J. Holroyd
Richard J. Holroyd
Affiliation:
Department of Engineering, University of Cambridge
Present address: Department of Engineering Science, University of Oxford.
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Abstract

A theoretical and experimental study has been carried out on the flow of a liquid metal along a straight rectangular duct, whose pairs of opposite walls are highly conducting and insulating, situated in a planar non-uniform magnetic field parallel to the conducting walls. Magnitudes of the flux density and mean velocity are taken to be such that the Hartmann number M and interaction parameter N have very large values and the magnetic Reynolds number is extremely small.

The theory qualitatively predicts the integral features of the flow, namely the distributions along the duct of the potential difference between the conducting walls and the pressure. The experimental results indicate that the velocity profile is severely distorted by regions of non-uniform magnetic field with fluid moving towards the conducting walls; even though these walls are very good conductors the flow behaves more like that in a non-conducting duct than that predicted for a duct with perfectly conducting side walls.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 96 , Issue 2 , 29 January 1980 , pp. 335 - 353
Copyright
© 1980 Cambridge University Press

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References

Holroyd, R. J. 1976 MHD duct flows in non-uniform magnetic fields. Ph.D. dissertation, University of Cambridge.
Holroyd, R. J. 1979 An experimental study of the effect 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.CrossRefGoogle 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.CrossRefGoogle Scholar
Hunt, J. C. R. & Ludford, G. S. S. 1968 Three-dimensional MHD duct flows with strong transverse magnetic fields. Part 1. Obstacles in a constant area duct. J. Fluid Mech. 33, 693.Google Scholar
Hunt, J. C. R. & Shercliff, J. A. 1971 MHD at high Hartmann number. Ann. Rev. Fluid Mech. 3, 37.Google Scholar
Hunt, J. C. R. & Stewartson, K. 1965 MHD flow in rectangular ducts. II. J. Fluid Mech. 23, 563.Google Scholar
Kaye, G. W. C. & Laby, T. H. 1973 Tables of Physical and Chemical Constants (and Some Mathematical Functions), 14th edn. Longmans.
Kit, L. G., Peterson, D. E., Platnieks, I. A. & Tsinober, A. B. 1970 Investigation of the influence of fringe effects on a MHD flow in a duct with non-conducting walls. Magnitnaya Gidrodinamika 6 (4), 47.Google Scholar
Kulikovskii, A. G. 1968 On slow steady flows of conductive fluid with high Hartmann number Izv. Akad. Nauk S.S.S.R. Mekh. Z. i Gaza 3 (2), 3.Google Scholar
Ludford, G. S. S. & Walker, J. S. 1980 Current Status of MHD duct flows. Proc. 2nd Boi. Sheva seminar on MHD and turbulence.
Shercliff, J. A. 1962 The Theory of Electromagnetic Flow Measurement. Cambridge University Press.
Shercliff, J. A. 1965 A Textbook of MHD. Pergamon Press Ltd.
Shercliff, J. A. 1975 Some duct flow problems at high Hartmann number. Z. angew. Math. Phys. 26, 537.Google Scholar
Vasil'ev, V. F. & Lavrent'ev, I. V. 1969 Potential distribution in an MHD channel with thin conducting walls. Magnitnaya Gidrodinamiko 5 (3), 142.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.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.Google Scholar