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Magnetohydrodynamic flow along cylindrical pipes under non-uniform transverse magnetic fields

Published online by Cambridge University Press:  28 March 2006

L. Todd
L. Todd
Affiliation:
Department of Mathematics, University of Strathclyde, Glasgow, C. 1
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Abstract

The unidirectional flow of an incompressible, electrically conducting, viscous fluid along cylindrical pipes is considered. An external magnetic field, B0, which lies in the plane transverse to the flow is applied. It is shown that the governing equations, written in the co-ordinate system traced out by B0, are mathematically very similar to those for a uniform field.

The paper deals mainly with ducts whose walls are insulators. Though exact solutions (valid for all values of the Hartmann number) are derived, the limit of high Hartmann number is taken for detailed discussion. Transition layers (or, loosely, ‘wakes’) can arise which are centred on curved field lines. In some cases, reversed flow occurs in part of the core (‘radial-type’ fields). Situations also arise where the magnitude (and sign) of the velocity remains the same as for B0 = 0, whatever the strength of the applied, transverse (azimuthal) magnetic field.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 31 , Issue 2 , 29 January 1968 , pp. 321 - 342
Copyright
© 1968 Cambridge University Press

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References

Eckhaus, W. & de Jager, E. M. 1966 Arch. Rat. Mech. Anal. 23, 26.
Globe, S. 1959 Phys. of Fluids, 2, 404.
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Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics, Volume 1. London: McGraw Hill.
Shercliff, J. A. 1953 Proc. Comb. Phil. Soc. 49, 136.
Shercliff, J. A. 1965 A Textbook of Magnetohydrodynamics. Oxford: Pergamon Press.
Todd, L. 1967 J. Fluid Mech. 28, 371.