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Steady electrically driven flows

Published online by Cambridge University Press:  24 October 2008

R. T. Waechter
R. T. Waechter
Affiliation:
School of Physical Sciences, Flinders University, Bedford Park, South Australia
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Abstract

Certain simple steady electrically driven flows under transverse applied magnetic fields, for which exact solutions are available, are considered. Electric potentials are prescribed on fixed perfectly conducting electrodes and the resulting Lorentz force j × B0 gives rise to a velocity field in the fluid. It is assumed that the magnetic Reynolds number of the flow is small (Rm ≪ 1) so that the induced magnetic field may be neglected. In particular, we examine in detail the simplest flat plate configuration which is correctly posed as a two-part mixed boundary value problem of the Wiener–Hopf type. At large Hartmann number, the fluid vorticity and the current flow transverse to the applied magnetic field are suppressed. Thin current transition layers, which emanate from an electrode edge and are aligned with the applied magnetic field, provide a smooth transition from one region of almost constant current to another. The thickness of these layers is found to be of the same order as the thickness of certain velocity transition layers occurring in other situations in magnetohydrodynamics.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 3 , July 1968 , pp. 871 - 894
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

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