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Steady rotation of a body of revolution in a conducting fluid

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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Extract

We investigate the steady rotation of an insulating body of revolution in an unbounded electrically conducting fluid permeated by a uniform axial applied magnetic field. The assumptions of a small magnetic Reynolds number (Rm ≪ 1, i.e. the weakly conducting situation) and negligible inertia forces compared with the magnetic forces (R/M2 ≪ 1) permit us to suppress the inflow at the poles and outflow at the equator, which normally occurs for a non-conducting viscous fluid ((12), pp. 436–439). Thus in the case of the sphere, we find an exact solution of the reduced equations in terms of an infinite series of Legendre polynomials of order 1 with coefficients which are the ratios of modified spherical Bessel functions. This is the canonical problem by which results for arbitrary bodies of revolution are obtained.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 1 , January 1969 , pp. 329 - 350
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

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