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The force on a sphere moving through a conducting fluid in the presence of a magnetic field

Published online by Cambridge University Press:  28 March 2006

J. R. Reitz  and
L. L. Foldy
J. R. Reitz
Affiliation:
Case Institute of Technology, Cleveland, Ohio
L. L. Foldy
Affiliation:
Case Institute of Technology, Cleveland, Ohio
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Abstract

The force on a sphere moving through an inviscid, conducting fluid in the presence of a uniform magnetic field B0 is calculated for the low-conductivity case where the hydrodynamic motion deviates only slightly from potential flow. The magnetic Reynolds number is assumed small. The force on the sphere is found to consist of both a drag and a deflective component which tends to orient its motion parallel to a magnetic field line; if the sphere's velocity is V, the force may be written $\bf {R} = -AB^2_0\bf {V} + \bf C(V.B_0)B_0$ where the coefficients A and C depend on the conductivities of both sphere and fluid. The coefficients are evaluated by calculating the Joule dissipation for particular orientations of V relative to B0. In one case the force is also calculated directly from the perturbed pressure distribution in the fluid. In an analogous way, a spinning sphere in a conducting fluid experiences both resistive and gyroscopic torques.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 11 , Issue 1 , August 1961 , pp. 133 - 142
Copyright
© 1961 Cambridge University Press

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