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The effect of a magnetic field on Stokes flow in a conducting fluid

Published online by Cambridge University Press:  28 March 2006

W. Chester
W. Chester
Affiliation:
Guggenheim Aeronautical Laboratory, California Institute of Technology
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Abstract

Low Reynolds number flow of a conducting fluid past a sphere is considered. The classical Stokes solution is modified by a magnetic field which, at infinity, is uniform and in the direction of flow of the fluid.

The formula for the drag is found to be $D = D_S \{ 1+\frac{3}{8}M+\frac{7}{960}M^2-\frac{43}{7680}M^3+O(M^4) \},$ Where DS is the Stokes drag and M is the Hartmann number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 3 , Issue 3 , December 1957 , pp. 304 - 308
Copyright
© 1957 Cambridge University Press

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References

Cowling, T. G. 1957 Magnetohydrodynamics. New York: Interscience.
Goldstein, S. 1929 Proc. Roy. Soc. A, 123, 225.
Lamb, H. 1932 Hydrodynamics, 6th Ed. Cambridge University Press.
Proudman, I. & Pearson, J. R. A. 1957 J. Fluid Mech, 2, 237.