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On the flow of a conducting fluid past a magnetized sphere

Published online by Cambridge University Press:  28 March 2006

G. S. S. Ludford  and
J. D. Murray
G. S. S. Ludford
Affiliation:
University of Maryland
J. D. Murray
Affiliation:
Harvard University Now at University College London.
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Abstract

In the steady flow of an incompressible, inviscid, conducting fluid past a magnetized sphere, the first-order effects of the magnetic field and the conductivity are studied. Paraboloidal wakes of vorticity and magnetic intensity are formed, the former being half the size of the latter. The vorticity, generated by the non-conservative electromagnetic force, is logarithmically infinite on the sphere. For the case of a dipole of moment M at the centre of a sphere of radius a, the drag coefficient is $C_D = \frac {144 \mu^{\prime 2}}{5(2\mu + \mu^{\prime})^2} \beta R_M,$ where μ and μ′ are the permeabilities of the fluid and sphere, respectively, β is the ratio of the representative magnetic pressure μM2/2a6 to the free-stream dynamic pressure, and RM is the magnetic Reynolds number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 7 , Issue 4 , April 1960 , pp. 516 - 528
Copyright
© 1960 Cambridge University Press

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References

Chopra, K. P. & Singer, S. F. 1958 Drag of a sphere moving in a conducting fluid in the presence of a magnetic field. 1958 Heat Transfer and Fluid Mechanics Institute, Berkeley, p. 155. Stanford University Press.
Copson, E. T. 1935 An Introduction to the Theory of Functions of a Complex Variable. Oxford University Press.
Yeh, G. C. K., Martinek, J. & Ludford, G. S. S. 1955 The potentials due to certain singularities in the presence of a fixed sphere. J. Soc. Indust. Appl. Math. 3, 142–52.Google Scholar