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The effect of a magnetic field on the flow of a conducting fluid past a circular disk

Published online by Cambridge University Press:  28 March 2006

W. Chester  and
D. W. Moore
W. Chester
Affiliation:
Department of Mathematics, University of Bristol
D. W. Moore
Affiliation:
Department of Mathematics, University of Bristol
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Abstract

In the previous paper (Chester 1961) it was shown that, for large values of the Hartmann number, the asymptotic solution for the flow past a body of revolution has a discontinuity on the surface of a cylinder which circumscribes the body. The flow in the region of this discontinuity is now investigated in more detail when the body is a circular disk broadside-on to the flow. It will be shown that there is actually a region of transition whose thickness is O(|x|½/M½), where x is the axial distance from the disk and M is the Hartmann number. This region is thin near the disk, but gradually thickens until it merges into the over-all flow field for x = O(M).

The leading terms in the expression for the drag are given by $\frac{D}{D_s} = \frac{M \pi }{8} \left( 1 + \frac{2}{M} \right) $, where Ds is the Stokes drag.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 10 , Issue 3 , May 1961 , pp. 466 - 472
Copyright
© 1961 Cambridge University Press

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References

Chester, W. 1950 Phil. Trans. A, 242, 527.
Chester, W. 1957 J. Fluid Mech. 3, 304.
Chester, W. 1961 J. Fluid Mech. 3, 459.
Gunn, J. C. 1947 Phil. Trans. A, 240, 327.
Lamb, H. 1932 Hydrodynamics, 6th ed. Cambridge University Press.