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Three-dimensional MHD duct flows with strong transverse magnetic fields. Part 2. Variable-area rectangular ducts with conducting sides

Published online by Cambridge University Press:  29 March 2006

J. S. Walker ,
G. S. S. Ludford  and
J. C. R. Hunt
J. S. Walker
Affiliation:
Department of Theoretical and Applied Mechanics, Cornell University
G. S. S. Ludford
Affiliation:
Department of Theoretical and Applied Mechanics, Cornell University
J. C. R. Hunt
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Cambridge University
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Abstract

In this paper the general analysis, developed in part 1, of three-dimensional duct flows subject to a strong transverse magnetic field is used to examine the flow in diverging ducts of rectangular cross-section. It is found that, with the magnetic field parallel to one pair of the sides, the essential problem is the analysis of the boundary layers on these (side) walls. Assuming that they are highly conducting and that those perpendicular to the magnetic field are non-conducting, the flow is found to have some interesting properties: if the top and bottom walls diverge, the side walls remaining parallel, then an O(1) velocity overshoot occurs in the side-wall boundary layers; but if the top and bottom walls remain parallel, the side walls diverging, these boundary layers have conventional velocity profiles. The most interesting flows occur when both pairs of walls diverge, when it is found that large, 0(M½), velocities occur in the side-wall boundary layers, either in the direction of the mean flow or in the reverse direction, depending on the geometry of the duct and the external electric circuit!

The mathematical analysis involves the solution of a formidable integral equation which, however, does have analytic solutions for some special types of duct.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 46 , Issue 4 , 27 April 1971 , pp. 657 - 684
Copyright
© 1971 Cambridge University Press

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References

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