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Some extremum principles for magnetohydrodynamic flow in conducting pipes

Published online by Cambridge University Press:  24 October 2008

P. Smith
P. Smith
Affiliation:
The University, Keele, Staffordshire
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Abstract

Extremum principles are obtained for the laminar flow of a conducting liquid in a straight pipe of arbitrary cross-section with conducting walls of arbitrary thickness, which is subject to a uniform applied magnetic field. These extrema provide upper and lower bounds for the mass-flow rate in the pipe. These bounds are particularly useful in the construction of asymptotic estimates for the flow rate at high Hartmann number. The method is illustrated by its application to the pipe of circular cross-section and to pipes with thin conducting walls.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 72 , Issue 2 , September 1972 , pp. 303 - 313
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

REFERENCES

(1)Shercliff, J. A.Steady motion of conducting fluids in pipes under transverse magnetic fields. Proc. Cambridge Philos. Soc. 49 (1953), 136–144.CrossRefGoogle Scholar
(2)Shercliff, J. A.The flow of conducting fluids in circular pipes under transverse magnetic fields. J. Fluid Mech. 1 (1956), 644–666.CrossRefGoogle Scholar
(3)Chang, C. C. and Luudgben, T. S.Duct flow in magnetohydrodynamics. Z. Angew. Math. Phys. 12 (1961), 100–114.CrossRefGoogle Scholar
(4)Smith, P.Some asymptotic extremum principles for magnetohydrodynamic pipe flow. Appl. Sci. Res. 24 (1971) 452–466.CrossRefGoogle Scholar
(5)Temperley, D. J. and Todd, L.The effects of wall conductivity in magnetohydrodynamic duct flow at high Hartmann number. Proc. Cambridge Philos. Soc. 69 (1971), 337–351.CrossRefGoogle Scholar
(6)Apostol, T. M.Mathematical analysis, Addison-Wesley, Reading, Mass. (1957).Google Scholar
(7)Synge, J. L.The hypercircle in mathematical physics (Cambridge University Press, 1957).CrossRefGoogle Scholar
(8)Abramowitz, M. and Stegun, Ibene A.Handbook of mathematical functions (Dover, New York, 1965).Google Scholar