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The effects of wall conductivity in magnetohydrodynamic duct flow at high Hartmann numbers

Published online by Cambridge University Press:  24 October 2008

D. J. Temperley  and
L. Todd
D. J. Temperley
Affiliation:
The University, Edinburgh; Laurentian University, Sudbury, Ontario
L. Todd
Affiliation:
The University, Edinburgh; Laurentian University, Sudbury, Ontario
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Abstract

Laminar motion of a conducting fluid in a rectangular duct is discussed. The applied magnetic field is uniform and parallel to one pair of sides of the duct. Classical theory is used and it is shown that the two successive limiting processes, lim (σwall → ∞; hσ wall → a finite, constant limit) and lim (M → ∞) are not always freely interchangeable; M being the Hartmann number, σwall the electrical conductivity of the duct wall and h the typical ratio of (wall thickness/duct width). A general expansion procedure for M ≫ 1, valid for all types of wall conductivities, is devised. A critical discussion of the deficiencies in the classical model is given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 69 , Issue 2 , March 1971 , pp. 337 - 351
Copyright
Copyright © Cambridge Philosophical Society 1971

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References

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