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Corner regions in the asymptotic solution of ε∇2u = ∂u/∂y with reference to MHD duct flow

Published online by Cambridge University Press:  24 October 2008

L. Pamela Cook
Affiliation:
Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, N. Y.
G. S. S. Ludford
Affiliation:
Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, N. Y.
J. S. Walker
Affiliation:
Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, N. Y.

Abstract

In the asymptotic solution of the title equation for simple boundary data on the rectangle 0 ≤ x ≤ l, 0 ≤ y ≤ 1 the bottom corners are not passive, as has previously been supposed, but in fact generate the parabolic side layers at x = o, l. The top corners, though passive, lead to unconventional elliptic quarter-plane problems. Implications for the MHD duct problem are indicated.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

REFERENCES

(1)Temperley, D. J. and Todd, L.The effects of wall conductivity in magnetohydrodynamic duct flow at high Hartmann numbers. Proc. Cambridge Philos. Soc. 69 (1971), 337.CrossRefGoogle Scholar
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