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Gravitational instability of a viscous fluid in a magnetic field

Published online by Cambridge University Press:  28 March 2006

Chia-Shun Yih
Chia-Shun Yih
Affiliation:
Department of Engineering Mechanics, University of Michigan
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Abstract

The instability of a viscous fluid between two infinite vertical plates and heated from below in the presence of a magnetic field perpendicular to the plates is investigated, and the most critical stability boundary in the space of the Rayleigh number R, Hartmann number M, and the horizontal wave number a is determined. It is found that the most unstable mode is a symmetric mode with zero wave-number, and that for any M the fluid is unstable for any non-zero R, however small.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 22 , Issue 3 , July 1965 , pp. 579 - 586
Copyright
© 1965 Cambridge University Press

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References

Dunwoody, N. T., 1964 J. Fluid Mech. 20, 103.
Ostrach, S., 1955 50 Jahre Grenzschichtforschung. Brunswick: Verlag Friedr. Vieweg und Sohn.
Wooding, R. A., 1960 J. Fluid Mech. 7, 501.
Yih, C.-S. 1959 Quart. Appl. Math. 17, 25.