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International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 2, Pages 365-375
http://dx.doi.org/10.1155/S0161171282000350

Instability through porous medium of two viscous superposed conducting fluids

1Department of Mathematics, Himachal Pradesh University, Simla 171005, India
2Department of Physics, University of Alberta, Edmonton T6G 2Jl, Canada

Received 11 July 1979; Revised 10 December 1980

Copyright © 1982 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The stability of the plane interface separating two viscous superposed conducting fluids through porous medium is studied when the whole system is immersed in a uniform horizontal magnetic field. The stability analysis is carried out for two highly viscous fluids of equal kinematic viscosities, for mathematical simplicity. It is found that the stability criterion is independent of the effects of viscosity and porosity of the medium and is dependent on the orientation and magnitude of the magnetic field. The magnetic field is found to stabilize a certain wave number range of the unstable configuration. The behaviour of growth rates with respect to viscosity, porosity and medium permeability are examined analytically.