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Magneto-gravitational convection in a vertical layer of ferrofluid in a uniform oblique magnetic field

Published online by Cambridge University Press:  22 April 2016

Habibur Rahman  and
Sergey A. Suslov
Habibur Rahman
Affiliation:
Department of Mathematics, H38, Swinburne University of Technology, John Street, Hawthorn, Victoria 3122, Australia
Sergey A. Suslov*
Affiliation:
Department of Mathematics, H38, Swinburne University of Technology, John Street, Hawthorn, Victoria 3122, Australia
*
†Email address for correspondence: [email protected]
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Abstract

The stability of base gravitational convection in a layer of ferrofluid confined between two vertical wide and tall non-magnetic plates, heated from one side, cooled from the other and placed in a uniform oblique external magnetic field is studied. Two distinct mechanisms, thermo-gravitational and thermo-magnetic, are found to be responsible for the appearance of various stationary and wave-like instability modes. The characteristics of all instability modes are investigated as functions of the orientation angles of the applied magnetic field and its magnitude for various values of magnetic parameters when both the thermo-magnetic and gravitational buoyancy mechanisms are active. The original three-dimensional problem is cast in an equivalent two-dimensional form using generalised Squire’s transformations, which significantly reduces a computational cost. Subsequently, full three-dimensional instability patterns are recovered using the inverse Squire’s transformation, and the optimal field and pattern orientations are determined.

JFM classification

Nonlinear Dynamical Systems: Bifurcation MHD and Electrohydrodynamics: Magnetic fluids MHD and Electrohydrodynamics: Magneto convection
Type
Papers
Information
Journal of Fluid Mechanics , Volume 795 , 25 May 2016 , pp. 847 - 875
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Copyright
© 2016 Cambridge University Press 

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Footnotes

‡

Present address: Department of Mathematics, Khulna University of Engingeering & Technology, Khulna 9203, Bangladesh.

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