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International Journal of Technology
Year : 2016, Volume : 6, Issue : 2
First page : ( 265) Last page : ( 277)
Print ISSN : 2231-3907. Online ISSN : 2231-3915.
Article DOI : 10.5958/2231-3915.2016.00041.9

Magneto-Thermosolutal Convection in Couple-Stress Fluid in a Porous Medium

Banyal Ajaib S.1,*, Singh Kamal2,**

1Department of Mathematics, Sidharth Govt. College Nadaun, Distt. Hamirpur, (HP), India, 177033

2Department of Mathematics, Govt. College Indora, Distt. Kangra, (HP), India, 176401

*Corresponding Author Email: ajaibbanyal@rediffmail.com

** singh_kamal1979@rediffmail.com

MSC 2000 No.: 76A05, 76E06, 76E15; 76E07

Online published on 2 February, 2017.

Abstract

Thermosolutal instability of Veronis(1965) type in a couple-stress fluid in the presence of uniform vertical magnetic field in a porous medium is considered. Following the linearized stability theory and normal mode analysis, the paper mathematically established the condition for characterizing the oscillatory motions which may be neutral or unstable, for any arbitrary combination of free and rigid boundaries at the top and bottom of the fluid. It is proved analytically that all non-decaying slow motions starting from rest, in a couple-stress fluid of infinite horizontal extension and finite vertical depth in a porous medium, which is acted upon by uniform vertical magnetic field opposite to force field of gravity and a constant vertical adverse temperature gradient, are necessarily non-oscillatory, in the regime established, the result is important since the exact solutions of the problem investigated are not obtainable in closed form, for any arbitrary combination of free and rigid boundaries. A similar characterization theorem is also established for Stern (1960) type of configuration.

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Keywords

Thermosolutal convection, couple-stress Fluid, Magnetic Field, Rayleigh number, Chandrasekhar number.

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