Volume No. :   9

Issue No. :  1

Year :  2017

ISSN Print :  0975-4393

ISSN Online :  2349-2988


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Onset of Thermosolutal Convection in Couple-Stress Fluid in a Porous Media in the Presence of Magnetic Field



Address:   Ajaib S. Banyal1, Kamal Singh2
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
DOI No: 10.5958/2349-2988.2017.00013.4

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.
KEYWORDS:
Thermosolutal convection; couple-stress Fluid; Magnetic Field; Rayleigh number; Chandrasekhar number. MSC 2000 No.: 76A05, 76E06, 76E15; 76E07.
Cite:
Ajaib S. Banyal, Kamal Singh. Onset of Thermosolutal Convection in Couple-Stress Fluid in a Porous Media in the Presence of Magnetic Field. Research J. Science and Tech. 2017; 9(1):81-92.
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