Volume No. :   9

Issue No. :  1

Year :  2017

ISSN Print :  0975-4393

ISSN Online :  2349-2988


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Magneto-Thermosolutal Convection in Rivlin-Ericksen Viscoelastic Fluid in a Porous Medium



Address:   Pawan Kumar* , Ajaib S. Banyal2 , Nirmal Singh3
1Department of Mathematics, NSCBM GC Hamirpur, (HP) INDIA 177005
2Department of Mathematics, Govt. College Nadaun (Hamirpur), (HP) INDIA 177033
3Department of Mathematics, NSCBM GC Hamirpur, (HP) INDIA 177005
*Corresponding Author
DOI No: DOI: 10.5958/2349-2988.2017.00015.8

ABSTRACT:
Thermosolutal instability of Veronis type in Rivlin-Ericksen viscoelastic 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 established that all non-decaying slow motions starting from rest, in a Rivlin-Ericksen viscoelastic fluid of infinite horizontal extension and finite vertical depth in the presence of uniform vertical magnetic field in a porous medium, are necessarily non-oscillatory, in the regime, where is the Thermosolutal Rayliegh number, Q is the Chandrasekhar number, is the magnetic Prandtl number, is the thermosolutal Prandtl number, is the medium permeability, is the porosity and F is the viscoelasticity parameter. The result is important since it hold for all wave numbers and for any arbitrary combination of free and rigid boundaries at the top and bottom of the fluid. A similar characterization theorem is also proved for Stern type of configuration.
KEYWORDS:
Thermosolutal convection; Rivlin-Ericksen Fluid; Magnetic Field; PES; Rayleigh number; Chandrasekhar number. MSC 2000 No.: 76A05, 76E06, 76E15; 76E07.
Cite:
Pawan Kumar, Ajaib S. Banyal, Nirmal Singh. Magneto-Thermosolutal Convection in Rivlin-Ericksen Viscoelastic Fluid in a Porous Medium. Research J. Science and Tech. 2017; 9(1):101-110.
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