Volume No. :   5

Issue No. :  1

Year :  2013

ISSN Print :  0975-4393

ISSN Online :  2349-2988


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Triple- Diffusive Convection in a Magnetized Ferrofluid with MFD Viscosity Saturating a Porous Medium: A Nonlinear Stability Analysis



Address:   Suresh Chand1, S.K. Kango2 and Vikram Singh3
1Department of Mathematics, SCVB Govt. College, Palampur, HP-176061 India
2Department of Mathematics, Govt. College, Haripur (Manali), HP-175136 India
3Department of Mathematics, Jwalaiji Degree College , Jwalamukhi, HP-176072 India
*Corresponding Author
DOI No:

ABSTRACT:
A nonlinear stability analysis is performed for a triple- diffusive convection in a magnetized ferrofluid with magnetic field –dependent viscosity (MFD)saturating a porous for stress- free boundaries. The major mathematical emphasis is on how to control the non-linear terms caused by magnetic body force and inertia forces. A suitable generalized energy functional is introduced to perform the nonlinear energy stability analysis. It is found that nonlinear critical stability magnetic thermal Rayleigh number does not coincide with that of linear instability, and thus indicate that the subcritical instabilities are possible. However, it is noted that in case of non-ferrofluid global nonlinear stability Rayleigh number is exactly same as that of linear instability. For lower values of magnetic parameters, this coincidence is immediately lost. The effects of magnetic parameter? M?_3, solute gradients ?S ?_1 & S_2, Darcy number Da and MFD viscosity parameter d, on the subcritical instability region have also been analyzed. The solutes gradients ?S ?_(1 )& S_2 have stabilizing effect, because ?both N_ef?_ , N_(lf ) increases as solute gradients increases and Darcy number has a destabilizing effect, because ?both N_ef?_ , N_(lf )decreases as Da increases. It has also been observed that in the presence of MFD viscosity (d), both N_(ef ) ,N_lf decrease for lower values of M_3 and increase for higher values of? M?_3.
KEYWORDS:
Nonlinear stability, magnetized ferrofluid, triple- diffusive convection, MFD viscosity , , porous medium, magnetization.
Cite:
Suresh Chand, S.K. Kango, Vikram Singh. Triple- Diffusive Convection in a Magnetized Ferrofluid with MFD Viscosity Saturating a Porous Medium: A Nonlinear Stability Analysis. Research J. Science and Tech 5(1): Jan.-Mar.2013 page 01-09.
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