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Singh, Vikram
- Triple- Diffusive Convection in a Magnetized Ferrofluid with MFD Viscosity Saturating a Porous Medium: A Nonlinear Stability Analysis
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Authors
Affiliations
1 Department of Mathematics, SCVB Govt. College, Palampur, HP-176061, IN
2 Department of Mathematics, Govt. College, Haripur (Manali), HP-175136, IN
3 Department of Mathematics, Jwalaiji Degree College , Jwalamukhi, HP-176072, IN
1 Department of Mathematics, SCVB Govt. College, Palampur, HP-176061, IN
2 Department of Mathematics, Govt. College, Haripur (Manali), HP-175136, IN
3 Department of Mathematics, Jwalaiji Degree College , Jwalamukhi, HP-176072, IN
Source
Research Journal of Science and Technology, Vol 5, No 1 (2013), Pagination: 1-9Abstract
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 M3, solute gradients S1& S2, Darcy number Da and MFD viscosity parameter δ, on the subcritical instability region have also been analyzed. The solutes gradients S1& S2 have stabilizing effect, Nef, Nlf increases as solute gradients increases and Darcy number has a destabilizing effect,Nef, Nlf decreases as Da increases. It has also been observed that in the presence of MFD viscosity δ, both Nef, Nlf decrease for lower values of M3 and increase for higher values of M3.
References
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- Triple-Diffusive Convection in Rivlin-Ericksen Fluid under varying gravity field in Porous Medium
Abstract Views :676 |
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Authors
Affiliations
1 Department of Mathematics, Govt. College, Haripur (Manali) Distt. Kullu (HP)-175 136, IN
2 Govt. College, Bassa, Dist. Mandi (HP), IN
3 Jwalaji Degree College, Jwalamukhi, Distt. Kangra (HP), IN
1 Department of Mathematics, Govt. College, Haripur (Manali) Distt. Kullu (HP)-175 136, IN
2 Govt. College, Bassa, Dist. Mandi (HP), IN
3 Jwalaji Degree College, Jwalamukhi, Distt. Kangra (HP), IN
Source
Research Journal of Science and Technology, Vol 5, No 1 (2013), Pagination: 96-103Abstract
The Triple-Diffusive convection in Rivlin-Ericksen fluid with varying gravity field is considered in the presence of uniform vertical magnetic field in porous medium. For the case of stationary convection, the magnetic field, varying gravity field and the stable solute gradients have stabilizing effects whereas the medium permeability has destabilizing (or stabilizing) effect on the system under certain conditions. A linear stability analysis theory and normal mode analysis method have been carried out to study the onset convection. The kinematic viscoelasticity has no effect on the stationary convection. The solute gradients, magnetic field, varying gravity field, porosity and kinematic viscoelasticity introduce oscillatory modes in the system, which were non-existent in their absence. The sufficient conditions for the non-existence of overstability are also obtained. The results are also shown graphically.Keywords
Triple-Diffusive Convection, Rivlin-Ericksen Fluid, Solute Gradients, Vertical Magnetic Field, Varying Gravity Field, Porous Medium.References
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