Triple-Diffusive Convection in a Magnetized Ferrofluid with MFD Viscosity Saturating a Porous Medium: A Nonlinear Stability Analysis Chand Suresh1, Kango S.K.2, Singh Vikram3 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:
Online published on 5 February, 2014. 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 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, because both Nef, Nℓf increases as solute gradients increases and Darcy number has a destabilizing effect, because both 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. Top Keywords Nonlinear stability, magnetized ferrofluid, triple-diffusive convection, MFD viscosity, porous medium, magnetization. Top |