Triple -Diffusive Convection in a Magnetized Ferrofluid With MFD Viscosity: A Nonlinear Stability Analysis

A nonlinear stability analysis is performed for a triplediffusive convection in a magnetized ferrofluid with magnetic field –dependent viscosity (MFD) for stressfree 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 S 1 & S2and MFD viscosity parameter δ , on the subcritical instability region have also been analyzed. The solutes gradients S 1 & S2have stabilizing effect, because bot𝑕 Nce , Nclincreases as solute gradients increases. It has also been observed that in the presence of MFD viscosity (δ), bot𝑕 Nce ,Ncl decrease for lower values of M3 and increase for higher values of M3 .