A nonlinear stability analysis of a double-diffusive magnetized ferrofluid with magnetic field-dependent viscosity

A rigorous nonlinear stability result is derived by introducing a suitable generalized energy functional for a magnetized ferrofluid layer heated and soluted from below with magnetic field-dependent (MFD) viscosity, for stress-free boundaries. The mathematical emphasis is on how to control the nonlinear terms caused by magnetic body and inertia forces. For ferrofluids, we find that there is possibility of existence of subcritical instabilities, however, it is noted that in case of non-ferrofluid, global nonlinear stability Rayleigh number is exactly the same as that for linear instability. For lower values of magnetic parameters, this coincidence is immediately lost. The effects of magnetic parameter, M3, solute gradient, S1 and MFD viscosity parameter, δ, on the subcritical instability region have also been analyzed.