A nonlinear stability analysis for thermoconvective magnetized ferrofluid with magnetic field dependent viscosity

The generalized energy method which gives sufficient condition for the stability is developed for convection problem in a magnetized ferrofluid with magnetic field dependent (MFD) viscosity heated from below. The mathematical emphasis is on how to control the nonlinear terms caused by magnetic body and inertia forces. Both linear and nonlinear analyses are carried out and comparison of results shows a marked difference in the stability boundaries and thus indicates that the sub-critical instabilities are possible. The effect of various parameters on the sub-critical region has also been analyzed.