Effects of variable viscosity and rotation modulation on ferroconvection

We theoretically explore the dynamics of a ferrofluid with temperature and magnetic field-dependent viscosity, which is in a Rayleigh-Benard situation and is subjected to rotation. The problem considers both sinusoidal and non-sinusoidal time-periodic variations of rotation to study the onset and post-onset regimes of Rayleigh-Benard ferroconvection. We perform a weakly nonlinear stability analysis using a truncated Fourier series representation and arrive at the third-order Lorenz system for ferrofluid convection with variable viscosity. By using the linearized form of the Lorenz system for ferrofluid convection with variable viscosity, we arrive at the critical Rayleigh number to study the onset of rotating ferroconvection. The heat transport is quantified in terms of the time-averaged Nusselt number and the effects of various parameters on it are studied. The effect of modulated rotation is found to have a stabilizing effect on the onset of ferroconvection while that of variable viscosity has a destabilizing effect. The effects of magnetorheological and thermorheological effects are antagonistic in nature. It is found that the square waveform modulation facilitates maximum heat transport in the system due to advanced onset of ferroconvection.