Instabilities in ferrofluids with temperature and magnetic field dependent viscosity under different modulations

Abstract

There has been a vigorous effort by researchers to study and characterize Rayleigh Be and#769;nard convection in ferrofluids owing to their interesting applications. From the survey of the literature pertinent to the problems under consideration in our study we realize the importance of using variable viscosity and thus explore the dynamics of a ferrofluid with temperature and magnetic field dependent viscosity which is in a Rayleigh- Be and#769;nard situation. The system under consideration is subjected to external constarints viz., an imposed time-periodic body force, rotation speed modulation, temperature modulation and magnetic field modulation. The problem considers both sinusoidal and non-sinusoidal time-periodic variations of these modulations to study the onset and post-onset regimes of Rayleigh-Be and#769;nard ferroconvection. We perform a weakly non-linear stability analysis using a truncated Fourier series representation and arrive at the Lorenz system for ferrofluid convection with variable viscosity. By using the linearized form of the Lorenz system we arrive at the critical Rayleigh There has been a vigorous effort by researchers to study and characterize Rayleigh Be and#769;nard convection in ferrofluids owing to their interesting applications. From the survey of the literature pertinent to the problems under consideration in our study we realize the importance of using variable viscosity and thus explore the dynamics of a ferrofluid with temperature and magnetic field dependent viscosity which is in a Rayleigh- Be and#769;nard situation. The system under consideration is subjected to external constarints viz., an imposed time-periodic body force, rotation speed modulation, temperature modulation and magnetic field modulation. The problem considers both sinusoidal and non-sinusoidal time-periodic variations of these modulations to study the onset and post-onset regimes of Rayleigh-Be and#769;nard ferroconvection.