Abstract
The present paper deals with a weakly nonlinear stability problem under an imposed time-periodic thermal modulation. The temperature has two parts: a constant part and an externally imposed time-dependent part. We focus on stationary convection using the slow time scale and quantify convective amplitude through the real Ginzburg-Landau equation (GLE). We have used the classical fourth order Runge-Kutta method to solve the real Ginzburg-Landau equation. The effect of various parameters on heat transport is discussed through GLE. It is found that heat transport analysis is controlled by suitably adjusting the frequency and amplitude of modulation. The applied magnetic field (effect of Ha) is to diminish the heat transfer in the system. Three different types of modulations thermal, gravity, and magnetic field have been compared. It is concluded that thermal modulation is more effective than gravity and magnetic modulation. The magnetic modulation stabilizes more and gravity modulation stabilizes partially than thermal modulation.
Highlights
We study the impact of time-periodic oscillations on Rayleigh-Benard convection in the presence of an applied magnetic field by weakly nonlinear analysis
We study heat transfer through Ginzburg-Landau equation (GLE) and discuss the impact of thermal modulation on heat transport
The effect of magnetic field modulation on a weakly nonlinear thermal instability was investigated by Bhadauria and Kiran [32] for stationary mode convection
Summary
We study the impact of time-periodic oscillations on Rayleigh-Benard convection in the presence of an applied magnetic field by weakly nonlinear analysis. The effect of magnetic field modulation on a weakly nonlinear thermal instability was investigated by Bhadauria and Kiran [32] for stationary mode convection. Keshri et al [44] studied the effect of solutal and gravity modulation on thermal instability in a fluid layer under applied magnetic field. They concluded that the effect of the applied magnetic field is to suppress the mass transfer irrespective of the modulation. To the best of the authors' knowledge, there is no nonlinear study available in the literature in which the effect of thermal modulation has been considered in a magnetic fluid layer with internal heating. Three types of different modulations, thermal, gravity and magnetic field modulations are investigated and the results compared
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