The effect of gravity driven thermal instability in the presence of applied magnetic field and internal heating

Abstract

This paper deals with the weakly nonlinear thermal instability problem between two infinite parallel surfaces under an imposed magnetic field and time-periodic gravity modulation. In this case gravity has two parts: a constant part and an externally imposed time-dependent part. In addition to applied magnetic field, the layer is heated internally. We focus on stationary convection using the slow time scale and arrive at the real Ginzburg-Landau equation. The classical fourth order Runge-Kutta method has been used to solve the real Ginzburg-Landau equation. This equation gives finite amplitude of convection and helps to analyze the effect of heat transfer in the presence of magnetic field and modulation. The effect of various parameters on heat transport has also discussed. It is found that, the heat transport can be controlled by suitably adjusting the frequency and amplitude of modulation. The applied magnetic field is to diminish the heat transfer in the system. It is concluded that both concepts internal heating and applied magnetic field regulate heat transfer.