Study of heat transport by stationary magneto-convection in a Newtonian liquid under temperature or gravity modulation using Ginzburg–Landau model

Abstract

The present paper deals with a weak non-linear stability problem of magneto-convection in an electrically conducting Newtonian fluid, confined between two horizontal surfaces, under a constant vertical magnetic field, and subjected to an imposed time-periodic boundary temperature (ITBT) or gravity modulation (ITGM). In the case of ITBT, the temperature gradient between the walls of the fluid layer consists of a steady part and a time-dependent oscillatory part. The temperature of both walls is modulated in this case. In the problem involving ITGM, the gravity field has two parts: a constant part and an externally imposed time periodic part, which can be realized by oscillating the fluid layer. The disturbance is expanded in terms of power series of amplitude of convection, which is assumed to be small. Using Ginzburg–Landau equation, the effect of modulations on heat transport is analyzed. Effect of various parameters on the heat transport is also discussed.