Weak Nonlinear Double Diffusive Magneto-Convection in a Newtonian Liquid under Gravity Modulation

Abstract

A theoretical analysis of thermo-convective instability in an electrically conducting two component fluid layer is carried out when the gravity field vary with time in a sinusoidal manner. Newtonian liquid is considered between two horizontal surfaces, under a constant vertical magnetic field. The disturbance is expanded in terms of power series of amplitude of convection, which is assumed to be small. We use the linear matrix differential operator method to find the Ginzburg–Landau amplitude equation for the modulated problem. Use the solution of the Ginzburg–Landau equation in quantifying the amount of heat and mass transports in terms of Nusselt and Sherwood numbers. It is found that, the effect of magnetic field is to stabilize the system. Effect of various parameters on the heat and mass transport is also discussed. Further, it is found that the heat and mass transports can be controlled by suitably adjusting frequency and amplitude of gravity modulation.

Keywords

• Double diffusive magnetoconvection; Gravity modulation; Weak nonlinear theory.