Onset of stability and heat transfer by Rayleigh-Bénard magnetoconvection with variable viscosity effect using Ginzburg-Landau model: Effect of thermal/gravity modulation

Abstract

In modulating the commencement of Rayleigh-Bénard convection, thermal/gravitational modulation refers to its promising uses in various technical and scientific disciplines, including crystal formation, space laboratory research, and atmospheric convection. The aim of the study is to demonstrate the effect of thermal/gravitational modulation on the onset of stability and heat transfer of the Rayleigh-Bénard magnetoconvection with variable viscosity. The disturbance produced by the thermal/gravitational modulation is expanded in terms of the power series of the amplitude of the convection, and a non-autonomous Ginzburg-Landau equation is derived. The numerical solution of the Ginzburg-Landau equation is obtained using the classical Runge-Kutta method, which helps to determine the necessary amplitudes for the quantification of heat transfer. The examination of the data demonstrates that the commencement of convection and heat transfer can be advanced or suppressed by appropriately adjusting the problem’s parameters. The issue also shows how different parameters affect the Nusselt number, which measures the heat transfer coefficient.

Keywords:

• Applied magnetic field
• Rayleigh-Bénard convection
• thermal/gravity modulation
• variable viscosity

Acknowledgments

The authors would like to acknowledge the support and encouragement given by the Management and Principal of M. S. Ramaiah Institute of Technology, Bengaluru, Karnataka, India.