Gravity modulation and its impact on weakly nonlinear bio-thermal convection in a porous layer under rotation: a Ginzburg-Landau model approach

Abstract

The effect of gravity modulation on weakly nonlinear bio-thermal convection in a porous rotating layer has been investigated in this study. The system under consideration is a porous medium layer saturated with a Newtonian fluid containing gyrotactic microorganisms, and it is subjected to both gravity modulation and rotation. Through a weakly nonlinear analysis, the behavior of the system at finite amplitudes is studied. The Ginzburg-Landau equation, obtained from perturbation analysis, provides insights into the system's behavior in the presence of gravity modulation. The amplitude of convection in the unmodulated case is determined analytically, serving as a reference for comparison. The research explores the influence of various parameters on the system, including the Vadasz number, modified Rayleigh-Darcy number, Taylor number, cell eccentricity, and modulation parameters such as amplitude and frequency. By varying these parameters, the heat transfer, quantified by the Nusselt number, is analyzed and compared in different cases. The modulation amplitude is found to have a significant effect on enhancing heat transfer, while the modulation frequency has a diminishing effect.