Derivation of the Ginzburg-Landau Equation and Estimation of the Heat Transfer in a Rayleigh-Bénard Convection of a Micropolar fluid with Time Periodic Body Force

Abstract

This study examines the behavior of a micropolar fluid in a Rayleigh–Bénard configuration under a time-varying gravitational force. A scaled fourth-order Lorenz model is employed to describe weakly nonlinear convection. The model conserves energy and retains all the essential characteristics of the classical Lorenz system. The scaled Rayleigh
number and the Ginzburg-Landau equation are derived using the Venezian method. The graphs showing the variation of the correction Rayleigh number with the modulation frequency for different parameter combinations are plotted, and it is found that the system supports supercritical motion. Furthermore, an analytical expression for the time-average Nusselt number is obtained and plotted for various values of the parameters, and it is found that the presence of micropolar fluid generally promotes the heat transfer.