Study of Heat Transport in Darcy–Bénard Convection With Feedback Control and <i>g</i>-Jitter

Abstract The paper deals with the study of Rayleigh–Bénard convection in a densely packed porous layer in the presence of gravity modulation and feedback control. The critical Rayleigh number in the absence of gravity modulation is evaluated using the single-term Galerkin method and the Maclaurin series expansion. Linear stability analysis is performed to evaluate the correction to the Rayleigh number using a modified Venezian approach. Weakly nonlinear stability analysis is performed using the three-dimensional Lorenz model and the multiscale method to derive the Ginzburg-Landau equation in order to study the heat transport in the system. The influence of various parameters pertaining to feedback control and modulation on the onset of convection and heat transport is discussed.