Weakly nonlinear analysis of Darcy–Brinkman gravity modulated biothermal convection in rotating porous media

Abstract The present study investigates the gyrotactic microorganism flow in a rotating porous medium containing Newtonian fluid. Using gravity modulation, Darcy–Brinkman biothermal convection is examined. Linear theory describes the stationary convective mode which derives the expression for critical Rayleigh number. This indicates the onset of bioconvection. The system's marginal stability is demonstrated by graphical and tabular representation which has a good agreement with each other. The Ginzburg–Landau equation governs the Nusselt number, which is used to further explore heat transfer. The study provides an explanation and graphical representation of the effects of the following factors on heat transfer: cell eccentricity, modified Vadasz number and bioconvective Rayleigh–Darcy number, modulation frequency, and amplitude along with Taylor number. The mean Nusselt number has been plotted in the current study. The effect of rotating porous media and gravity modulation is explained in this work. Additionally, a comparison graph is plotted to examine the effects of gravity, both modulated and unmodulated, on the Nusselt number. This demonstrates how well gravity modulation on rotating porous media controls the system's heat transfer. A comparison between numerical and analytical results for unmodulated cases is also explained graphically.