Darcy–Brinkman gravity modulated biothermal double diffusive convection in rotating porous media

In this paper, we investigate the thermo bioconvective double diffusion of a Newtonian fluid in a rotating porous medium that contains gyrotactic microorganisms. The effect of gravity modulation and the motion of microorganisms on the system are studied. Linear and weakly nonlinear theory for stationary biothermal double diffusive convection is applied to derive critical Rayleigh number, Nusselt, and Sherwood number to study the onset of convection, heat, and mass transport, respectively, in the system. Nonlinear theory leads to Ginzberg–Landau (GL) equation, which is called as amplitude equation. The GL equation governs the expressions for heat and mass transmission. In this study, Darcy–Brinkman model is adapted due to the presence of porous media. Here, the perturbation technique is used to bring the GL equation analytically. We come across several parameters such as modified Vadasz number, cell eccentricity, bioconvective Rayleigh–Darcy number, solutal Rayleigh number, Taylor number, Lewis and bioconvection Lewis number, and amplitude and frequency of modulation. The effect of these parameters on the system is depicted graphically to study heat and mass transfer. Critical Rayleigh number obtained from linear study describes the onset of convection. The marginal(threshold) stability curves are plotted that describe the onset of convection. Darcy number, Taylor number, solutal Rayleigh number, and Lewis number result in stabilizing the system. Whereas, the modified bioconvective Darcy–Rayleigh number and eccentricity of the cell destabilize the system by advancing the onset of convection. Also, the rotation effect decreases heat and mass transfer, as observed in the current study. Streamlines and isotherms demonstrate the convection cell formation as a result of thermal variation between horizontal parallel plates. The biological application is studied mathematically in this present work. The shape of microorganisms together with various effects in a rotating porous medium plays an important role in heat and mass transfer in the system. This is one such multidisciplinary area of research that has a wide scope in the present scenario, which is predominantly an analytical study.