The Effect of Throughflow and Gravitational Modulation on Weakly Nonlinear Bio-Thermal Convection in a Porous Medium Layer

Abstract

We investigate the impact of periodically varying gravitational fields and a throughflow on the bio-thermal Darcy–Brinkman convection within a porous medium layer saturated with a Newtonian fluid containing gyrotactic microorganisms. The study includes an examination of two types of a throughflow: one directed against the gravity field and another one along it. We assume that the gravitational modulation has a small amplitude, quantified as a second-order smallness in the dimensionless parameter ϵ, which represents the supercritical parameter of the Rayleigh number. For weakly nonlinear convection, a Ginzburg–Landau (GL) equation with a periodic coefficient is derived in the third order in ϵ. To analyze the heat and mass transfer, we numerically solve the GL equation. The numerical results reveal that the vertical throughflow in the bio-thermal convection exhibits a dual nature, allowing for both augmentation and a reduction of the heat and mass transfers. We investigate the influence of variations in the Vadasz number, Peclet number, bioconvective Peclet number, frequency, and amplitude of modulation on the heat and mass transfer. The effects of these parameters are depicted graphically, illustrating that higher values of the Vadasz and Peclet numbers, as well as increased modulation amplitude, positively impact the heat and mass transfer. In addition, a comparative analysis of modulated and non-modulated systems shows a significant effect of the modulation on the stability of systems.