Analysis of weakly nonlinear Darcy–Brinkman bio-thermal convection in a porous medium under gravity modulation and internal heating effect

Abstract

In this study, we consider Newtonian fluid with gyrotactic microorganisms flowing through a porous medium. The effects of gravity field and internal heating are investigated on Darcy–Brinkman bio-thermal convection. The threshold Rayleigh number expression in the form of stationary mode is derived to study the onset of bioconvection. Further, heat transfer is investigated using Nusselt number, which is governed by Ginzburg–Landau equation. The influence of internal Rayleigh number, Vadasz number, modified bioconvective Rayleigh–Darcy number, cell eccentricity, modulation frequency and modulation amplitude on heat transfer is explored by the research and depicted graphically. Also the effect of the above parameters on the threshold Rayleigh number against the wave number is studied graphically. These graphical study is called as marginal stability analysis. Also, a comparative graph is plotted to study modulated and unmodulated effect of gravity on Nusselt number. This highlights the effectiveness of the gravity modulation and internal heating effect in controlling heat transport within the system.