Impact of an Anisotropic Porous media on Thermo-bio-convection instability in presence of Gyrotactic microorganisms and heating from below

Abstract

The onset of thermo-bio-convection in a horizontal fluid layer saturated by gyrotactic microorganisms into an anisotropic porous medium is examined. The modeling of the governing equations considers heating from below, Darcy flow, and Boussinesq approximations along with the presence of gyrotactic microorganisms. The system of ordinary differential equations is obtained using linear stability analysis and the normal mode technique. The single-term Galerkin method casts the analytical solutions while the higher-order Galerkin technique is employed to compute the numerical solutions. The influence of the mechanical and the thermal anisotropy parameters along with all bioconvection parameters on the onset of thermo-bio-convection are analytically as well as numerically discussed. It is perceived that bioconvection Rayleigh-Darcy number $Rb$, the gyrotactic number $G$, and P{\'e}clet number $Q$ are to fast-forward the beginning of bioconvection motion. On the other hand, thermal anisotropy produces a stable system and acts to postpone the bio-convection pattern formulation. Mechanical anisotropy is found to have a destabilizing impact on the stability of the suspension and helps in the development of bio-convection. The measure of cell eccentricity parameter $\alpha$ has a dual effect on system stability and stabilizes the system if $\frac{\delta^2_{c}}{\pi^2}>1$.