Analysis of onset of bio-thermal convection in a fluid containing gravitactic microorganisms by the energy method

The bio-thermal convection in a suspension containing gravitactic microorganisms saturated by a fluid is investigated within the framework of linear and nonlinear stability theory. Energy method is used for nonlinear stability analysis. Effect of Péclet number (swimming speed of microorganisms) and bioconvection Rayleigh number (concentration of microorganisms) on the stability of the system is analyzed numerically by using the Galerkin weighted residual method. The subcritical region of instability for faster swimmers is large as compared to slowly swimmers. Bioconvection Rayleigh number destabilizes the onset of bio- thermal convection and this effect is more predominant for high speed of microorganisms. The Péclet number, bioconvection Rayleigh number increase the size of cell.