  In this study, we investigate the impact of heating or cooling in a
suspension experiencing phototactic bioconvection. The suspension is
illuminated by collimated irradiation from the top and subjected to heating or
cooling from the bottom. The governing equations include the Navier Stokes
equations with the Boussinesq approximation, the diffusion equation for motile
microorganisms, and the energy equation for temperature. Employing linear
perturbation theory, we analyse the linear stability of the suspension. The
findings predict that the suspension undergoes destabilization when heated from
below and stabilization when cooled from below. This suggests a sensitive
dependence of the system's stability on the thermal conditions, providing
valuable insights into the behavior of phototactic bioconvection under
different heating or cooling scenarios.
