Effect of heating or cooling in a suspension of phototactic algae with no-slip boundary conditions

Abstract

This study presents a comprehensive analysis of the influence of temperature on bioconvective patterns in an algal suspension, exposed to collimated irradiation from above and heating or cooling from below. The linear stability analysis predicts that the critical bioconvective Rayleigh number is inversely related to the thermal Rayleigh number, suggesting a pronounced destabilization when the system is heated from below, and enhanced stability under cooling conditions. Additionally, the pattern wavelength increases as the thermal Rayleigh number decreases. Furthermore, the results reveal that reducing the critical light intensity and increasing cell motility can significantly bolster the system’s stability. This study also predicts the emergence of limit cycles and/or orbits via bifurcation analysis. These insights advance our understanding of thermal convective interactions in photo-driven bioconvection, with potential implications for optimizing bioreactor designs and other applications involving microalgal systems.