Ginzburg–Landau equations for the salt fingering region with the onset of microorganisms

This work is an analytical investigation of Rayleigh–Bénard convection in the presence of microorganisms in the salt fingering region. The stream function is used to perform a two-dimensional stability study. The amplitudes of the functions are determined using the Lorenz technique, and the stationary curves are drawn with regard to the Rayleigh thermal number and wave number. The stationary curves depicted indicate the stable and unstable zones. The Ginzburg–Landau equation is solved analytically to determine heat and mass transmission. The Nusselt and Sherwood numbers are effectively represented, and a straightforward relationship is discovered using the Lewis number. Based on the results, it is concluded that, in contrast to constant wall temperature, where microorganisms cause Nusselt number attenuation in the majority of the considered cases, microorganisms improve heat transfer in all of the considered cases in linear temperature distribution. These new discoveries are expected to result in significant shifts in the usage of microbes in the heat transfer firms.