A mathematical model for bioconvection flow with activation energy for chemical reaction and microbial activity

In most of the industrial processes, it is of paramount importance to control the heat and mass transfer rates to ensure high-quality products. Using nanofluids instead of ordinary fluids and using motile micro-organisms are some of the techniques to control heat and mass transfer rates. In some recent studies of bioconvection flow, activation energy, Brownian motion and thermophoretic effects are considered only for the solute and not for the microbes. Our current study incorporates these effects for the motile micro-organisms too. Few, if any results of this nature exist in literature. A system of partial differential equations is formulated to incorporate the effects of these parameters. The system of equations are solved numerically using the spectral quasi-linearisation method to gain an insight into the influence of key parameters on the fluid and flow properties. The thermophoretic force, the Brownian motion and activation energy are significant contributors in the microbes’ dynamics. The concentration of microbes decreases with an increase in the thermophoretic force and increases with increasing microbe’s Brownian motion parameter. Based on our results, we conclude that increasing activation energy leads to a decrease in microbes’ velocity. The inclusion of the microbes’ Brownian motion proved to be significant as this was shown to have an impact on the temperature, solute concentration and microbes’ concentration in the boundary layer.