Second-grade bioconvection flow of a nanofluid with slip convective boundary conditions

Controlling the heat and mass transfer rates is critical in a wide range of industrial processes because it sometimes determines the quality of the end-product and prevents run-away reactions. In an ongoing basis, a variety of techniques are being introduced, tested and improved to achieve this goal. Among these are the use of nanofluids and microbes. The addition of microbes leads to the rise of a phenomenon known as bioconvection. Although bioconvection has been used for a while now, some of its aspects like the Brownian motion and thermophoresis force on the microbes have been ignored in the past. The current study took into account the microbes' Brownian motion and thermophoresis parameters, which were previously overlooked by many researchers, to understand their contribution to heat and mass transfer from a theoretical perspective. To gain insight into the new paradigm's effect, a system of differential equations was formulated and solved using the spectral quasilinearisation method. Our findings revealed that including Brownian motion and thermophoresis parameters was critical in understanding heat and mass transfer in bioconvection models. The microbes' Brownian motion raises the temperature while simultaneously decreasing the solute and microbe concentrations. The thermophoresis parameter raises the temperature, concentration of solutes and concentration of microbes in the boundary layer.