SUMMARY
The study of thermal convection in porous media saturated by nanofluid and microorganisms is an important problem for many geophysical and engineering applications. The concept of a mixture of nanofluids and microorganisms has attracted the interest of many researchers due to its ability to improve thermal properties and, as a result, heat transfer rates. This property is actively used both in electronic cooling systems and biological applications. Thus, the purpose of this research is to study biothermal instability in a porous medium saturated by a water-based nanofluid containing gyrotactic microorganisms in the presence of a vertical magnetic field. Given the presence of an external magnetic field in both natural and technological situations, we were motivated to perform this theoretical research. Using the Darcy-Brinkman model, a linear analysis of the convective instability has been considered for both-free boundaries, taking into account the effects of Brownian diffusion and thermophoresis. The Galerkin method was used to perform this analytical study. We have established that heat transfer is accomplished by stationary convection without oscillatory movements. In stationary convection regimes, metal oxide nanofluids (Al2O3), metallic nanofluids (Cu, Ag), and semiconductor nanofluids (TiO2, SiO2) are analyzed. Increasing the Chandrasekhar and Darcy numbers improve system stability significantly, but increasing porosity and modified bioconvection Rayleigh-Darcy number speed up the beginning of instability. To determine the transient behavior of heat and mass transports, a non-linear theory based on the representation of the Fourier series method is applied. In small time intervals, the transitional Nusselt and Sherwood numbers exhibit an oscillatory character. The Sherwood numbers (mass transfer) in the time interval reach stationary values faster than the Nusselt numbers (heat transfer). This research might help with seawater convection in the oceanic crust as well as the construction of biosensors.