In this study, an incompressible, steady, and magnetohydrodynamic flow of Buongiorno nanofluid through a stretchable surface has been analyzed by adopting a theoretical and numerical approach. This paper involves the impacts of buoyancy forces, thermal conductivity, chemically diffusion, and Arrhenius activation energy. Moreover, the influence of the suspension of gyrotactic microorganisms in the nanofluids is also a part of this study. It is assumed that the behavior of viscosity varies as a function of time and the suspension of microorganisms remain consistent throughout the study. A system of PDEs is reduced to a solvable system of ODEs by applying a suitable similarity transformation. For the sake of numerical solutions, the shooting method has been employed. Wolfram Mathematica has been used to deal with the BVP. In addition, the behaviors of different emerging parameters comprising velocity outline, temperature outline, concentration distribution, the density outline of gyrotactic microorganisms have also been demonstrated by graphical illustrations. From the extracted results, it has been observed that the rising values of viscosity of fluid produce a decline in the velocity parameter. Also, an increment has been noticed in the temperature profile for the growing behavior of the mixed convective factor.
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