Reiner-rivlin nanofluid behavior with gyrotactic microorganisms and slip conditions in a rotating disk configuration

In the realm of fluid mechanics, the behavior of materials often defies simplistic characterization, requiring sophisticated models to capture their intricate dynamics, especially when involving non-Newtonian fluids. This research endeavors to elucidate the bioconvection flow of Reiner-Rivlin nanofluid incorporating gyrotactic microorganisms in the presence of magnetohydrodynamics (MHD), multiple slip, and thermal radiation over a rotating surface. Thermal and solutal convective boundary conditions have also been considered. The Buongiorno model is added together with the governing equations in partial differential equations (PDEs). By the adoption of transformation, the complex PDEs are transformed into ordinary differential equations (ODEs). The physical quantities of interest in this study are drag friction, heat, mass, and local motile microorganism density. Numerical solutions are calculated by the bvp4c solver in MATLAB, and the impacts of the governing parameters are visualized through graphical representations and tabulated data. Visual representations are used to inspect the significant effects of the changing parameters on the involved fields. The results demonstrate that radial velocity and temperature are improved for a strong Reiner-Rivlin material parameter. Enhancing slip variables lessens the shear stress by up to 30%, considerably. Tables show the relation between various estimations of emergent parameters and the behavior of microorganism density, friction coefficients, rate of heat and mass are provided. By comparing the reported results to an existing published study, we can verify that the intended model is authentic. We get a proper correlation between the two sets of results. These findings emphasize the possibility for enhancing refrigeration procedures for spinning systems like windmills and disk-based thermal exchangers by combining viscous nanofluids and microbial growth. This study sheds light on the development of innovative bio-nanofluidic technologies and effective heat control techniques for commercial and medical uses.