Synergistic influence of gyrotactic microorganisms and bimolecular reaction on bidirectional tangent hyperbolic fluid with Nield boundary conditions: A biomathematical model

In biomedical engineering, the behavior of gyrotactic microorganisms with non-Newtonian fluids such as tangent hyperbolic fluids improve the design of targeted drug delivery systems. In this system control over microorganism movement is essential. The present study deals with the synergistic influence of gyrotactic microorganisms and bimolecular reactions on the bidirectional flow of tangent hyperbolic fluids under Nield boundary conditions. Further, the flow characteristic of the non-Newtonian fluid is enhanced by incorporating the impact of thermal radiation, heat sources, Brownian motion, and thermophoresis. The presentation of these phenomena is vital for an extensive range of applications, including industrial processes, biomedical engineering, and environmental management. The analysis employs advanced mathematical modeling which needs suitable transformation rules to get the non-dimensional form and further numerical simulation is presented with the assistance of the “shooting-based fourth-order Runge–Kutta technique”. The results are depicted for the several contributing factors via the built- in-house function bvp4c in “MATLAB”. The authentication of the study with the prior research is a benchmark to precede further research in this direction. However, the outstanding results are; the fluid velocity is controlled by increasing non-Newtonian Weissenberg number whereas the velocity slip shows dual characteristics on the axial velocity distribution. Further, the motile microorganism profile is controlled by the enhanced bioconvection Lewis number.