Bio-microsystem transport in unsteady MHD Powell-Eyring nanofluid flow through porous medium with radiation and microbes

This study investigates the unsteady magnetohydrodynamic (MHD) stagnation-point flow of Powell-Eyring nanofluid in a Darcy-Forchheimer permeable medium, including the influences of radiant heat, higher-order chemical reactions, suction, and bioconvective transport of gyrotactic microorganisms. The complex governing partial differential equations, which include the conservation rules of interconnected momentum, thermal energy, solute, and microorganisms, are reduced to a framework of nonlinear ordinary differential equations by similarity transformations. The equations were solved numerically using a suitable shooting method, together with the Runge-Kutta algorithm and the bvp4c MATLAB package. The results demonstrate that the factors of magnetic and porous resistance impede velocity while simultaneously enhancing temperature profiles due to Joule heating. The augmentation of chemical processes and Schmidt number results in a decrease in the thickness of the concentration boundary layer. In contrast, elevated bioconvective Lewis and Peclet numbers result in a reduction in microbial population near the surface. The evaluation of local skin friction, Nusselt number, Sherwood number, and motile microbe density ratio provides further empirical information. The core outcome of this study highlights that magnetic and porous resistances effectively regulate fluid velocity, while simultaneously elevating the thermal profile via Joule heating. The proposed theoretical model holds significant practical implications for the design of advanced bio-microsystems, smart electro-conductive coatings, and targeted drug delivery mechanisms where precise control of heat and microbial transport is essential.