Magnetic dipole effects on unsteady nanofluid flow over a curved surface

Although considerable research has been devoted to non-Newtonian nanofluid flows, the combined influence of a magnetic dipole, Stefan blowing, wall slip, thermal radiation, second-order chemical reactions, and bioconvection on the unsteady flow of a second-grade nanofluid over a curved surface remains largely unexplored. Motivated by thermal management challenges in fusion reactor walls, where intense heat and particle fluxes must be effectively dissipated while preserving structural integrity, the present study addresses this notable gap in the literature. Specifically, it investigates the coupled effects of Stefan blowing and slip boundary conditions in conjunction with magnetic dipole interactions, while incorporating thermal radiation and higher-order chemical reactions into the heat and mass transfer analysis. Furthermore, bioconvection is employed to enhance nanofluid stability, providing a more comprehensive and realistic modeling framework that has not been adequately examined in previous studies. Using similarity transformations, the modeled equations for momentum, thermal, concentration, and bioconvection are converted to ordinary differential equations, which the numerical scheme bvp4c is used to solve. The ranges of distinct parameters during computation are presented. Findings are presented in graphs and tables, including calculations of the surface friction coefficient, motile microorganism density, heat transmission rate, and Sherwood number. The results demonstrate that Stefan’s blowing parameter improves the velocity pattern, while the radiative parameter improves the thermal pattern. Furthermore, the surface friction coefficient increases abruptly with the rising ferrohydrodynamic interaction factor. The impact of curvature and Brownian motion on the species transfer rate reveals a contradictory pattern. The species distribution exhibits a declining trend as the reaction parameter rises, while the unsteadiness parameter improves the outcomes. In addition, it has been noted that raising the unsteadiness parameter reduces the surface friction coefficient by 0.6083% and the Nusselt number by 0.8203%, implying a slight reduction in heat transfer efficiency. Additionally, the skin friction coefficient rises by 2.6580% when the curvature parameter is increased (i.e., it becomes less negative), reducing the Sherwood number and motile microorganism density by 3.8926% and 2.6424%, respectively. These results offer helpful recommendations for microfluidic applications, biomedical devices, and curved-surface thermal systems where controlled heat transfer, mass transport, and bioconvective behavior are crucial. It exhibits a minor error of 0.00375% to 0.06150% relative to a published study, which is negligible and thus confirms the model’s validity. The current study is distinct in that it looks at the combined ramifications of magnetic dipoles, thermal radiation, and gyrotactic microorganisms on unsteady second-grade nanofluid flow along a curved geometry. The findings are useful for developing and optimizing advanced thermal management systems, microfluidic devices, solar energy systems, electronic cooling, biomedical engineering applications, and polymer processing technologies.