Computational exploration of dual slip mechanisms in MHD Williamson hybrid-nanofluid flow over a thin needle

Improving heat transmission is a modern challenge that affects a wide range of industries, including electronics, heat exchangers, biochemical reactors, and others. Nanofluids (NFs) hold considerable potential as a valuable tool in an effort for increased energy transfer efficiency. Therefore, the objective of this work is to learn the way to use Nanofluids (NFs) to improve heat transmission. This study examines the flow and heat transfer characteristics of Williamson hybrid nonfluids (HNF) containing graphene oxide (GO) and copper (Cu) nanoparticles. The HNF is applied across a thin needle with an applied magnetic field. Viscous dissipation effects and dual slip boundary conditions are imposed to account for energy dissipation and slip effects. Applying similarity transformations, the governing partial differential equations are converted into non-linear ordinary differential equations, numerically solved using the Bvp4c technique in MATLAB. The study identifies that increments in factors such as the magnetic factor M, needle size a, and velocity slip factor β, lead to a reduction in the velocity profile. The variations in factors such as a and thermal slip factor γ correspond to an increase in the temperature profile. A 200% increase in M results in approximately a 25% reduction in velocity, whereas the temperature increases by nearly 18% for a comparable rise in the Eckert number Ec. The hybrid nanofluid (Cu–GO/H2_22O) shows enhanced thermal transport compared to its mono-nanofluid counterpart. Skin friction increases with M and We, while the Nusselt number decreases with larger γ. The investigation focuses on potential applications such as polymer ejection for fiber technology and blood flow dynamics. These results highlight the strong coupling between magnetic effects, non-Newtonian rheology, and dual-slip mechanisms, offering insights for applications involving microscale controlled cooling and precision fluid transport. Graphical and tabular results are presented and discussed, providing a visual and quantitative analysis of the observed trends.