Heat transfer optimization using computational insights into nodal/saddle point flow patterns of tera-hybrid nanofluid containing microbes in a cylindrical shells

Tetra hybrid nanofluids enhance heat transfer efficiency in advanced thermal management systems, benefiting industries like electronics cooling, automotive, aerospace, and renewable energy. In this study, we examine the impact of magnetohydrodynamic tetra-hybrid nanofluid on nodal/saddle stagnation points in a rounded cylinder with a sinusoidal radius. The analysis focuses on optimizing energy and mass transfer rates around a circular cylinder with a sinusoidal surface, simulating thermal processes in biological systems. By utilizing similarity variables, a complex set of nonlinear partial differential equations is transformed into ordinary differential equations and solved numerically using MATLAB's bvp4c solver. The effects of several parameters are discussed graphically for the nodal stagnation point as well as numerically for both the nodal and saddle points. At $R=4.5$, the heat transfer rate for the tetra hybrid nanofluid shows a 1.36 % increase compared to the nanofluid, underscoring the enhanced thermal efficiency of hybrid nanofluids in radiative conditions. indicates that the application of a magnetic field, combined with variations in d, results in significant improvements in shear stress and heat transfer, reflecting enhanced velocity and thermal profiles compared to Madhukesh et al. (Gangadhar et al., 2024) [21]. The results indicate that increasing ${\varphi }_1$ enhances the Nusselt number and improves heat transfer, while the accompanying rise in flow resistance typically leads to a decrease in mass transfer rate.