Thermal performance analysis of magnetohydrodynamic Al2O3-SiO2-TiO2/water ternary hybrid nanofluid in converging and diverging channels with nanoparticle shape effects

Improving heat transfer in thermal systems is critical to achieving better results in a variety of systems. The study aims to investigate the laminar flow dynamics of Al${}_2$O${}_3$-SiO₂-TiO${}_2$/water hybrid nanofluids, emphasizing how the channel geometry affects the velocity, temperature distribution, and heat transfer efficiency. This understanding is crucial for optimizing industrial processes, such as cooling systems and heat exchangers. Effects of various nanoparticle shapes, joule heating, viscous dissipation, thermal radiation, and heat source/sink on the system’s behavior are evaluated. Governing partial differential equations are transformed into ordinary differential equations using similarity variables and are solved semi-analytically via the homotopy analysis method. As the Hartmann number increases from 1 to 7, the heat transfer rate rises from 0.02% to 0.9%. When the radiation parameter and Eckert number are varied from 0.05 to 0.2, the heat transfer rate increases significantly, from 1.2% to 4.86% and 3.43% to 13.73%, respectively. Heat transfer rate increased by 16.28% with heat source ($Q=2$) and decreased by -16.12% with heat sink ($Q=-2$). Platelet-shaped nanoparticles demonstrate lower skin friction in divergent channels, whereas spherical nanoparticles exhibit higher skin friction; this trend reverses in convergent channels. Suspensions of nanoparticles with a 5% volume fraction achieve heat transfer rates of 1.88%, 4.07%, 10.54%, 19.20%, and 8.74% for spheres, bricks, cylinders, platelets, and blades, respectively. The study reveals that Al${}_2$O${}_3$/H${}_2$O, Al${}_2$O${}_3$-TiO${}_2$/H${}_2$O, and Al${}_2$O${}_3$-SiO₂-TiO${}_2$/H${}_2$O nanofluids have the best heat transfer rates for mono nanofluid, hybrid nanofluid, and ternary hybrid nanofluid by 15.24%, 19.92%, and 19.20%, respectively. Finally, multiple linear regression is employed to analyze the impact of relevant parameters on heat transfer rate and skin friction.