Thermal analysis of ternary hybrid nanofluid flow in convergent/divergent channel using Box-Behnken design of response surface methodology

Convergent/divergent channels represent a critical advancement in thermal management systems, offering enhanced heat transfer capabilities through geometrically optimized flow paths. This study investigates the thermal and hydrodynamic characteristics of UO₂-ZnO-Fe₃O₄/EG-water ternary hybrid nanofluid in rotating convergent/divergent channels with magnetohydrodynamic and radiation effects, a critical area for enhancing heat transfer efficiency in modern thermal management systems. Employing the Runge-Kutta-Fehlberg method coupled with a Box-Behnken design approach, we analyzed how key parameters affect flow behavior and heat transfer performance. The numerical simulations reveal that increasing the nanoparticle volume fraction from 0.01 to 0.06 enhances the Nusselt number by 27.3 %, while an increase in the magnetic parameter reduces the friction coefficient by 41.2 %. The Reynolds number demonstrates a strong positive correlation with the Nusselt number (R² = 0.978). Maximum heat transfer (Nu = 33.4859) achieved at: α = 1°, Re = 40, φ = 3 %, Ha = 50, Rd = 1, Kn = 0.04, De = 0.5, Ro = 50, ε = 0, λ = 0.5 whereas a minimum flow resistance (Cf = -2.60454) occurred at: α = -3°, Re = 60, φ = 6 %, Ha = 25, Rd = 1, Kn = 0, De = 0.5, Ro = 50, ε = 0.2, λ = 0.5. For the convergent channel configuration (α = -3°), the friction coefficient was 28.3 % higher than in the divergent channel (α = 5°) under identical flow conditions. This work advances the field beyond previous studies by comprehensively analyzing the synergistic effects of rotation, magnetohydrodynamic, radiation, and channel geometry on the performance of ternary hybrid nanofluids, providing crucial insights for designing more efficient thermal systems in electronics cooling, heat exchangers, and industrial processing applications.