Heat transfer optimization and sensitivity analysis of ternary hybrid nanofluid flow over a moving surface with joule heating

Efficient heat transfer is a major challenge in systems like MHD pumps, electromagnetic cooling units and rotating heat exchangers especially under extreme conditions. The combined effects of magnetic fields, Joule heating and multiple nanoparticles create complex behaviors that are hard to solve using analytical methods. Therefore, reliable numerical methods and statistical optimization tools are needed to analyze and improve these systems. Hence, this work highlights ternary hybrid nanofluid flow over a permeable moving surface with the influence of magnetohydrodynamic (MHD), Joule heating and suction effects, integrating both computational and optimization techniques. The fluid comprises water-based ternary hybrid nanofluid containing aluminum oxide (Al2O3), copper (Cu) and titanium dioxide (TiO2) nanoparticles. The governing partial differential equations are transformed into a system of ordinary differential equations using similarity transformations and solved using the bvp4c solver (MATLAB). Validation of the numerical approach is carried out by comparing results with existing literature which showing excellent agreement for limiting cases. Response surface methodology (RSM) is applied to analyze interactions between the key parameters. Results indicate that both magnetic parameter and titania concentration significantly enhance the velocity profile due to the induced Lorentz force and altered thermal gradient. Analysis of variance (ANOVA) confirms that magnetic parameter and titania concentration are the most influential on thermal and flow responses. Sensitivity analysis further highlights strong linear and interaction effects.