Exploration of the Arrhenius activation energy in unsteady ternary hybrid nanofluid flow past a slendering stretching sheet: RSM analysis

Abstract

This paper examines how a ternary hybrid nanofluid made by combining ${\text{TiO}}_2$, ${\text{SiO}}_2$, and ${\text{Al}}_2{\text{O}}_3$ in water behaves when flowing across a stretching sheet with varying thickness. The motivation comes from real world needs in systems like solar collectors, biomedical devices, and industrial cooling, where better heat transfer with minimal drag is essential. Using a blend of the Differential Transformation Method (DTM) and statistical optimization techniques like Response Surface Methodology (RSM) and Central Composite Design (CCD), we study how magnetic field, radiation, nanoparticle volume fraction, and activation energy affects the system. The hybrid nanofluid’s improved thermal behavior is a key focus. It is found that the increasing sheet thickness leads to higher temperatures, while velocity and concentration drop. Greater thermal radiation and more silicon dioxide particles enhance the heat transfer, improving efficiency by 12% and reducing drag (skin friction) by 15% under optimized conditions. Thermal conductivity improves with more nanoparticles, raising the Nusselt number. Meanwhile, mass diffusion behavior captured by the Sherwood number is influenced by activation energy and the Schmidt number. Magnetic field and nanoparticle volume fraction effects together help lower surface drag.