Statistical analysis of 3D MHD Williamson ternary nanofluid flow and heat transfer behaviour over a bilinear horizontally stretching sheet with activation energy, heat generation and Soret–Dufour effects

Abstract This study investigates the non-transient three-dimensional MHD boundary layer behaviour of a non-Newtonian Williamson ternary nanofluid over a stretching horizontal sheet. The ternary nanofluid consists of Cu, TiO 2 , and Fe 3 O 4 nanoparticles suspended in propylene glycol base fluid. Key physical Parametric effects are considered involve a Magnetic field acting in the transverse direction, chemical reaction process influenced by activation energy, Soret and Dufour effects, and heat generation or absorption. To analyse the system, the governing set of non-linear PDEs for the flow, heat, and mass transport have been simplified into a system of ordinary differential equations by similarity transformations. These equations are numerically Solved through MATLAB’s boundary value solver, bvp4c with the shooting method. Furthermore, Response Surface Methodology (RSM) is used to determine parameter sensitivity and show the cumulative effects of key factors. The findings show that greater Weissenberg numbers enhance both tangential and transverse velocities due to viscoelastic characteristics. Increasing porosity improves flow penetration and momentum dispersion. Thermal radiation and heat source enhance fluid temperature, but the Dufour effect cools through concentration-induced heat transfer. Quantitative findings from RSM indicate up to 11.6 % improvement in tangential velocity and 9.8 % temperature enhancement with higher Weissenberg and radiation parameters, while concentration decreases by 7.4 % under stronger chemical reaction effects. Statistical analysis via RSM and ANOVA confirms excellent model predictability, with R 2 values exceeding 97 % for all responses, reinforcing the reliability of the results. This comprehensive model provides a realistic depiction of tri-hybrid nanofluid dynamics under coupled thermal, chemical, and electromagnetic impacts. It has important implications for advanced thermal systems, energy-efficient reactors, and magneto-thermal flow control technologies.