Computational analysis and data-driven optimization of radiative magnetohydrodynamic Williamson ternary hybrid nanofluid at separated stagnation-point flow

The goal of this study is to analyze, predict, and optimize the thermal and frictional properties of the unsteady separated stagnation-point flow of a radiative magnetohydrodynamic (MHD) Williamson ternary hybrid nanofluid to minimize skin friction and maximize heat transfer. The nonlinear governing boundary-layer equations were derived to account for the combined effects of unsteady separated stagnation point flow of MHD Williamson ternary hybrid nanofluid over a stretching surface, incorporating thermal radiation and mass suction, and were solved numerically using MATLAB's bvp4c method. Using the data, a scaled conjugate gradient-based Artificial Neural Network (SCG-ANN) demonstrated exceptional predictive performance, with MSE ranging from 10#8315;⁶ to 10#8315;⁷ and correlation coefficient (R) exceeding 0.999, indicating high model accuracy and generalization potential. To determine the best operating conditions, the effect and interaction of unsteadiness (β), nanoparticle volume fraction (ϕ), Weissenberg number (We), and radiation (Rd) on the skin friction coefficient and local Nusselt number were quantified using the Response Surface Methodology (RSM) with a Central Composite Design (CCD). The ANOVA findings showed significant models with R2 = 95.09% for skin friction and 95.46% for Nusselt number. With a composite desirability of 100%, the RSM optimization projected the minimal skin friction (0.4686) at β=1.68179,ϕ=−1.61384, and We=1.68179, and the highest Nusselt number (129.68) at β=−1.68179,ϕ=−1.68179, and Rd=1.68179. Research shows that increasing the Weissenberg number and flow deceleration (negative β) reduce drag, while increasing nanoparticle volume fraction and radiation intensity enhance heat transfer. For designing advanced cooling, energy, and drag-reduction applications, the integrated SCG-ANN-RSM framework predicts and optimizes thermo-hydrodynamic transport in radiative non-Newtonian nanofluid systems using a computationally efficient and powerful hybrid modelling strategy.