Unsteady Ternary Hybrid Nanofluid Flow with Variable Thermophysical Properties: A Physics-Informed Neural Network and Sensitivity Analysis Approach

The investigation of ternary hybrid nanofluids (THNFs) has garnered significant attention due to their exceptional thermophysical properties and potential applications in advanced thermal management systems. This study presents a comprehensive numerical investigation of unsteady stagnation-point flow of a ternary hybrid nanofluid over a convectively heated sheet, incorporating temperature-dependent viscosity and thermal conductivity variations, magnetohydrodynamic (MHD) effects, Brownian motion, thermophoresis, viscous dissipation, and chemical reaction. The governing partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations using similarity transformations. Physics-Informed Neural Networks (PINNs) are employed to obtain accurate numerical solutions, with the framework incorporating the governing equations, boundary conditions, and informed initial guesses into the loss function. The thermal performance of various ternary nanofluid compositions is evaluated, with MWCNTs/Al₂O₃/TiO₂ demonstrating the highest efficiency enhancement of 15.097%. A comprehensive parametric analysis reveals that the viscosity variation parameter (Λ) exerts the most dominant influence on momentum and transport characteristics, followed by unsteadiness (β) and thermal conductivity (ε). Response Surface Methodology (RSM) coupled with Central Composite Design (CCD) establishes quadratic regression models for skin friction, Nusselt, and Sherwood numbers, with ANOVA confirming statistical significance (R² > 0.987). Sensitivity analysis quantifies the relative impact of parameters, showing that Λ positively influences all transport quantities, while ε negatively affects skin friction and Nusselt number. This study demonstrates that PINNs provide a robust, mesh-free computational framework for complex nanofluid flows, offering superior accuracy and flexibility compared to traditional numerical methods.