Intelligent deep learning analysis of MHD williamson ternary hybrid nanofluid thin film transport with heat and mass transfer under multiple slip effects

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This study explores the unsteady, incompressible magnetohydrodynamic (MHD) flow of a Williamson-type ternary hybrid nanofluid (THNF) over a thin film on a stretching sheet embedded in a Darcy–Forchheimer porous medium. The THNF comprises A u , A l 2 O 3 , and T i O 2 nanoparticles suspended in a water–ethylene glycol base fluid, incorporating Soret and Dufour effects, activation energy, thermal radiation, and a non-uniform heat source/sink. The resulting nonlinear boundary value problem is numerically solved using MATLAB's bvp5c solver and validated via an Artificial Neural Network (ANN) model, which achieves excellent accuracy with a minimal mean squared error of 1.1976 × 10 − 13 . Key results indicate that increasing the Hartmann number, Forchheimer parameter, and velocity slip parameter suppresses fluid velocity due to enhanced magnetic drag, porous resistance, and reduced momentum transfer. The unsteadiness parameter and film thickness further diminish velocity by limiting momentum development and increasing viscous resistance. In contrast, a higher Weissenberg number boosts velocity and wall shear stress due to elastic effects. The ANN-predicted concentration profiles show strong agreement with bvp5c results under varying radiation and Schmidt numbers, confirming its reliability as a surrogate model. Physically, the concentration increases with the radiation parameter and decreases with Schmidt number, attributed to enhanced radiative energy transfer and reduced mass diffusivity, respectively. Additionally, thicker films lower skin friction, Nusselt, and Sherwood numbers by thickening boundary layers. Conversely, rising Prandtl and Weissenberg numbers steepen thermal and velocity gradients near the wall, enhancing heat transfer and skin friction. The ANN framework proves to be a fast and robust predictive tool, offering significant potential for applications in polymer extrusion, thin-film cooling, microfluidics, and biomedical devices requiring precise control over flow and heat transport in deformable, heat-sensitive environments.