Thermal Performance of Williamson Fluid Flow over Vertical Stretching Sheet: A Mathematical and Machine Learning Perspective

Stagnation flow of Williamson fluid over nonlinearly stretching vertical sheet with heat generation, viscous dissipation and thermal slip has been analyzed. Governing equations have been formulated using boundary layer approximation and expressed as differential equations. Then, we transformed into dimensionless form through suitable similarity variables. Applying the boundary layer approximation, the governing Partial Differential Equations (PDEs) have been transformed into Ordinary Doifferential Equatiuons (ODEs). Hybrid techniques has been adopted which combined the numerical technique and Artificial Neural Networks (ANN) to enhance prediction and analysis. Results have indicated that governing parameters have strongly influenced flow and heat transfer characteristics, while ANN predictions have accurately validated numerical outcomes. The integrated approach has demonstrated the capability of ANN in complementing numerical simulations for complex fluid dynamics systems. Effects of key physical parameters have been illustrated through graphs and tables, showing that an increasing Grashof number has strengthened buoyancy-driven flow and enhanced fluid motion near the surface. Response Surface Methodology (RSM) is presented and sensitivity of Nusselt number in relation with various parameters is discussed in detail.