Optimization of 3D hydromagnetic Casson fluid flow over a permeable stretching surface using RSM and AI

This study explores the pour behavior of Casson liquid along a stretching sheet implanted in a permeable way through practical applications in industrial coating, polymer extrusion, and biomedical processes. The prototypical features the properties of thermal energy, Dufour property, and a first-order compound response, making it relevant for temperature and mass transmission phenomena in industrial approaches. The governing equations are explained by applying the BVP4C shooting method; in addition, the results are presented graphically to illustrate the speed, intensity, and hotness outlines. The findings indicate that the Casson fluid parameter reduces the fluid velocity in both axial and transverse directions, which has direct implications for drag reduction and flow control in manufacturing processes. Additionally, the enhancement of thermal and solutal boundary layers with increasing Casson fluid effects is significant for improving heat exchanger efficiency and controlling chemical reaction rates. A comparative analysis using prior analyses confirms the precision and reliability of the results, making this model a valuable tool for industrial and engineering applications.