Numerical and neural network analysis of rotating hybrid Cu–Al ₂ O ₃ /water nanofluid flow with Hall current, Joule heating, and nonlinear thermal radiation effects

This study investigates the combined effects of rotation, Hall current, chemical reaction, and nonlinear thermal radiation on the flow and heat transfer of a rotating hybrid nanofluid (Cu–Al₂O₃/water) over a stretching surface with an internal heat source. The governing partial differential equations are transformed into nonlinear ordinary differential equations using similarity transformations and solved numerically via the shooting method. The results indicate that an increase in the Hall current parameter enhances transverse velocity and temperature while reducing longitudinal velocity. A higher chemical reaction parameter decreases nanoparticle concentration due to intensified species depletion. Variations in skin friction coefficients, Nusselt number, and Sherwood number are also analyzed. Furthermore, a neural network model is developed to predict skin friction coefficients (Cfx and Cfy). Comparative analysis shows that the Levenberg–Marquardt algorithm achieves higher accuracy, whereas the BFGS method ensures faster convergence, demonstrating the effectiveness of machine learning in modeling complex nanofluid transport phenomena.