Hall-effect flow and heat transfer over stretching sheets: a comparison of PINNs and RK-shooting methods

A novel class of similarity transformations with Lie parameters is derived using Lie symmetries for three-dimensional fluid flow and heat transfer with the Hall effect. The flow equations are transformed via the deduced mappings incorporating Lie parameters that are shown to regulate the stretching-induced thermal transport and thermal convection, resulting in a strong response of the thermal field. These influences are illustrated through velocity and temperature profiles obtained by applying the RK-Shooting method using MAPLE and Python, as well as Physics-Informed Neural Networks-PINNs in Python on the transformed equations. A comparative analysis of these solutions is conducted to validate the deduced fluid dynamics. RK-Shooting in MAPLE is found to be computationally more efficient than PINNs and RK-Shooting-based frameworks in Python. The core contributions of this work are derivation of similarity transformations with Lie parameters and application of PINNs to the considered flow, which have not previously been reported.