Numerical–ANN Framework for Thermal Analysis of MHD Water-Based Prandtl Nanofluid Flow over a Stretching Sheet Using Bvp4c

The main goal of this study is to create a computational solver that analyzes the effects of magnetohydrodynamics (MHD) on heat radiation in Cu–water-based Prandtl nanofluid flow using artificial neural networks. Copper nanoparticles are utilized to boost the water-based fluid’s thermal effect. This study primarily focuses on heat transfer over a horizontal sheet, exploring different scenarios by varying key factors such as the magnetic field and thermal radiation properties. The mathematical model is formulated using partial differential equations (PDEs), which are then transformed into a corresponding set of ordinary differential equations (ODEs) through appropriate similarity transformations. The bvp4c solver is then used to simulate the numerical behavior. The effects of relevant parameters on the temperature, velocity, skin friction, and local Nusselt number profiles are examined. It is discovered that the parameters of the Prandtl fluid have a considerable impact. The local skin friction and the local Nusselt number are improved by increasing these parameters. The dataset is split into 70% training, 15% validation, and 15% testing. The ANN model successfully predicts skin friction and Nusselt number profiles, showing good agreement with numerical simulations. This hybrid framework offers a robust predictive approach for heat management systems in industrial applications. This study provides important insights for researchers and engineers aiming to comprehend flow characteristics and their behavior and to develop accurate predictive models.