Artificial neural networks framework for investigating Hall and ion slip dynamics in Prandtl nanofluids using non-Fourier heat and mass transfer models

Abstract

Artificial neural networks (ANNs) are widely applied in fluid mechanics and engineering to model complex relationships between input and output data. They facilitate pattern recognition, process optimization, and material property prediction. This study focuses on resolving the Hall ion effect in Prandtl nanofluid using a non-Fourier double diffusion theory-based model (HIE-PNF-NFDDT). The Levenberg-Marquardt backpropagated neural network (LMBNN) method is employed to analyze temperature, velocity, and concentration distributions. The dataset for training the ANN is obtained using the bvp4c solver. The study investigates the impact of the Hall effect and ion slip phenomena on the Cattaneo-Christov double heat flow model, leveraging the LMBNN algorithm to obtain solutions. Results indicate a direct correlation between velocity and the Hall parameter. Temperature increases with the Brownian motion parameter but decreases as the Hall parameter rises. Similarly, concentration increases with the Hall parameter but exhibits an inverse relationship with the relaxation time parameter. The performance of the proposed ANN model is evaluated using key metrics range of Mean Squared Error is detected as ${10}^{-9}-{10}^{-10}$, while the Error Histograms ranges between ${10}^{-05}-{10}^{-07}$.The gradient lies near ${10}^{-08}$, while the $\mathrm{Mu}$ ranges between the interval ${10}^{-08}-{10}^{-09}$. The AE lies in ${10}^{-03}-{10}^{-08}$, which shows the accuracy and reliability of the suggested method. The proposed approach demonstrates rapid convergence, efficient modeling, and reduced computational costs, making it a powerful tool for solving complex nonlinear problems in engineering and fluid mechanics.