A multi-layer neural network-based evaluation of MHD radiative heat transfer in Eyring-Powell fluid model.

In the modern era, artificial intelligence (AI) has been applied as one of the transformative factors for scientific research in many fields that could provide new solutions to extremely complicated and complex physical models. In this paper, a multi-layer neural network combined with Bayesian regularization procedure (MNNs-BRP) is utilized to evaluate the model MHD radiative heat in non-uniform heating Eyring Powell fluid (EPF-MHD-RHS). The mixed convection parameter, Prandtl number, and heat emission or immersion parameter are studied in relation to momentum and heat transfer. To facilitate analysis, governing partial differential equations (PDEs) are converted into ordinary differential equations (ODEs) only with the aid of similarity transformations. From there, a dataset is created and later trained, tested, and validated by the MNNs-BRP model for efficient estimating of fluid models. The MNNs-BRP model is robust and demonstrates high accuracy, which compares well with the benchmark solutions. Performances of which are confirmed by metrics like error histograms, mean squared-error (MSE) check-ups, and regression analysis with MSEs all over the interval [10(-09) - 10(-04)] to ensure a sustained model. The obtained outcomes indicate that the model built and implemented utilizing a neural network offers precise performance ranging from 3.25E-13 to 5.41E-13 with a mean error of around 3.25E-13, 1.56E-11, 5.41E-13, 2.97E-12, 1.03E-11, 2.05E-12, 1.49E-12, and 5.01E-12, across eight different circumstances, suggesting improved capability and reliability of the developed predictive model. After careful review and analysis, we have found that the temperature of the fluid decreases with the increase of Prandl number, while an inverse result is noticed with heat emission. However, the velocity of the fluid have an increasing trend with increasing values of mixed convection parameter, and heat generation or absorption parameter. In contrast the velocity profile have a decreasing trend with the increasing values of magnetic field parameter and stratification parameter. This work on integrating AI into this classical fluid dynamics problem is an entirely new paradigm that involves a smart combination of computational strategies with advanced physical modeling techniques. Our investigation is not just raising the bar for predicting complex fluid dynamics but also showing how AI can truly transform the entire research domain of fluid mechanics and related scientific disciplines. All the numerical and graphical illustrations attained by employing the AI-based techniques authenticates the solution methodology for the evaluation of fluid dynamics problems.