Modeling the Effectiveness of Chemical Reactions in Magnetized Nanofluids: The Influence of Activation Energy and CattaneoChristov Transport Phenomena

The remarkable capacity of artificial neural networks to simulate complex and nonlinear mathematical phenomena, particularly in domains such as thermal engineering and nanotechnology, is a primary reason for their widespread application. Thus, ANNs provide a flexible computational framework that can be applied in a wide range of fields, including fluid mechanics, biological sciences, and computational biology. In this work, the boundary-layer flow and heat transfer properties of a magnetized Powell-Eyring nanofluid containing microorganisms across a bidirectional stretchable sheet are analyzed using a computational ANN paradigm. The model considers the combined effects of Darcy-Forchheimer, thermal radiation, and internal heat generation, as well as modified CattaneoChristov heat and mass flux, magnetohydrodynamics (MHD), and activation energy. The governing system of equations is reduced to a set of nonlinear ordinary differential equations through a similarity transformation. The BVP4C solver in MATLAB is then used to numerically solve the ODEs. An Artificial Neural Network Backpropagation Levenberg–Marquardt technique (ANN-BPLMT) customized for the radiative Powell-Eyring nanofluid system is trained using the resultant numerical solutions as a reference dataset. The numerical solutions are then approximated under various parametric settings by training, testing, and validating the LMT-ABPNN. Performance indicators, including mean squared error, fitness curves, error histograms, and statistical transition analyses, are used to validate models. The results reveal that the numerical reference data and the ANN predictions correspond extremely well. The high accuracy, robustness, and predictive reliability of the suggested LMT-ABPNN framework for simulating radiative Powell-Eyring nanofluid flows are confirmed by the low MSE and minimal absolute error, both of which approach zero.