Intelligent mathematical modeling of non-Newtonian MHD nanofluid flow in Eyring–Powell systems for advanced thermal applications

This study explores the effect of nanoparticles on the magnetohydrodynamic (MHD) flow, heat transfer and mass transfer of Eyring–Powell fluid, which flows over a convectively heated stretching surface in two lateral directions. This study is the first to integrate a multi-layer neural network trained with the Levenberg–Marquardt backpropagation algorithm (MLNNs-LMBA) for accurately modeling three-dimensional MHD Eyring–Powell nanofluid flow over a convectively heated stretching surface under the coupled effects of Brownian motion, thermophoresis, thermal radiation and internal heat generation achieving exceptionally low MSE with near-ideal regression fits. Unlike conventional numerical methods such as the shooting method with Runge-Kutta schemes, the proposed AI-based paradigm eliminates iterative guesswork, provides rapid predictions after training and establishes a new benchmark for surrogate modeling in non-Newtonian nanofluid systems. The capabilities of artificial intelligence-based techniques Multilayer neural networks with Levenberg Marquardt backpropagation algorithm (MLNNs-LMBA) are utilized to investigate this problem. Using the Adams Method in Mathematica, a library of reference data is created that quantifies the effects of key parameters related to Brownian motion, thermophoresis, thermal radiation, and internal heat generation/ absorption. The original governing equations form can be perfectly transformed into nonlinear ODEs and then we can observe the behavior using reference data. The library of reference data is used to train on MLNNs-LMBA, 70% of the dataset is used to train the library data and 30% of the data is used for validation and testing. Model performance and accuracy is measured using regression assessments, mean square error curves, error histograms and mean absolute error metrics; these demonstrate that both models can predict well against the reference solutions. The best metrics of presentation in terms of MSE are attained at level 9.5171E-09, 6.2384E-08, 3.8596E-09, 1.9699E-08, 3.1551E-08, 6.6115E-09, 6.5633E-08, 2.7412E-09, 1.247E-08,4.1632E-09 and 1.313E-07 against 461, 425, 247, 444, 777, 483, 169, 511, 412, 665 and 248 epochs. The investigation suggests that MLNNs-LMBA is legitimate and precise. We observe that the effect of a magnetic field acts to reduce the velocity components and increase the skin-friction coefficient, while the Eyring–Powell fluid parameters have an opposite effect, augmenting the velocity fields and providing reduction in skin-friction coefficient indicating the opposing relationships between these measures and effects. Thickness of the thermal border layer undergoes significant expansion by escalating values of M2, Nb, Nt, R, Q, and Bi, whereas it exhibits a pronounced contraction with increasing values of c, ε, and Pr. Meanwhile, the nanoparticles concentration boundary layer thickness demonstrates dual behavior, increasing with M2, Nt, Q, and Bi, while decreasing with Nb, c, ε, and Le.