Intelligent computational modeling of Maxwell–Smoluchowski thermal slip effects under non-uniform heat sources using radial basis networks

The current article investigates the application of Artificial Intelligence (AI) to evaluate the Buongiorno thermal enhancement model with a Darcy–Forchheimer formulation (BTEM-IDFE). AI-driven radial basis function neural networks (RBFNNs) are employed to accurately forecast magnetohydrodynamic (MHD) nanofluid flow over a stretching boundary, accounting for entropy production and fluctuating fluid properties. RBFNNs are used to simulate and predict complex heat-transfer dynamics in such environments, yielding more accurate and efficient analyses than conventional numerical methods. We investigate the effects of the Maxwell slip velocity, the Smoluchowski slip temperature, and the Arrhenius activation energy. A synthetic dataset was generated via the Lobatto III-A computational integration approach. The proposed RBFNN algorithm is then applied to the obtained datasets, yielding outputs with negligible error that closely align with the numerical experiments across all model variants. A comprehensive graphical examination of liquid motion, entropy generation, concentration, and temperature distribution is conducted. Our findings indicate that applying the RBFNN to the proposed framework effectively captures the interactions and interdependencies among key parameters, including radiation parameters, temperature-dependent conductivity, porosity, velocity slip parameters, and thermophoresis effects, in relation to temperature and entropy rates. The efficacy of RBFNN is demonstrated through comprehensive experiments, including iterative convergence curves for mean squared error, optimization control measures, error distributions via histograms, and robust regression analysis. • This study investigates the Buongiorno thermal enhancement model with a Darcy–Forchheimer formulation (BTEM-IDFE). It employs radial basis function neural networks to accurately predict magnetohydrodynamic nanofluid flow over a stretching boundary, while capturing entropy generation and variable fluid properties. • The suggested AI-based RBFNN guarantees accelerated convergence and reduced computational errors relative to traditional approaches. • The proposed solver presents compelling numerical evidence that enhances our comprehension of the mathematical nonlinear (BTEM-IDFE), facilitating significant insights and advancements. • The dataset was split into three segments: 10\% for testing, 20\% for validation, and 70\% for training. The results closely correspond with Adam optimization outcomes, underscoring the model’s stability and effectiveness. • Velocity diminishes with increasing magnetic parameter $M$, indicating stronger Lorentz drag. • Absolute error plots validate the high accuracy and numerical stability of the proposed approach. • Skin friction coefficient $C_{fs}$ shows minor to moderate variations with respect to physical parameters such as $M,\beta_2$ and $\epsilon_1$, but remains nearly constant in response to changes in $\beta_1$. • Heat transfer rate $Nu_s$ reduces with stronger magnetic and stretching effects but is enhanced with increased porosity and thermal conductivity variations. • Mass transfer rate $Sh_s$ increases significantly across all cases, emphasizing the dominance of thermophoretic and chemical reaction parameters. • Graphical illustrations are presented that underscore the model’s ability to accurately capture the complex behavior of velocity, temperature, and concentration fields influenced by slip effects and diffusive parameters in magnetized, chemically reactive nanofluid flows.