Cross-thermal streamline patterns and heat transfer in EP-nanofluids: a neural network approach with uncertainty analysis

This study presents a mathematical model of tissue adhesive based on stretched surfaces with emphasis on flow and thermal characteristics using artificial neural networks with a Levenberg-Marquardt backpropagation scheme (ANN-LMBS). The model investigates Eyring-Powell nanofluids (EP-NF) with ferric oxide (Fe2O3) and silicon dioxide (SiO2) nanoparticles dispersed in water (H2O), focusing on magnetic strength, Darcy drag, viscous dissipation, joule heating and thermal radiation effects. Validation consists of 70 % training, 15 % testing, and 15 % validation. This dataset covers four scenarios and nine EP-NF cases. The resulting domain is divided into 300 grid points for velocity and temperature profiles. The ANN-LMBS model demonstrated excellent robustness in terms of accuracy, precision, and convergence, as verified by error histograms and regression optimization. The main findings include: as M increases from 1 to 4, the Nusselt number decreases by 2.48 %–2.16 % for Fe2O3 and by 1.71 %–1.54 % for SiO2; as Rd increases from 0.3 to 1.2, the Nusselt number increases by −10.17 % to −6.52 % for Fe2O3 and by −10.19 % to −6.58 % for SiO2; The influence of porosity (ϵ) and Eckert number (Ec) is less pronounced but still noticeable (∼3 % and 1.2 %, respectively). The governing equations, solved numerically via non-similarity transformation and the BVP4C algorithm, align with boundary conditions across all scenarios, with uncertainty analysis confirming solution robustness. Cross-thermal streamline patterns further enhance insights into flow dynamics, underscoring the model's potential in biomedical applications.