Cross-thermal streamline patterns and heat transfer in EP-nanofluids: a neural network approach with uncertainty analysis
Umar Farooq, Ali Alshamrani, Muhammad Mahtab Alam, Khadija Rafique
Abstract
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 ( F e 2 O 3 ) and silicon dioxide ( S i O 2 ) nanoparticles dispersed in water ( H 2 O ) , 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 F e 2 O 3 and by 1.71 %–1.54 % for S i O 2 ; as R d increases from 0.3 to 1.2, the Nusselt number increases by −10.17 % to −6.52 % for F e 2 O 3 and by −10.19 % to −6.58 % for S i O 2 ; The influence of porosity ( ϵ ) and Eckert number ( E c ) 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 .