Machine learning-driven modeling and prediction of flow and heat transfer of water-based nanolayered nanofluid using Koo–Kleinstreuer–Li and Cattaneo–Christov heat flux models

This work addresses the three-dimensional flow and heat transfer characteristics of nanolayered water-based nanofluid across a stretching sheet. The Boger fluid model is integrated with the Powell–Eyring fluid model to reduce the impacts of inertial forces. A high-viscosity fluid is mixed with water (base fluid) during the mixture preparation. The Koo–Kleinstreuer–Li correlation is deployed, which accounts for effective viscosity and thermal conductivity. The non-Fourier thermal relaxation effects are captured via the Cattaneo–Christov heat flux model. The governing equations are derived under the Oberbeck–Boussinesq approximation. The obtained equations are converted into dimensionless form and solved numerically using the three-stage Lobatto method. A robust Levenberg–Marquardt (LM) backpropagated artificial neural network (ANN) is trained to forecast flow dynamics. The numerical dataset is split in such a way that 15% is used for testing, 15% for validation, and 70% for training. Regression analysis, surface stresses, error histogram, correlation index, heat transfer, and MSE-based fitness curves, which range from 10−10 to 10−8 are used to validate the consistency and efficacy of LM-ANN. The findings suggest that Marangoni convection improves the axial and transverse velocities. The temperature and transverse velocity are increasing functions of the Powell–Eyring viscosity parameter, while a decreasing trend was seen for axial velocity. The temperature profile is suppressed by the thermal relaxation parameter. The ANN predicted R2 values for skin friction and Nusselt number are above 99%, which is in good agreement with the numerical results. The ANN model provides enhanced predictive ability with less processing load than traditional methods for modeling fluid dynamics.