Machine Learning-Enhanced Simulation of Maxwell Nanofluid Flow: A Bayesian Neural Network Approach with Thermal Relaxation and Variable Viscosity Effects

This study examines the Maxwell nanofluid's movement along an inclined plate, incorporating couple stress and variable viscosity effects via a machine learning approach. Key innovations include: (1) a hybrid numerical-ML framework using MATLAB's bvp4c and Bayesian Neural Networks (BNN) for uncertainty quantification; (2) the novel integration of Cattaneo-Christov heat flux with Brownian motion and thermophoresis; and (3) rigorous validation through grid tests and ANN correlations (R ≈ 1). Results show the Maxwell parameter increases the friction factor by 5.82%, while thermophoresis parameter reduces the Nusselt number by 9.59% and the Brownian motion parameter enhances mass transfer by 1.74%. The BNN model achieves high accuracy (error < 0.5%), bridging non-Fourier heat transfer with data-driven methods to optimize thermal and microfluidic systems.