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.