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

Document Type : Research Paper

Authors
S. Mamatha Upadhya 1
M. Jayachandra Babu 2
K.S. Srinivasa Babu 3
1 Faculty of Mathematics, School of Business and Management, Kristu Jayanti Deemed to be University, K. Narayanapura, Kothanur, Bengaluru, Karnataka - 560077, India
2 Department of Mathematics, Government Degree College, Rajampeta, Annamayya district, Andhra Pradesh – 516115, India
3 Department of EM&H, S.R.K.R. Engineering College, Bhimavaram – 534204, Andhra Pradesh, India
10.22055/jacm.2025.48495.5275
Abstract
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.
Keywords
Non-Newtonian fluid
Variable Viscosity
Thermophoresis
Brownian motion
Activation energy
bvp4c
Subjects

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Journal of Applied and Computational Mechanics
Volume 12, Issue 3
Summer 2026
Pages 815-827