Computational study of magnetohydrodynamics Williamson fluid flow over stretching surface with Soret and Dufour effects using machine learning

Understanding non-Newtonian fluid behavior with bioconvection is crucial for biomedical engineering, enhanced oil recovery, and microfluidic device applications. This study investigates the combined influence of Soret–Dufour cross-diffusion effects, thermal radiation, and microbial bioconvection on the magnetohydrodynamic Williamson fluid flow over exponentially stretching surfaces using a hybrid numerical-machine learning approach. Governing partial differential equations were transformed via similarity transformations and solved numerically using MATLAB's fourth-order boundary value solver. The research integrates machine learning-enhanced multiple linear regression analysis with cross-validation and hold-out testing, combining numerical accuracy with predictive efficiency. The hybrid approach achieved exceptional accuracy with R2 values ranging from 0.977 to 0.996 across all transport phenomena. Results demonstrate that magnetic fields significantly influence skin friction through Lorentz forces, while mass transfer is governed by the Schmidt number and heat transfer by Prandtl number effects. This methodology provides computational efficiency improvements while maintaining physical accuracy for biomedical devices, industrial heat exchangers, and environmental systems.