A Comprehensive Numerical and Data-Driven Investigations of Nanofluid Heat Transfer Enhancement Using the Finite Element Method and Artificial Neural Network

This study outlines a quantitative and data-driven study of the mixed convection heat transfer processes that concern Cu-water nanofluids in a $\mathrm{\Gamma }$-shaped enclosure with one to five rotating cylinders. The dimensionless equations of mass, momentum, and energy are solved using the finite element method as implemented in the COMSOL Multiphysics 6.3 software in different rotating Reynolds numbers and cylinder geometries. An artificial Neural Network that is trained using Bayesian Regularization on data produced by the COMSOL is utilized to estimate the average Nusselt numbers. The analysis is conducted for a wide range of rotational Reynolds numbers $({\text{Re}}_{\omega }=0-100)$, with the fixed Prandtl number. Results are presented in terms of streamline patterns, isotherm contours, and Nusselt numbers to assess heat transfer behavior. Findings revealed that increasing the number of cylinders and optimizing their placement significantly enhances convective mixing and thermal transport. The ANN model accurately predicts the Nusselt numbers across all configurations with negligible errors. Among all configurations, the third arrangement in Scenario 5 exhibits the highest heat transfer rates, attributed to intensified vortex interaction and reduced thermal resistance. Artificial neural networks and finite element-based models will be of great value to the design of miniature and energy-efficient enclosures and electronics cooling mechanisms that make use of nanofluids.