Hybrid numerical–machine learning framework for heat transfer prediction in TiO₂ nanofluid microtubes

Abstract

Heating and cooling processes using microtubes are crucial for the thermal management of electronic devices. The investigation of such complex conjugate heat transfer systems via traditional numerical methods demands significant computational time and resources. Therefore, the necessity of this study arises from the need for faster, cost-effective, and highly accurate prediction models to accelerate the design and optimization of micro-scale cooling systems. The primary aim of this study is to numerically investigate the thermal performance of a water-based TiO₂ nanofluid flowing through thick-walled microtubes and, crucially, to develop a robust hybrid numerical–machine learning framework capable of offering high predictive accuracy. This study aims to address a gap in the literature. The model considers an infinitely long microtubes with a heated section of length L, where a constant surface heat flux is applied. The governing two-dimensional laminar flow and energy equations, expressed in cylindrical coordinates, were non-dimensionalized, discretized via finite and central difference schemes, and solved numerically. Viscous damping and slip velocity boundary conditions were also incorporated. Results show that conjugate heat transfer effects intensify with increasing wall thickness but diminish with lower wall–fluid interface and Peclet parameters. These parameters influence transient and steady-state behavior differently. The distinctive contribution of this work lies in the data-driven modeling and prediction of the microtube heat transfer parameter (Qwi) using six regression methods: Linear Regression, Random Forest, Support Vector Regression (RBF kernel), Extreme Gradient Boosting (XGBoost), Multi-Layer Perceptron (MLP), and one-dimensional Convolutional Neural Network (1D-CNN). All models achieved high predictive accuracy (R² > 0.96), with ensemble and kernel-based methods—particularly XGBoost and SVR—producing the best results (R² = 0.9999, RMSE < 0.001). The findings demonstrate that while tree- and kernel-based models outperform the linear baseline, deep learning architectures exhibit strong generalization to nonlinear behaviors, underscoring the potential of AI-driven modeling in nanofluid-based thermal systems.