# Bayesian-optimized machine learning and experimental study of Al₂O₃-CuO hybrid nanofluid thermal performance in turbulent circular tube flow

## TL;DR

This study investigates how Al₂O₃-CuO hybrid nanofluids improve heat transfer and reduce entropy in turbulent tube flow using experiments and machine learning.

## Contribution

The novelty lies in combining Bayesian-optimized XGBoost machine learning with experimental and numerical analysis to model hybrid nanofluid thermal performance.

## Key findings

- Hybrid nanofluids reduced total entropy generation by 71% compared to water.
- XGBoost achieved high accuracy in predicting thermal parameters with R² values up to 1.000 for training data.
- Empirical correlations were developed to accurately predict Nusselt number and friction factor.

## Abstract

This study explores the thermal behavior of hybrid nanofluids (HNFs) composed of water mixed with equal proportions (50:50) of Al₂O₃ and CuO nanoparticles (NPs) under turbulent flow regimes. The nanofluids (NFs) are prepared in the volume concentrations range of 0–1%. Both experimental investigations and numerical simulations were carried out to evaluate the effects of NP concentration and Reynolds number (Re) on Nusselt number (Nu), friction factor, and entropy generation. Results demonstrated a marked enhancement in heat transfer with increasing NP concentration and flow rate. Notably, the use of HNFs led to a 71% reduction in total entropy generation (TEG) compared to water alone. Empirical correlations were developed to predict the Nu and friction factor accurately. Furthermore, an XGBoost machine learning model was employed to estimate thermal parameters with high precision. The model achieved an R² of 1.000 (training) and 0.991 (testing) with an MSE of 0.001 for TEG. For the friction factor, R²training as 0.686 and R²test as 0.916 (testing) were obtained. Nu model achieved perfect training accuracy (R² = 1.000) and strong testing performance (R² = 0.975, MSE = 29.457). These results affirm the effectiveness of XGBoost in modeling thermofluidic behavior in HNF systems.