Precise forecasting of shear stress, viscosity, and density for an aqueous CuO/CaCO3/SiO2 ternary hybrid nanofluid utilizing the artificial neural network

Abstract

The accurate prediction of thermophysical properties in hybrid nanofluids is crucial for enhancing the efficiency of advanced heat transfer and energy conversion systems. Most published research has largely concentrated on single- or binary-nanoparticle systems, and ternary hybrid systems are still poorly understood in terms of interactions. The present study, however, developed two-layer feedforward artificial neural networks to predict shear stress, viscosity, and density for a water-based nanofluid containing copper oxide, calcium carbonate, and silicon dioxide in volume ratios of 60, 30, and 10%, respectively. Training and validation of the networks were based on experimental data collected at temperatures ranging from 25 to 70 °C and nanoparticle volume fractions ranging from 0.5 to 3%. That model achieved outstanding predictive performance, with average root-mean-square errors (evaluated via K-fold cross-validation) of 0.0008 Pa for shear stress, 0.0097 mPa s for viscosity, and 0.0003 g/cm³ for density. Minimum mean squared errors were 1.63 × 10⁻⁶, 3.11 × 10⁻⁵, and 4.03 × 10⁻⁵, respectively, with correlation coefficients over 0.999 across all data sets. The calculated maximum relative errors were 0.71% for shear stress, 1.34% for viscosity, and 0.06% for density, which endorse the reliability and precision of the produced model. Further sensitivity analysis demonstrated that temperature dominance over shear stress and viscosity, although nanoparticle concentration exerted a significantly stronger impact on density. The proposed framework served as an accurate, data-driven tool for modeling ternary hybrid nanofluids, providing practical insights into their optimized formulations for high-performance thermal management applications.