Prediction of the dynamic viscosity, electrical conductivity, thermal conductivity, and pH of Fe₃O₄/TiO₂ hybrid nanofluids using a proposed framework with a machine learning method

Accurate prediction of the thermophysical and physicochemical properties of hybrid nanofluids is essential for their reliable use in thermal management systems, while extensive experimental characterization is often costly and time-consuming. In this study, a feedforward artificial neural network was developed to simultaneously predict the dynamic viscosity, electrical conductivity, thermal conductivity, and pH of Fe₃O₄/TiO₂ hybrid nanofluids using nanoparticle volume fraction and temperature as inputs. The optimized network contained two input neurons, seven hidden neurons, and four output neurons. Five-fold cross-validation confirmed the model's stability and generalization, yielding low prediction errors across all four properties. Independent testing produced mean relative errors of 2.78% for dynamic viscosity, 2.11% for electrical conductivity, 0.11% for thermal conductivity, and 0.43% for pH. The corresponding absolute-error analysis also confirmed close agreement between the experimental and predicted values throughout the investigated operating domain. More importantly, the model provided physically meaningful insight into the governing behavior of the hybrid nanofluid. Variance-based Sobol sensitivity analysis showed that temperature was the dominant factor controlling dynamic viscosity and thermal conductivity, with first-order sensitivity indices of 0.6402 and 0.5170, respectively. In contrast, nanoparticle volume fraction predominantly governed electrical conductivity and pH, with first-order sensitivity indices of 0.9342 and 0.9750. These results reflect the strong influence of temperature on molecular mobility and heat transport, as well as the dominant role of nanoparticle loading in forming conductive pathways and in surface-related physicochemical processes. The small interaction contributions and narrow 95% bootstrap confidence intervals confirmed the statistical robustness of sensitivity rankings. The proposed framework therefore provided a rapid, accurate, and physically interpretable tool for analyzing and optimizing Fe₃O₄/TiO₂ hybrid nanofluids under the investigated conditions.