Prediction of heat transfer and fluid flow performance of fly ash–Cu hybrid nanofluid using machine learning approaches

Accurate prediction of thermal–hydraulic characteristics is essential for the efficient design and optimization of nanofluid (NF)-based heat transfer systems. In this study, Support Vector Regression (SVR) and Gradient Boosting (GB) models were developed to simultaneously predict the heat transfer coefficient (HTC), Nusselt number (Nu), pressure drop (ΔP), and friction factor (f) of fly ash–Cu hybrid nanofluids under turbulent forced-convection conditions. A total of 75 data samples derived from the experimental study of Kanti et al. served as the basis for training and evaluating the predictive models. This data set covering Reynolds number (Re) from 6,807 to 45,155, nanofluid concentrations from 0 to 2.0 vol.%, and temperatures of 30, 45, and 60 °C was utilized for model development and validation. Both machine-learning approaches exhibited excellent predictive capability. SVR achieved regression coefficient (R 2 ) values of 0.9931, 0.9929, 0.9913, and 0.9727 for HTC, Nu, ΔP, and f, respectively, with an average mean absolute percentage error (MAPE) of 3.13%. Correspondingly, the GB model produced R 2 values of 0.9934, 0.9926, 0.9660, and 0.9826, with an average MAPE of 3.62%. Five-fold cross-validation yielded mean R 2 values of 0.9590 for SVR and 0.9691 for GB, confirming strong model robustness. Feature importance analysis revealed that Reynolds number contributed 76.7% to the predictive performance, followed by nanoparticle concentration (18.9%) and temperature (4.4%). The results demonstrate that both models can accurately predict the thermal–hydraulic behavior of fly ash–Cu hybrid nanofluids, providing efficient alternatives to extensive experimental testing. These models offer a computationally efficient design-support tool for the investigated operating range; however, given the modest 75-sample dataset restricted to a single fly ash–Cu formulation, they should be regarded as interpolative within the investigated range rather than broadly generalizable.