CFD-informed machine-learning surrogates for free-surface jet impingement with Al2O3/water, TiO2/water, and Al2O3–TiO2/water hybrid nanofluids

Free-surface liquid jet impingement can provide high local cooling rates, but its use with hybrid nanofluids remains poorly documented. This study develops CFD-informed machine-learning surrogates for an axisymmetric free-surface jet impinging on a uniformly heated target. The volume-of-fluid model was validated against water-jet measurements, giving mean deviations of 3.0% for the radial Nusselt-number distribution and 3.3% for the stagnation-point Nusselt number across four Reynolds numbers. The database contains 91 CFD cases covering deionized water, Al₂O₃/water, TiO₂/water, and a 1:1 Al₂O₃–TiO₂/water hybrid at total particle loadings of 1–4 vol.% and Reynolds numbers of approximately 4,234–10,590. Wall temperature, heat transfer coefficient, and local Nusselt number were extracted at r/D=0, 2, 4, and 6 , yielding 364 observations. MLP, SVR, and CNN–LSTM models were evaluated using case-grouped cross-validation. MLP produced the highest R2 values for wall temperature, heat transfer coefficient, and Nusselt number, with values of 0.999, 0.998, and 0.997, respectively. CNN–LSTM ranked second, while SVR showed larger prediction errors. Permutation analysis identified Reynolds number as the dominant input, followed by radial position; composition effects were smaller. Physically constrained response maps within the sampled flow and composition ranges showed that increasing Reynolds number produced the largest thermal improvement, while nanoparticle composition provided a secondary adjustment. The surrogate models therefore provide a rapid screening tool within the investigated parameter range.