Comparative analysis of ANN and COMBI models for predicting thermal-hydraulic performance of fly ash nanofluid

Abstract This study presents a machine learning–based comparative analysis of artificial neural network (ANN) and Combinatorial Algorithm (COMBI) models for predicting the thermal–hydraulic performance of fly ash nanofluids under turbulent flow conditions. Fly ash, an abundant industrial by-product, is employed as a sustainable and cost-effective nanoparticle source for enhanced heat transfer applications. Published experimental data (75 observations) from Kanti et al. was used in this study, with Reynolds number (7,042–45,155), nanoparticle concentration (0–2 vol%), and inlet fluid temperature (30–60 °C) as input variables, while heat transfer coefficient, Nusselt number, pressure drop, and friction factor were output responses. Both ANN and COMBI models were trained using an 80/20 train–test split with Min–Max normalization and evaluated using R², RMSE, MAE, and MAPE metrics. The COMBI model demonstrated consistently superior performance over the ANN across all outputs, achieving higher predictive accuracy with R² values up to 0.9968 for pressure drop prediction. In contrast, the ANN exhibited comparatively lower accuracy across the same outputs. Five-fold cross-validation confirmed the robustness of the COMBI model, with a mean R² of 0.9841 (σ = 0.0027), indicating stable generalization compared to ANN (0.9759, σ = 0.0061). Sensitivity analysis identified Reynolds number as the most influential parameter (~ 83.6%), followed by inlet temperature (~ 9.2%) and concentration (~ 7.2%). A key advantage of the COMBI framework is its ability to generate explicit polynomial equations for all output variables, enabling transparent interpretation and direct implementation without retraining.