Empirical modelling of supercritical Nusselt number correlations with possible combinations of indicative dimensionless variables (Validation)

There are currently over 100 correlations for estimating the Nusselt number in supercritical heat transfer, with over 30 dimensionless variables utilized to model the correlation. However, a systematic approach to identify the optimal correlation form that best represents the underlying dataset has yet to be established. Therefore, in this study, a comprehensive model for supercritical Nusselt number correlations was developed through a preliminary Spearman's rank correlation analysis and empirical modelling for conceivable combinations of dimensionless variables. The dataset validated with Bae's experimental dataset for upward supercritical carbon dioxide flow at 8.12 MPa inside 6.32 mm diameter channel was post-processed to 33 commonly used dimensionless variables and 1,149,016 dimensionless groups. Through Spearman's rank correlation analysis, 7408 dimensionless groups with a strong positive monotonic relationship with Nusselt number were identified. Subsequently, the 1,149,016 dimensionless groups were empirically correlated and compared to the Spearman's rank correlation coefficients. The present study reveals one correlation that has a minimum RMSPE of 0.595% with no outliers exceeding 5%. Overall, this study provides valuable insights into the empirical modelling of supercritical Nusselt number correlations for millions of dimensionless groups, and can be applied to the modelling of Nusselt number correlations under various heat transfer conditions.