Empirical modelling of supercritical Nusselt number correlations with possible combinations of indicative dimensionless variables (Parametric, Grid Sensitivity)

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.