General heat transfer correlations for supercritical carbon dioxide heated in vertical tubes for upward and downward flows

Supercritical CO2 is a promising working fluid for many industrial applications. To improve the performances of relevant components and systems, the prediction of the heat transfer of supercritical CO2 is an important research topic. General explicit heat transfer correlations of supercritical CO2 for upward and downward flows heated in circular tubes were established using the genetic programming (GP) method. A total of 12720 experimental data points from 22 publications were collected to develop the models. The data included hydraulic diameter from 0.0992 to 22 mm, bulk temperature from -6.0 to 134.5°C, pressure from 7.44 to 10.50 MPa, mass flux from 50 to 4834 kg•(m2•s)−1, heat flux from 2.9 to 748 kW•m−2 and wall temperature from 6.4 to 368.2°C. The database was divided into four parts according to the flow direction and the relationship between the bulk temperature and the pseudo-critical temperature. The developed correlations considered various non-dimensional parameters as the independent variables to reflect the effects of supercritical properties, flow acceleration and buoyancy on the heat transfer. The results showed that the proposed correlations had excellent accuracy with a mean absolute relative error (MARE) of 20.10% based on prediction with the iterated wall temperature. The developed correlations outperformed the existing correlations in the literature. Compared to other correlations, the trend analysis indicated that these newly developed correlations could appropriately present the physics sense when the condition parameters varied.