Empirical heat transfer correlations of high-pressure transcritical fluids at low numbers

Empirical heat transfer correlations serve as indispensable tools for predicting and optimizing the thermal performance of a wide range of engineering devices, like for example in energy conversion and propulsion applications. Although a remarkable number of correlations exist for systems at low (atmospheric) pressures, accurately quantifying heat transfer under high-pressure transcritical conditions poses a notable challenge, especially at low Reynolds numbers due to the scarcity of correlations available in the literature. This difficulty has prompted the widespread use of general empirical correlations, which are inadequate for such flow conditions, and hold significant implications, for instance, in fields like microfluidics technology. In this regard, the aim of this study is to develop novel heat transfer correlations tailored for high-pressure transcritical fluids at relatively low Reynolds numbers. These correlations are derived from a dataset of 18 direct numerical simulations of carbon dioxide confined between differentially heated walls, which induce a transcritical trajectory through the pseudo-boiling region. The correlations are developed for both the cold liquid-like and hot gas-like regions, resulting in a total of 6 correlations that encompass the laminar, transitional, and turbulent flow regimes. In particular, as a function of Reynolds, Prandtl, Eckert and Mach numbers, the proposed empirical correlations provide accurate estimations with relative errors below 8%, which significantly surpass existing literature correlations.