A mathematical correlation for predicting the thermal performance of cross, parallel, and counterflow PCHEs

The printed circuit heat exchanger (PCHE) is regarded an essential component in the S-CO2 (supercritical carbon dioxide) cycle due to its high compactness and structural rigidity. In this study, a mathematical expression for predicting the thermal performance of cross, parallel, and counterflow PCHE with semicircular channels is proposed as a closed-form, based on an extensive numerical study. The effects the channel size and the channel length are particularly considered. The conduction heat transfer between the hot and cold channels in PCHE is characterized in terms of the conduction shape factor. The convection heat transfer performance in the semicircular channels is also expressed as a function of Graetz number. The overall heat transfer coefficient is then obtained based on the conduction thermal resistance and the convection thermal resistance. Based on the obtained overall heat transfer coefficient, an expression for the effectiveness of the PCHE is developed as a function of geometric parameters, material properties, and the flow condition. The proposed correlation can be widely utilized for designing the PCHEs.ope