Investigation of the thermal development length in annular upward heated laminar supercritical fluid flows

Supercritical fluids are being used more commonly today in industrial applications, such as heat exchangers and coal fired power plants. Heat transfer to supercritical fluids shows complex behavior because the fluid properties vary sharply with temperature. As a consequence, the development length of the thermal boundary layer is expected to show complex behavior as well. In this paper the development length of the thermal boundary layer in supercritical CO2 and water flowing upward at laminar flow conditions is investigated analytically and numerically. An annulus configuration was selected as this geometry can be typically found in heat exchangers and a new nuclear reactor concept, the supercritical water reactor (SCWR). The laminar flow condition has been chosen in order to fully focus on the effect that temperature variations have on the development of the thermal boundary layer and to exclude any influence turbulence models might induce. It is analytically shown that the thermal development length is not only a function of the Peclet number, but also of dimensionless numbers that represent fluid property changes, as well as the inlet temperature. The analytical model also explains how the varying properties affect heat transfer. Analytical insights and numerical results are then combined to show that the thermal development length can be written as a dimensionless ratio of wall heat flux and mass flux for given temperature and pressure. Although mostly CO2 (9.52 MPa) was investigated, it is shown that a similar result can be obtained for water (25 MPa).