Correlations for heat transfer coefficients and wall-temperatures for laminar and turbulent free convection from plane vertical surfaces to supercritical fluids

Abstract

Correlations for heat transfer coefficient and wall-temperature are proposed for free convection from a plane vertical surface to super critical water and super critical carbon-dioxide based on numerical solutions using modified Patankar-Spalding implicit finite difference scheme For turbulent flow, the proposed correlations are based on the numerical solutions using turbulent kinetic energy model with Van Driest’s mixing length. In the papers published earlier by us, the numerical predictions presented cannot be used directly. Hence, in this paper correlations based on these predictions have been proposed for both laminar and turbulent flows for both constant wall-temperature and constant wall-heat flux conditions. The correlations cover a wide range of Rayleigh number, Ra∞x from 10 7 to 2.1 x 10 16 for a pressure ratio, P/Pcr = 1.01 to 1.5.The maximum deviation of the proposed correlations are within ± 10 percent with respect to numerical predictions except for heat transfer coefficient for turbulent flow for which the maximum deviation is within ± 15 percent. The maximum deviations are found to occur whenever the pseudo-critical temperature (pseudo-critical temperature is the temperature at which the specific heat at constant pressure is maximum for the given supercritical pressure) is within the thermal boundary layer.