| The main objective of this study is to calculate the heat-transfer coefficients for natural convection from a heated, vertical flat plate into a supercritical fluid. In the first part of this work, an equation for the coefficient of thermal expansion or expansivity for a van der Waals gas was derived as a function of the temperature, the pressure, the van der Waals constants, and the compressibility factor. The trend of the curves obtained with this equation and with values from tables of thermodynamic properties was similar and they diverge at critical point. These features confirm the validity of equation obtained in this work.; In the second part, this expansivity was used in the momentum equation, which, with the energy and continuity equation, forms a set of coupled equations. This set of equations was solved numerically by finite differences. A FORTRAN code was written to obtain the velocity and temperature profiles along the plate. The local Nusselt number was then calculated and plotted as a function of the local Rayleigh number. It is observed in these plots that a curve obtained with temperature and pressure far from the critical region approaches the line obtained with a classic correlation. It was also observed that the curves corresponding to supercritical conditions are notably above of the line corresponding to the classic correlation, which means that the heat transfer considerably increases in the critical region. |
