Gravitational effects on laminar convection to near-critical water in a vertical tube

Abstract

Numerical calculation is performed to study the strongly coupled heat transfer and flow of water at near critical conditions in laminar flow in a vertical tube. Near the critical region fluid flow and heat transfer depend on the temperature and pressure because of large property variations that include transition between liquid-like behavior and gas-like behavior. The two-dimensional (r, z) model includes the effects of variable thermodynamic and transport properties such as density, specific heat, viscosity, and conductivity. Heat transfer coefficient and profiles of temperature and velocity are shown in the developing region of the tube. The very large influence of gravity on the two-dimensional flow and temperature profiles in the tube is shown. The effect of proximity to the pseudocritical point is considered. The tube wall is heated with constant wall heat flux and uniform flow is assumed in the inlet of the tube. Inlet fluid temperature, pressure, and Reynolds number are used as the main parameters. Nomenclature Cp = specific heat at constant pressure, J/kg D = tube diameter, m / = friction factor Gr = Grashof number, p^ng^inQwR4/kin^n g = acceleration caused by gravity, m/s2 h = convective heat transfer coefficient, W/m2 K k = thermal conductivity, W/m K L - tube length, m m = mass flow rate, kg/s PR - reduced pressure, plpc Pr = Prandtl number p = pressure, N/m2 Q = heat flux, W/m2 R = radius, m Re = Reynolds number at inlet, pmuinD/iJiin r = radial distance, m T = temperature, K Tpc = pseudocritical temperature, K u = local velocity in axial direction, m/s v = local velocity in radial direction, m/s y = nondimensional distance from the wall, 1 — (r/R) z - axial distance, m a — nonuniform parameter /3 = compressibility, 1/K AT = wall to bulk temperature difference, K 9 = dimensionless temperature, kin(T — Tin)/QwD jit - absolute viscosity, kg/s m p = density, kg/m3 r = shear stress, N/m2 = function variable