Effect of Turbulent Prandtl Number on Convective Heat Transfer to Turbulent Flow of a Supercritical Fluid in a Vertical Round Tube

A two-dimensional numerical model is developed to study the effect of the turbulent Prandtl number $Prt$ on momentum and energy transport in a highly variable property flow of supercritical fluids in a vertical round tube. Both regimes of enhanced and deteriorated heat transfer have been investigated. The equations of the $Prt$ leading to the best agreement with the experiments in either regime of heat transfer were specified. The results of this study show that the increase in the $Prt$ causes the heat transfer coefficients to decrease. When the buoyancy force increases, a better agreement with the experimental data is reached if values lower than 0.9 are used for the $Prt$⁠. A decrease in the $Prt$ values results in an increase in turbulent activities. From the effect that the $Prt$ has on heat transfer coefficients, it may be deduced that the buoyancy effects in the upward flow of a supercritical fluid lead to the decrease in the $Prt$ value and hence to the increase in the heat transfer coefficients. Furthermore, the value of the $Prt$ in the laminar viscous sublayer as expected does not have a significant effect on heat transfer rate. The effect of the turbulence model on the extent to which the $Prt$ influences the rate of heat transfer is also examined. The results obtained are shown to be valid regardless of the turbulence model used.