The dependence of Nusselt number on Reynolds number for a hot-wire sensor in supercritical CO$_{2}$ flow

An analysis of the heat transfer mechanism around a hot-wire sensor in superctitical CO$_{2}$ flow has been performed, and the dependence of the Nusselt number (N$_{u})$ on the Reynolds number (R$_{e})$ has been determined. A special, closed flow loop, capable of inducing variable speed flow at different pressures and temperatures in the ranges of 0.15-2 m/s, 15-70$^{\circ}$C and 1-100 bar, has been used to create a supercritical CO$_{2}$ flow around a hot-wire sensor operated in the constant temperature mode. The N$_{u}$ and R$_{e}$ numbers were determined based on the known heat convected from the sensor, the flow speed and the sensor temperature and dimensions. The experiment was performed along a line of constant 80 bar pressure in the temperature range of 25-65$^{\circ}$C. It was found that, at a given pressure and temperature, the relation N$_{u}$=F(R$_{e})$ has the classical form N$_{u}$=M+NR$_{e}^{n}$, with the parameters M and N being functions of pressure and temperature. The dependence of these parameters on temperature was analyzed, and the most convenient reference temperature was chosen. In contrast to the operation of hot-wires in air and water, the dependence of the parameters M and N on the Prandtl number can result in nonunique solutions.