## 2 Thermodynamic and Transport Properties  
In this work, the correlations reported by [PERSON] and [PERSON] [20] for calculating CO\({}_{2}\) density and the correlations developed by [PERSON] et al. [21] and [PERSON] et al. [22] for the transport properties of CO\({}_{2}\) are used. Using these correlations, we calculate the thermodynamic and transport properties of CO\({}_{2}\) for temperatures ranging from 300 K to 600 K and for pressures up to 60 MPa; we then compare the results with those obtained from the NIST database [23]. The average deviations of about 0.2% to 2.5% are obtained for the thermal conductivity and less than 0.1% for all other properties. For air, we found that the correlation reported by [PERSON] [24] is valid for temperatures higher than 1273 K while the equation of state reported by [PERSON] et al. [25; 26] is applicable for the temperatures ranging from 59.75 K to 2000 K and for pressures up to 2000 MPa. In the range from the solidification point to 873 K at pressures of 70 MPa, the uncertainty of the density values calculated using the equation of state reported in [25; 26] is 0.1%. For the transport properties, the correlations reported in [24] can predict both thermal conductivity and viscosity with less than 0.3% uncertainty for the range of temperatures from 300 K to 600 K and pressures up to 100 MPa. Thus, we decided to use these equations in our present study. Figure 1 shows the thermal and transport properties of both gaseous CO\({}_{2}\) and air in the range of pressures and temperatures that are typically found in practical power plant cooling applications. Effects of both pressure and temperature on these properties are shown. The thermal conductivities of both gaseous CO\({}_{2}\) and air increase slightly with temperature but significantly when pressure increases. By comparing the thermal conductivity and the viscosity of the gaseous CO\({}_{2}\) and air for the range of pressures and temperatures reported here, it can be seen that the air viscosity is about 1.2 times higher than that of CO\({}_{2}\) and the thermal conductivity of air is about 1.3 times higher than that of CO\({}_{2}\). The specific heat of CO\({}_{2}\) is somewhat lower than that of air. The density of CO\({}_{2}\) is about 1.5 times higher than that of air. Although air has higher specific heat and thermal conductivity than those of CO\({}_{2}\), the flow heat capacity of CO\({}_{2}\), which is proportional to \(\rho c_{p}/\mu\), is found to be more than 1.6 times higher than that of air for the range of pressures and temperature used here (see Figure 2). Thus, it means that, for the same driving force, the ability of CO\({}_{2}\) to remove heat is significantly higher than that of air. In addition to the flow heat capacity, the cooling effectiveness of a fluid also depends on its initial temperature when it enters a cooling device. This temperature can be controlled by an important property called the Joule-Thomson coefficient. The coefficient describing such effect, \(\mu_{JT}\), which depends on the type of gas and on the temperature and pressure of the gas before expansion, is given as (see [27], p. 250)  
\[\mu_{JT}=\left(\frac{\partial T}{\partial P}\right)_{h} \tag{1}\]From Equation (1), the temperature and the mass flux \(\dot{m}_{fl}^{\prime\prime}\) (kg/m\({}^{2}\)-s) of a fluid in a flow path after it expands from a high-pressure container is approximated as  
\[T_{fl}\approx T_{stor}-\mu_{fl}\Big{(}P_{stor}-P_{fl}\Big{)} \tag{2}\]  
Figure 1: Thermophysical properties of gaseous CO\({}_{2}\) and air for pressures from 0.1 to 0.5 MPa and temperature from 300 to 400 K.  
Figure 2: Flow heat capacity of gaseous CO\({}_{2}\) and air. \[\dot{m}_{fl}^{n}=\rho_{fl}\left(\frac{P_{Stor}-P_{fl}}{\rho_{fl}}\right)^{1/2} \tag{3}\]  
where \(P_{Stor}\) is the pressure of the fluid in the high-pressure container, and \(P_{fl}\), \(\rho_{fl}\) are the pressure and density of the fluid in the flow path, respectively.