## 2 Material and Methods
### The Investigated Solar-Driven Power Unit  
The objective of this study is the detailed investigation of a solar-fed power cycle. The system is a transcritical Rankine cycle operating with CO\({}_{2}\) as the working fluid. Solar parabolic trough collector is used for giving the heating in the system and its module is given in Figure 1.  
Figure 1: The examined module of the parabolic trough collector (with permission from [30]. Copyright 2017 Elsevier). It has to be said that in this work, 10 modules of the LS-3 are used in this study, they have been examined in Ref. [30]. The solar field has 10 modules connected in series and the total length is 40.6 m (=10 \(\times\) 4.06 m). The solar collector has an evacuated tube receiver and its details are summarized in Table 1[29; 30; 33]. An important modification of the LS-3 module is the thickness of the absorber tube which is 10 mm in this work in order to withstand the high-pressure levels [29; 30]. Regarding the thermodynamic cycle, it is a Rankine cycle that uses CO\({}_{2}\) as the working fluid and it is depicted in Figure 2. The state point \"1\" after the condenser is saturated liquid and it has the saturation temperature and pressure of the condenser. It is compressed up to the high pressure in the state point \"2\" which is in a supercritical situation. The compression consumes an important amount of work but it is not as high as in compressors because the CO\({}_{2}\) has liquid characteristics in this region. The fluid of the state point \"2\" recovers heating from the recuperator by exploiting waste heat after the turbine outlet. The state point \"3\" has a higher temperature and enthalpy compared to the state point \"2\" and so lower amounts of heat source energy rate are needed. The PTC is used for providing the heating in the CO\({}_{2}\) which warms up to the high cycle temperature (turbine inlet temperature--TIT) which is a characteristic parameter of the cycle. During the heating process in the PTC, there is an extremely small pressure drop, as it has been calculated, which has no practical effect on the pressure level at the state point \"4\". The turbine is used in order to expand the CO\({}_{2}\) of high-pressure to the lower pressure (state point \"5\"). This situation has high enthalpy and so the recuperator is used for heat recovery. The fluid gives heat to the other stream and so it reaches the state point \"6\". The next step is the pass through the condenser in order to reject heat to the ambient and so the cycle closes and the fluid goes again in the state point \"1\". \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol** & **Value** \\ \hline Width of the module & (W) & 5.6 m \\ Length of the module & (L) & 4.06 m \\ Number of modules & (MOD) & 10 \\ Total length & (L\({}_{\text{row}}\)) & 40.6 m \\ Focal distance & (F) & 1.71 m \\ Module area & (A\({}_{\text{mod}}\)) & 22.74 m\({}^{2}\) \\ Total collecting area & (A\({}_{\text{a}}\)) & 227.4 m\({}^{2}\) \\ Inner diameter of the absorber & (D\({}_{\text{ri}}\)) & 0.05 m \\ Outer diameter of the & (D\({}_{\text{ro}}\)) & 0.07 m \\ absorber & (D\({}_{\text{ci}}\)) & 0.108 m \\ Inner diameter of the cover & (D\({}_{\text{co}}\)) & 0.115 m \\ Cover emittance & (\(\varepsilon_{\text{c}}\)) & 0.86 \\ Maximum optical efficiency & (\(\eta_{\text{topt,max}}\)) & 0.8419 \\ Absorber absorbance & (\(\alpha\)) & 0.96 \\ Cover transmittance & (\(\tau\)) & 0.96 \\ Reflector reflectance & (\(\rho\)) & 0.94 \\ Intercept factor & (\(\gamma\)) & 0.972 \\ Concentrating ratio & (C) & 25.46 \\ Heat convection coefficient & (h\({}_{\text{out}}\)) & 10 W / m\({}^{2}\) K \\ between cover and ambient & (T\({}_{\text{am}}\)) & 298.15 K \\ Ambient temperature & (T\({}_{\text{sky}}\)) & 290.15 K \\ Equivalent sky temperature & (T\({}_{\text{sun}}\)) & 5770 K \\ Default solar beam irradiation & (G\({}_{\text{b}}\)) & 800 W/m\({}^{2}\) \\ Default solar angle & (\(\theta\)) & 0\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table}