## 2 Materials and Methods
### Validation with Experimental Results  
The calculated results by the developed numerical model were validated based on experimental tests. A schematic of the investigated experimental setup is shown in Figure 5. It should be mentioned that the validation section was presented based on the reported experimental results in Ref. [39] by the authors. A summary of the experimental tests is presented here. As shown in Figure 5, the experimental setup consisted of a dish concentrator system with aperture diameter of 1.9 m, cavity receiver with aperture diameter of 12.5 cm and cavity tube diameter of 10 mm, an oil pump, an inlet tank and a heat exchanger. The dimensions and properties of the experimental dish and cavity receiver are shown in Table 6. Experimental tests were conducted at the Renewable Energy Research Center of \begin{table}
\begin{tabular}{l l l} \hline Evaporating pressure & \(P_{exp}\) & 2.5 MPa \\ Condensing temperature & \(T_{cont}\) & 38 \({}^{\circ}\)C \\ Thermal oil mass flow rate & \(\dot{m}_{all}\) & 60 mL/s \\ Thermal oil inlet & \(T_{inlet}\) & 40 \({}^{\circ}\)C \\ temperature & & \\ Turbine mechanical & \(\eta_{mt}\) & 100\% \\ efficiency & & \\ Turbine isentropic & \(\eta_{st}\) & 100\% \\ efficiency & \(\eta_{p}\) & 100\% \\ Heat exchanger efficiency & \(\eta_{exch}\) & 100\% \\ \hline \end{tabular}
\end{table} 
Table 4: Input parameters for the thermodynamic investigation of the solar ORC. \begin{table}
\begin{tabular}{c c c c c} \hline
**Working Fluid** & **Type** & **Molecular Mass (kg/kmol)** & \(T_{bp}\) (\({}^{\circ}\)C) & \(T_{cr}\) (\({}^{\circ}\)C) & \(P_{cr}\) (MPa)** \\ \hline Methanol & wet & 32.04 & 64.48 & 239.45 & 8.104 \\ \hline \end{tabular}
\end{table} 
Table 5: Thermo-physical properties of the working fluid [35]. Tarbiat Modares University, Tehran, Iran (35.68\({}^{\circ}\) N latitude and 51.42\({}^{\circ}\) E longitude). Solar working fluid was pumped to the cavity receiver with the oil pump. The concentrated solar energy from the dish concentrator was absorbed by the solar working fluid in the cavity receiver. The absorbed heat by the working fluid is then cooled by the heat exchanger. Finally, the working fluid is depleted in the inlet tank for re-circulation in the solar system. It should be mentioned that the outlet and inlet temperatures of the solar working fluid at the cavity receiver were found using K-type thermocouples (Chromel-Alumel). The volume flow rate of the working fluid was determined with a volume flow meter (FLUIDWELL model: F016-P). Also, ambient conditions such as wind speed and solar radiation were measured using an anemometer (CT model: AM-4220) and Hukesflux pyranometer (model: SR12), respectively. The average uncertainty of the thermal efficiency was found to be about 1.06% using Equation (41). The uncertainty and ranges of the measuring instruments are given in Table 7.  
\[\frac{\delta\eta_{th}}{\eta_{th}}=\sqrt{\left(\frac{\delta\dot{Q}_{solar}}{ \dot{Q}_{solar}}\right)^{2}+\left(\frac{\delta\Delta T}{\Delta T}\right)^{2}+ \left(\frac{\delta\dot{m}}{\dot{m}}\right)^{2}} \tag{41}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Concentrator diameter & 1.9 m \\ Focal distance & 1 m \\ Rim angle & 50.82\({}^{\circ}\) \\ Collector aperture area & 2.835 m\({}^{2}\) \\ Cavity tube outer diameter & 10 mm \\ Cavity tube inner diameter & 9 mm \\ Number of cavity coils & 10 \\ Cavity inner diameter & 0.141 m \\ Cavity outer diameter & 0.161 m \\ Absorber emittance & 0.1 \\ Mirror reflectance & 0.84 \\ Depth of the cavity receiver & 0.07 m \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Dimensions and properties of the experimental dish and cavity receiver [36]. Figure 5: A schematic of the investigated experimental setup. The cavity receiver was constructed during three stages: coiling the copper tube, coating the receiver tubes with a black chrome (Cr-Cr\({}_{2}\)O\({}_{3}\)) as selective coating for increasing absorption, and insulating the cavity receiver with mineral wool for reducing heat losses.