## 2 Materials and Methods
### Research Subject  
The isometric and cross-sectional views of the analyzed SC type is shown in Figure 1.  
Figure 1 shows a relatively simple solar construction that may have a larger commercial application. Its simplicity is reflected in the application of the following main components (Table 2): GT (the main feature of the ETCs), selective FAP (the main feature of the FPCs) and a VL between them. The surface of the FAP is coated using the SnAl2O3 chemical compound with excellent optical performance (Table 2). The working fluid (water) flows through a circular cross-sectional channel with a diameter of \(\mathcal{O}\)15 mm (Figure 1b). Water enters the SC from one side and exits from the other side--the water flow is g  
Figure 1: Design of the SGVTC: (**a**) isometric view and (**b**) cross-sectional view. List of symbols: \(d_{gt}\) [m] is the glass tube thickness (variable 2, i.e., V2) and \(L_{abs,app}\) [m] is the upper side width of the absorber (variable 1, i.e., V1). Two variables (\(L_{abs,up}\) [m] and \(d_{gt}\) [m]) influence the optimal dimensions of the SC in the transversal plane (Figure 1b). The dimensions of the \(D_{gt,i}\) [m] Equation (1) and \(D_{gt,e}\) [m] Equation (2) are determined as follows:  
\[D_{gt,i}\ =\ L_{abs,up}+2+2\ =\ L_{abs,up}+4 \tag{1}\]  
\[D_{gt,e}\ =\ D_{gt,i}+d_{gt}\ =\ D_{gt,i}+2d_{gt} \tag{2}\]  
where: the adopted value of 2 mm in Equation (1) is the safety factor for the linear thermal expansion of the aluminum absorber, \(D_{gt,i}\) [m] is the internal glass tube diameter and \(D_{gt,e}\) [m] is the external glass tube diameter. The following tables (analogous to Figure 1) show the geometric performances of the FAP (Table 3) and the GT (Table 4) for different (adopted) values of \(L_{abs,up}\) (V1) and \(d_{gt}\) (V2). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Scenario** & \(m\) [kg] & \(SO\) [m\({}^{2}\)] & \(TSO\) [m\({}^{2}\)] & \(VO\) [m\({}^{3}\)] \\ \hline \multirow{3}{*}{\(L_{\text{abs},up}=50\) mm} & \(d_{gt}=3\) mm & 0.946 & 0.048 & 0.151 & 0.00226 \\ \cline{2-5}  & \(d_{gt}=4\) mm & 1.283 & 0.0496 & 0.156 & 0.00241 \\ \cline{2-5}  & \(d_{gt}=5\) mm & 1.632 & 0.0512 & 0.161 & 0.00257 \\ \hline \multirow{3}{*}{\(L_{\text{abs},up}=75\) mm} & \(d_{gt}=3\) mm & 1.361 & 0.068 & 0.214 & 0.00454 \\ \cline{2-5}  & \(d_{gt}=4\) mm & 1.836 & 0.0696 & 0.219 & 0.00475 \\ \cline{2-5}  & \(d_{gt}=5\) mm & 2.323 & 0.0712 & 0.224 & 0.00497 \\ \hline \multirow{3}{*}{\(L_{\text{abs},up}=100\) mm} & \(d_{gt}=3\) mm & 1.775 & 0.088 & 0.276 & 0.0076 \\ \cline{2-5}  & \(d_{gt}=4\) mm & 2.389 & 0.0896 & 0.281 & 0.00788 \\ \cline{2-5}  & \(d_{gt}=5\) mm & 3.014 & 0.0912 & 0.286 & 0.00816 \\ \hline \multirow{3}{*}{\(L_{\text{abs},up}=125\) mm} & \(d_{gt}=3\) mm & 2.19 & 0.108 & 0.339 & 0.01145 \\ \cline{2-5}  & \(d_{gt}=4\) mm & 2.942 & 0.1096 & 0.344 & 0.01179 \\ \cline{2-5}  & \(d_{gt}=5\) mm & 3.706 & 0.1112 & 0.349 & 0.01213 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Geometric performances of the GT in SGVTC construction, depending on the simulation scenario. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Component** & **Material** & \(\rho\) [kg/m\({}^{3}\)] & \(k\) [W/(mK)] & \(\tau\) [-] & \(\alpha\) [-] & \(\varepsilon\) [-] \\ \hline FAP & Aluminum & 2700 & 203 & - & 0.88 & 0.25 \\ \hline GT & Glass & 2200 & 0.8 & 0.9 & - & 0.9 \\ \hline \hline \end{tabular} List of symbols: \(k\) [W/(mK)] is the thermal conductivity. List of Greek letters: \(\alpha\) [-] is the nominal absorptance, \(\varepsilon\) [-] is the nominal emissivity, \(\rho\) [kg/m\({}^{3}\)] is the density and \(\tau\) [-] is the nominal transmittance.  
\end{table} 
Table 2: Thermal and optical performances of the main SGVTC components.