## 3 Materials and Methods
### General Thermal Resistance Model for GTCs
#### 3.1.1 Thermal Resistance Model for SGTCs  
In this case (for SGTCs), the total thermal resistance to heat transfer (in the transverse plane) can be calculated as Equation (2) [38]:  
\[\sum R_{loss}\approx\sum R_{loss,\perp}\approx R_{abs-igt}+R_{igt}+R_{igt-o} \tag{2}\]  
where \(R_{abs-igt}\) [K/W] is the resistance to heat transfer between the absorber and the internal glass tube, \(R_{igt}\) [K/W] is the resistance to heat transfer through the internal glass tube, and \(R_{igt-o}\) [K/W] is the resistance to heat transfer between the internal glass tube and the ambient air.  
The next figure (Figure 3) illustrates the heat transfer and resistance network for the two analyzed SGTC types: SGTC with an air layer (Figure 3a) and SGTC with a vacuum layer (Figure 3b). For the SGTC with an air layer, thermal energy (heat losses) between the  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Component** & **Material** & \(\rho\) & \(c_{p}\) & \(k\) & \(\varepsilon\) & \(L\) \\ \hline ABS & Aluminum & 2700 & 900 & 203 & 0.25 & \\ \hline IGT & & & & & \\ \hline EGT & Glass & 2200 & 660 & 0.8 & 0.9 & 0.8 \\ \hline \end{tabular} where \(\rho\) [kg/m\({}^{3}\)] is the density, \(c_{p}\) [J/(kgK)] is the specific heat, \(k\) [W/(mK)] is the thermal conductivity, \(\varepsilon\) [-] is the emissivity, and \(L\) [m] is the length.  
\end{table}
Table 1: Geometric and thermal characteristics of the GTCs [19; 35; 36].  
Figure 2: DGTC view in the transverse plane.  
ABS and the IGT is exchanged through radiation and convection. In contrast, for the SGTC with a vacuum layer, the convective component is eliminated.  
All values presented in Equation (2) are calculated using the simple and double iterative calculation algorithm (calculation method developed for this study). Figure 4 shows an iterative calculation algorithm for SGTC with an air layer.  
\[h_{rad(abs-igt)}=\frac{\left(T_{abs}^{2}+T_{igt}^{2}\right)\left(T_{abs}+T_{igt }\right)}{\frac{1}{\sigma_{abs}}+\frac{A_{abs-igt}}{A_{igt,tot}}\left(\frac{1 }{\sigma_{igt}}-\frac{1}{\sigma}\right)} \tag{3}\]  
\[h_{conv(abs-igt)}=\frac{Nu_{ia}k_{ia}}{D_{igt,t,\rho}} \tag{4}\]  
\[h_{rad(igt-o)}=\sigma e_{igt}\Big{(}T_{igt}^{2}+T_{o}^{2}\Big{)}\left(T_{igt} +T_{o}\right) \tag{5}\]  
\[h_{conv(igt-o)}=2.8+3W \tag{6}\]  
where [39; 40]\(\sigma\) [W/(m\({}^{2}\)K\({}^{4}\))] is the Stefan-Boltzmann constant, \(A_{igt,tot}\) [m\({}^{2}\)] is the total internal area of the internal glass tube, \(Nu_{ia}\) [-] is the Nusselt number of the internal air layer [41; 42; 43; 44], \(k_{ia}\) [W/(mK)] is the thermal conductivity of the internal air layer, \(D_{igt,i\
eq q}\) [m] is the equivalent diameter of the internal air layer, and \(W\) [m/s] is the wind speed.  
Before entering the calculation algorithm, two data groups must be adopted: SGTC geometric, thermal, and optical characteristics (Chapter 2)--first group, and meteorological parameters (values \(T_{o}\) and \(W\))--second group. After that, the first stage (step I) of calculation is approached--adopting initial values of \(T_{abs}\) and \(T_{igt}\). In step II, Equations (3)-(6) are used to determine all components in Equation (2) and then the total heat losses from Equation (1). In step III, the control \(q_{abs-igt}\) and \(q_{igt-o}\) equations are used to check the agreement of the adopted \(T_{abs}\) and \(T_{igt}\) values with the obtained results \(q_{abs-igt}\approx q_{igt-o}\) (step IV) [45]. If the control heat flux results were approximately equal (\(q_{abs-igt}\approx q_{igt-o}\), i.e., deviation \(\leq 0.1\) W/m\({}^{2}\)), the iterative procedures would be completed, and the results would be finally printed (step V).  
Figure 3: Heat transfer and resistance network for SGTC with an air layer (**a**) and SGTC with a vacuum layer (**b**): \(T_{igt}\) [K] is the internal glass tube temperature.