## 3 Materials and Methods
### General Thermal Resistance Model for GTCs
#### 3.1.2 Thermal Resistance Model for DGTCs  
The total thermal resistance to heat transfer for DGTCs is given by Equation (7) [38]:  
\[\sum R_{loss}\approx\sum R_{loss,\perp}\approx R_{abs\text{-}igt}+R_{igt}+R_{igt \text{-}g\text{t}}+R_{g\text{t}}+R_{g\text{t}}+R_{g\text{t}\text{-}o} \tag{7}\]  
where \(R_{igt\text{-}g\text{t}}\) [K/W] is the resistance to heat transfer between the internal and external glass tubes, \(R_{g\text{t}}\) [K/W] is the resistance to heat transfer through the external glass tube, and \(R_{g\text{t}\text{-}o}\) [K/W] is the resistance to heat transfer between the external glass tube and the ambient air. On the one side, values \(R_{abs\text{-}igt}\) and \(R_{igt\text{-}eg\text{t}}\) could be a function of the _rad_(_abs-_igt_) and _conv_(_abs-_igt_), that is, in the function of the _rad_(_igt-_eg_t) and _conv_(_igt-_eg_t)--for air layers (Figure 5a). On the other side, for vacuum layers (Figure 5b), the same values are only in function of the _rad_(_abs-_igt_) and _rad_(_igt-_eg_t), respectively. Due to the larger number of boundary (glass) surfaces in the construction of DGTCs, the iterative calculation algorithm should satisfy one more criterion--based on a triple check (calculation method developed for this study). For example, for triple-glazed tube collectors (TGTCs), the iterative calculation algorithm would be based on a quadruple check. In Figure 6, the triple iterative calculation algorithm for a double-glazed tube collector (DGTC) with an air layer is shown. This algorithm incorporates various parameters and coefficients, including heat transfer coefficients and areas, which are essential for accurate thermal analysis. Each coefficient and parameter depicted in the figure plays a crucial role in determining the overall thermal performance of the DGTC. Figure 4: Double iterative calculation algorithm for SGTC with an air layer [35; 36; 37]: \(A_{abs\text{-}g\text{t}}\) [m\({}^{2}\)] is the total external area of the absorber, \(h_{rad\text{(}abs\text{-}igt\text{)}}\) [W/(m\({}^{2}\)K)] is the radiation heat transfer coefficient between the absorber and the internal glass tube (Equation (3)), \(h_{conv\text{(}abs\text{-}igt\text{)}}\) [W/(m\({}^{2}\)K)] is the convection heat transfer coefficient between the absorber and the internal glass tube (Equation (4)), \(A_{igt\text{,}ag\text{,}tot}\) [m\({}^{2}\)] is the total average area of the internal glass tube, \(D_{igt\text{,}t}\) [m] is the external diameter of the internal glass tube, \(D_{igt\text{,}t}\) [m] is the internal diameter of the internal glass tube, \(A_{igt\text{,}tot}\) [m\({}^{2}\)] is the total external area of the internal glass tube, \(h_{rad\text{(}igt\text{-}o}\) [W/(m\({}^{2}\)K)] is the radiation heat transfer coefficient between the internal glass tube and the ambient air (Equation (3)), \(h_{conv\text{(}ig\text{-}o}\)) [W/(m\({}^{2}\)K)] is the convection heat transfer coefficient between the internal glass tube and the ambient air (Equation (4)), \(q_{abs\text{-}igt}\) [W/m\({}^{2}\)] is the specific heat flux exchanged between the absorber and the internal glass tube, and \(q_{igt\text{-}o}\) [W/m\({}^{2}\)] is the specific heat flux exchanged between the internal glass tube and the ambient air. The figure illustrates the calculation process involving various heat transfer coefficients and areas.