## 4 Results and Discussion
For the DGTC with an air layer (Figure 10a), heat losses are the highest (\(Q_{loss}\) = 47.14 W) when \(t_{o}\) = 10 \({}^{\circ}\)C, \(t_{abs}\) = 90 \({}^{\circ}\)C, and \(W\) = 5 m/s and the smallest (\(Q_{loss}\) = 12.65 W) when \(t_{o}\) = 10 \({}^{\circ}\)C, \(t_{abs}\) = 40 \({}^{\circ}\)C, and \(W\) = 1 m/s. The internal glass tube temperatures are between  
Figure 10: Characteristic temperatures and heat losses for DGTC with an air layer (**a**) and DGTC with a vacuum layer (**b**). \(t_{g\text{f}t}=23.4\)\({}^{\circ}\)C (\(t_{o}\) = 10 \({}^{\circ}\)C, \(t_{abs}\) = 40 \({}^{\circ}\)C, and \(W\) = 5 m/s) and \(t_{g\text{f}t}=59.8\)\({}^{\circ}\)C (\(t_{o}\) = 30 \({}^{\circ}\)C, \(t_{abs}\) = 90 \({}^{\circ}\)C, and \(W\) = 1 m/s). In contrast, the external glass tube temperatures are between \(t_{g\text{f}t}=12.8\)\({}^{\circ}\)C and \(t_{g\text{f}t}=42.3\)\({}^{\circ}\)C (the same boundary conditions apply as for \(t_{g\text{f}t}\)). The highest \(Q_{loss}\) = 23.35 W (\(t_{o}\) = 10 \({}^{\circ}\)C, \(t_{abs}\) = 90 \({}^{\circ}\)C, and \(W\) = 5 m/s) and the smallest \(Q_{loss}\) = 6.48 W (\(t_{o}\) = 10 \({}^{\circ}\)C, \(t_{abs}\) = 40 \({}^{\circ}\)C, and \(W\) = 1 m/s) heat losses in the DGTC with a vacuum layer can be seen in Figure 10b. Compared with the DGTC with an air layer, heat losses in the DGTC with a vacuum layer are on average 1.92 times lower (maximum is 2.07 times, minimum is 1.78 times). The internal glass tube temperatures are between \(t_{g\text{f}t}=18.6\)\({}^{\circ}\)C and \(t_{g\text{f}t}=51.8\)\({}^{\circ}\)C. The external glass tube temperatures are between \(t_{g\text{f}t}=11.4\)\({}^{\circ}\)C and \(t_{g\text{f}t}=37.4\)\({}^{\circ}\)C.  
The diagrams in Figure 10 are interesting because of another phenomenon. Namely, it can be seen that the analytical calculation results are missing when \(t_{o}\) = 20 \({}^{\circ}\)C (\(t_{abs}\) = 40 \({}^{\circ}\)C). They are also missing when \(t_{o}\) = 30 \({}^{\circ}\)C (\(t_{abs}\) = 40 \({}^{\circ}\)C and \(t_{abs}\) = 50 \({}^{\circ}\)C). This anomaly is characteristic of the triple iterative calculation algorithm for DGTCs (Figure 6). As the ambient temperature increases, the convergence of results for values of tabs close to that is impossible. Temperatures \(t_{abs}\), \(t_{g\text{f}t}\), and \(t_{g\text{f}t}\) are approaching, while the control equations tend to divagation. It proves that DGTCs operate at higher operating temperatures than SGTCs. Experimental validation of the heat losses analytical model for the SGTC with an air layer is shown in Figure 11 (for \(t_{o}\) = 20 \({}^{\circ}\)C) and Figure 12 (for \(t_{o}\) = 30 \({}^{\circ}\)C). Figure 11: Experimental validation results of SGTC with an air layer for \(t_{o}\) = 20 \({}^{\circ}\)C.  
Figure 12: Experimental validation results of SGTC with an air layer for \(t_{o}\) = 30 \({}^{\circ}\)C.  
Experimental heat losses were determined using Equation (12), as previously described. The \(Q_{loss}\) values were obtained from a four-month measurement period (15 July to 15 October 2021), ensuring that the experimental values for \(t_{o}\) and \(W\) align with the corresponding values used in the mathematical (analytical) model. This alignment provided the necessary conditions to validate the model for initial research on glass tube collectors (GTCs). The validated model is designed to function without requiring additional inputs, such as solar radiation intensity or mass flow rate, while maintaining accuracy within the desired limits. As illustrated in Figure 11, the experimental data points grouped between \(t_{abs}\) = 70 \({}^{\circ}\)C and \(t_{abs}\) = 90 \({}^{\circ}\)C (\(W\) = 1 m/s and \(W\) = 3 m/s) and between \(t_{abs}\) = 60 \({}^{\circ}\)C and \(t_{abs}\) = 90 \({}^{\circ}\)C (\(W\) = 2 m/s). Similar phenomena are shown in Figure 12. If it is known that the absorber temperature in classic single-glazed solar collectors is between 30 and 80 \({}^{\circ}\)C [55], it can be concluded that the presented method has accuracy within satisfactory limits.