## 5 Conclusions  
In the first part of this paper, the heat losses of four types of glass tube collectors (GTCs) are analyzed mathematically: the single-glazed glass tube collector with an air layer, the single-glazed glass tube collector with a vacuum layer, the double-glazed glass tube collector with an air layer, and the double-glazed glass tube collector with a vacuum layer. Appropriate mathematical models and calculation algorithms were developed, employing double iteration for single-glazed collectors and triple iteration for double-glazed collectors. The results indicate that the minimum and maximum heat loss values \(Q_{loss}\) are as follows: 5.29 W and 64.42 W for the single-glazed collector with an air layer, 2.74 W and 27.11 W for the single-glazed collector with a vacuum layer, 12.65 W and 47.14 W for the double-glazed collector with an air layer, and 6.48 W and 23.35 W for the double-glazed collector with a vacuum layer, depending on the ambient temperature (\(t_{o}\)) and wind speed (W). It was concluded that heat losses are proportional to the absorber temperature and wind speed while inversely proportional to the ambient temperature. In the second part of the paper, the theoretical results of heat losses are compared with experimental measurements obtained over a four-month period. The experimental values, which align with the theoretical values, were assessed according to two criteria: ambient \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Specific Indicator**} & \multicolumn{2}{c}{**SGTC**} & \multicolumn{2}{c}{**DGTC**} \\ \cline{2-5}  & **Air Layer** & **Vacuum Layer** & **Air Layer** & **Vacuum Layer** \\ \hline Final results & 0.30266 & 0.19563 & 0.29481 & 0.20690 \\ \hline Final ranking & 4 & 1 & 3 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Final ranking of GTCs. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Specific Indicator**} & \multicolumn{2}{c}{**SGTC**} & \multicolumn{2}{c}{**DGTC**} & \multicolumn{1}{c}{**Rank SGTC with**} \\ \cline{2-5}  & **Air Layer** & **Vacuum Layer** & **Air Layer** & **Vacuum Layer** & **a Vacuum Layer** \\ \hline \(Q_{min}\) & 0.0160 & 0.0099 & 0.0147 & 0.0094 & 2 \\ \hline \(Q_{min}\) & 0.0124 & 0.0077 & 0.0182 & 0.0116 & 1 \\ \hline \(Q_{min}\) & 0.0050 & 0.0031 & 0.0073 & 0.0047 & 1 \\ \hline \(Q_{min}\) & 0.0054 & 0.0034 & 0.0068 & 0.0044 & 1 \\ \hline \(Q_{min}\) & 0.1184 & 0.0669 & 0.1058 & 0.0589 & 2 \\ \hline \(Q_{max}\) & 0.0505 & 0.0286 & 0.0456 & 0.0253 & 2 \\ \hline \(Q_{min}\) & 0.0500 & 0.0310 & 0.0514 & 0.0477 & 1 \\ \hline \(Q_{min}\) & 0.0450 & 0.0450 & 0.0450 & 0.0450 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Ranking of the specific geometric, economic, and ecological indicators. temperature and wind speed. The agreement between the theoretical and experimental models indicates that the developed calculation algorithms are validated experimentally. In the third part of the paper, three primary groups of indicators, along with their corresponding sub-indicators, are defined to determine the optimal design of GTCs using the multi-criteria decision-making (MCDM) method with simple additive weighting (SAW). These groups include geometric indicators (mass, surface occupation, total surface occupation, volume occupation), economic indicators (production costs and exploitation costs), and ecological indicators (embodied energy and greenhouse gas emissions). The multidisciplinary analysis reveals that the single-glazed collector with a vacuum layer is the most favorable option, while the single-glazed collector with an air layer is the least favorable. For example, the literature often neglects the inclusion of economic and ecological factors in assessing the thermal performance of solar collectors, which challenges the justification of many solar applications. The primary objective of the proposed methodology is to offer a novel perspective for future research on the shortcomings of solar collectors and to underscore the significance of a comprehensive approach.