## 2 Materials and Methods
### Multi-Criteria Analysis
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Scenario**} & \multicolumn{1}{c}{**CM [c]**} & \multicolumn{1}{c}{**CE [c]**} & \multicolumn{1}{c}{**\(E_{emb}\) [kWh]**} & \multicolumn{1}{c}{**\(\epsilon_{CO2}\) [kg]**} \\ \hline \multirow{3}{*}{\(L_{\text{abs},app}\) = 50 mm} & \(d_{gt}\) = 3 mm & 57.605 & 28.803 & 2.46 & 1048.943 \\ \cline{2-7}  & \(d_{gt}\) = 4 mm & 72.047 & 36.024 & 2.895 & 1043.093 \\ \cline{2-7}  & \(d_{gt}\) = 5 mm & 86.963 & 43.482 & 3.344 & 1037.29 \\ \hline \multirow{3}{*}{\(L_{\text{abs},app}\) = 75 mm} & \(d_{gt}\) = 3 mm & 79.303 & 39.651 & 3.28 & 1625.579 \\ \cline{2-7}  & \(d_{gt}\) = 4 mm & 99.664 & 49.832 & 3.894 & 1617.312 \\ \cline{2-7}  & \(d_{gt}\) = 5 mm & 120.499 & 60.249 & 4.522 & 1609.072 \\ \hline \multirow{3}{*}{\(L_{\text{abs},app}\) = 100 mm} & \(d_{gt}\) = 3 mm & 101 & 50.5 & 4.1 & 2202.293 \\ \cline{2-7}  & \(d_{gt}\) = 4 mm & 127.28 & 63.64 & 4.892 & 2191.592 \\ \cline{2-7}  & \(d_{gt}\) = 5 mm & 154.034 & 77.017 & 5.699 & 2180.907 \\ \hline \multirow{3}{*}{\(L_{\text{abs},app}\) = 125 mm} & \(d_{gt}\) = 3 mm & 122.697 & 61.349 & 4.921 & 2779.042 \\ \cline{2-7}  & \(d_{gt}\) = 4 mm & 154.897 & 77.448 & 5.891 & 2765.9 \\ \cline{2-7}  & \(d_{gt}\) = 5 mm & 187.57 & 93.785 & 6.876 & 2752.768 \\ \hline \multirow{3}{*}{\(L_{\text{abs},app}\) = 150 mm} & \(d_{gt}\) = 3 mm & 144.395 & 72.197 & 5.741 & 3355.801 \\ \cline{2-7}  & \(d_{gt}\) = 4 mm & 182.513 & 91.257 & 6.89 & 3340.215 \\ \cline{1-1} \cline{2-7}  & \(d_{gt}\) = 5 mm & 221.105 & 110.553 & 8.053 & 3324.632 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Economic and ecological indicators (GT and FAP) of SGVTC construction depending on the simulation scenario. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Criterion** & \multicolumn{3}{c}{**Geometric**} & \multicolumn{3}{c}{**Economic**} & \multicolumn{3}{c}{**Ecological**} & \multicolumn{1}{c}{**Sum**} \\ \hline \(w_{j}\) [\%] & \multicolumn{3}{c}{14} & \multicolumn{3}{c}{50} & \multicolumn{3}{c}{36} & 100 \\ \hline Sub-criterion & \(m\) & \(SO\) & \(TSO\) & \(VO\) & \(CM\) & \(CE\) & \(E_{emb}\) & \(e_{CO2}\) & SGVTC \\ \hline \(w_{j,sc}\) [\%] & 5 & 5 & 2 & 2 & 35 & 15 & 18 & 18 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Weight of importance of each criterion for the SAW analysis. rameter, and thermal efficiency, the second parameter). This means that two independent groups of specific indicators have been created: for useful heat power (\(Q_{heat}/m\) [W/kg], \(Q_{heat}/SO\) [W/m\({}^{2}\)], \(Q_{heat}/TSO\) [W/m\({}^{2}\)], \(Q_{heat}/VO\) [W/m\({}^{3}\)], \(Q_{heat}/CM\) [W/\(\xi\)], \(Q_{heat}/CE\) [W/\(\xi\)], \(Q_{heat}/E_{emb}\) [W/kWh] and \(Q_{heat}/e_{CO2}\) [W/kg]) and for thermal efficiency (\(\eta/\) m [kg\({}^{-1}\)], \(\eta/SO\) [m\({}^{-2}\)], \(\eta/VO\) [m\({}^{-3}\)], \(\eta/CM\) [\(\xi^{-1}\)], \(\eta/CE\) [\(\xi^{-1}\)], \(\eta/E_{emb}\) [kWh\({}^{-1}\)] and \(\eta/e_{CO2}\) [kg\({}^{-1}\)]). For the adopted values of weight factors (Table 7) and the calculated specific indicators, the MCA aimed to perform a dimensionless ranking (final results, i.e., final marks) within both independent groups, i.e., evaluation of the results according to the used variables: V1, V2, V3, V4 and V5. The final results, i.e., the final ratings (ordinate axis), depending on the absorber widths (abstract axis), were then graphically represented by logarithmic functions (Section 4). Three (for \(d_{gt}=3\) mm, \(d_{gt}=4\) mm and \(d_{gt}=5\) mm) logarithmic curves for useful heat power and another three for thermal efficiency were obtained. The optimal dimensions of the SGWTC (for three pairs) were located at the intersection of the logarithmic functions of useful thermal power and thermal efficiency.