## 2 Materials and Methods
### Multi-Criteria Analysis  
In this study, an MCA is used to identify the optimal dimension (\(L_{abs,opt}\) [m] and \(d_{gt,opt}\) [m]) of the SGVTC. The analysis incorporates geometric (\(m\), \(SO\), \(TSO\) and \(VO\)), economic (manufacturing costs, i.e., \(CM\) [C] and operational costs, i.e., \(CE\) [C], Table 6) and ecological (embodied energy \(E_{emb}\) [kWh], Equation (34), and greenhouse gas emissions \(e_{CO2}\) [kg], Equation (35), Table 6) indicators. Economic, environmental and economic indicators are indispensable when carrying out sustainability analyses (following the global policy of sustainable development). Economic indicators are important from the point of view of the end user of the solar system. Environmental indicators are important from the point of view of view of environmental protection and solar system manufacturers (directly), as well as from the point of view of the end user (indirectly). \[E_{emb}\ =\ \frac{mE_{emb,spec}}{20} \tag{34}\] \begin{table}
\begin{tabular}{c c c} \hline  & **Variable** & **Used Values** \\ \hline V3 & \(t_{abs}\) [\({}^{\circ}\)C] & 20; 30; 40; 50; 60; 70; 80; 90 \\ \hline V4 & \(t_{o}\) [\({}^{\circ}\)C] & 10; 20; 30; 40 \\ \hline V5 & \(W\) [m/s] & 1; 3; 5 \\ \hline \end{tabular}
\end{table} 
Table 5: Adopted variable values in the iterative calculation algorithm. \[e_{CO2}\ =\ e_{CO2,spec}E_{pyr}\ =\ e_{CO2,spec}K_{pyr}E_{fin}\ =\ e_{CO2,spec}K_{pyr} \frac{Q_{heat}time}{1000\eta_{el}} \tag{35}\]  
where \(E_{emb,spec}\) [kWh/kg] is the specific embodied energy (\(E_{emb,spec}\) = 53 kWh/kg for aluminum [56] and \(E_{emb,spec}\) = 25.8 kWh/kg for glass [57]), \(e_{CO2,spec}\) [kg/kWh] is the specific CO\({}_{2}\) emission (\(e_{CO2,spec}\) = 0.53 kg/kWh for electricity [58]), \(E_{pyr}\) [kWh] is the primary energy consumption, \(K_{pyr}\) [-] is the primary energy transformation coefficient (\(K_{pyr}\) = 2.5 for electricity [58]), \(E_{fin}\) [kWh] is the final energy consumption, \(time\) [h] is the working time and \(\eta_{el}\) [-] is the efficiency of the electric boiler (adopted \(\eta_{el}\) = 0.98). Several MCA approaches are described in the literature. In this case, the double multi-criteria decision-making method (MCDM) using simple additive weighting (SAV) was applied [59; 60; 61; 62]. It is a relatively simple model that provides relevant and reliable results. It is explained in detail (mathematically and graphically) in [30]. The values of the weight factors \(w_{j}\) [-] are determined by their importance (their sum should be 1, i.e., 100%). When defining the value of \(w_{j}\) (Table 7), The greatest priority was given to economic criteria (50%), followed by environmental criteria (36%). From the end user's point of view, monetary costs are a priority, while overall dimensions are often less important in practice, except for some specific circumstances. Environmental protection is still not in its desired stage, but much work is being performed on it, especially in Europe. Unlike in the previous study [30], where the MCA was applied to heat losses, in this paper, the MCA was applied to two thermal parameters (useful heat power, the first pa