## 5 Discussion and Applicability of Results
It is due to the extreme climatic conditions  
The proposed model requires design and sizing of the active ceiling to incorporate active modules of solution (length and diameter of tubes), a number of modules connected in series (circuits), and sizing of the hot/cold water production system. Also, it is possible to estimate thermal behaviour in any operational conditions. Then, this section shows the optimal way for integrating the solution. The applicability of the proposed model and the correlations obtained based on experimentation allow replicating the tested technology under any conditions and knowing the system's performance under different operating conditions. For this, _NTU's_ efficiency method is proposed as it is most used for the design and dimensioning of heat exchange systems [41; 42]. Efficiency is the indicator that shows the quality of the future designs carried out, and the _NTU_ parameter is linked to the dimensioning of the element. Efficiency is defined as the quotient between the temperature difference in the fluid that circulates through the active surface and the maximum possible temperature difference. This water temperature difference corresponds to the difference in the water flow temperature and the equivalent room temperature (See Equation (14)). \[\epsilon=\frac{T_{water\ in}-T_{water\ out}}{T_{water\ in}-T_{eq}} \tag{14}\]  
The number of transfer units (_NTU_) is defined in Equation (15):  
\[NTU=\frac{U\cdot A}{C_{min}} \tag{15}\]  
where \(T_{water\ in}\) [\({}^{\circ}\)C] is the inlet water temperature and \(T_{water\ out}\) [\({}^{\circ}\)C] is the outlet water temperature of the radiant element, \(T_{eq}\) [\({}^{\circ}\)C] is the equivalent convective radiant temperature linked to the room (see Equation (11)), \(U\) [\(\frac{W}{m^{2}\cdot K}\)] is the heat transfer coefficient (see Equation (10)), \(A\) [m\({}^{2}\)] is the active surface of the radiant element, and \(C_{min}\) [\(\frac{W}{K}\)] is the thermal capacity of water flow inside the tubes. The active surface relates to the size of the element. Also, the \(U\)-value is linked with the thermal characteristic of water flow (convection). Furthermore, the efficiency can be approximated as a function of the _NTU_ using the expression proposed by [PERSON] [37] in Equation (16):  
\[\epsilon=1-e^{-\mathrm{NTU}} \tag{16}\]  
The procedure allows for assessment in different operating conditions and designs. The following results demonstrate the influence of design parameters. For example, Figures 19 and 20 analyse the effect of size. Figure 19 shows the variation in efficiency as a function of the number of modules for a series of possible flow rates. The number of modules is the same as the length of the radiant exchanger. In this case, one module corresponds to a linear tube length of 18 m. These results were calculated for a mean air temperature of 25 \({}^{\circ}\)C, mean radiant temperature of 24 \({}^{\circ}\)C, and inlet water temperature of 15 \({}^{\circ}\)C. The results obtained were as expected. If the water flow is the minimum (2 \(\frac{1}{\mathrm{min}}\)), the maximum length per m\({}^{2}\) of active surface is required to achieve the same efficiency as the other cases. This result allows deciding which is the most interesting solution: a low operation cost (pumping cost) or a high initial cost (diameter of tubes). Figure 19 shows the efficiency of 80% when the water flow is 2 \(\frac{1}{\min}\) and the length of the radiant exchanger is 108 m. This length is linked to the surface of the radiant ceiling. On the other hand, Figure 20 shows the variation in efficiency as a function of the number of transfer units (_NTU_). In the cases of Figure 20, _NTU_ is the combination of active surface and water flow effects. Then, a higher _NTU_ implies a greater linear length of tubes through which a low flow circulates. In addition to the results before, \(\varepsilon-NTU\) procedure allows evaluating the results for a known solution (108 m of the radiant exchanger and water flow of 2 \(\frac{1}{\min}\)).