## 4 Results
### Radiant Systems Efficiency
Figure 6: Efficiency of the radiant systems limited to the period from December to February, obtained considering the same operative temperature of the ideal convective simulations and (in green) efficiency calculated by FDM in steady-state conditions. Figure 7: Efficiency of the radiant systems over the whole heating season and (in green) efficiency in steady-state conditions. As regards the efficiency values which can be found in the standards, the old version of EN ISO 15316-2-2007 [37] recommends to use an embedded and control efficiency value which is equal to 90% for the wet floor and ceiling systems (\(\eta_{ctr}\) = 0.95, \(\eta_{emb}\) = 0.94) considered in this study and 91.3% for the dry floor system (\(\eta_{ctr}\) = 0.95, \(\eta_{emb}\) = 0.955). No difference in the efficiency values in the old version of the standard is considered to take into account the different insulation level and thermal inertia of the building. In the last version of the standard EN ISO 15316-2-2017 [38], the calculation method to evaluate the energy required by a heating or cooling system is only based on internal temperature variations, while the calculation method based on efficiency values was removed. Therefore, in the present work besides efficiency values, also the internal temperature variation was calculated from the results of the simulations for the period from December to February. As can be seen in Table 8, the current standard overestimates the losses of the radiant systems: in the non-insulated case the difference is about 0.7 \({}^{\circ}\)C for the radiant floor and 1.5 \({}^{\circ}\)C for the ceiling. In insulated buildings the difference is 1.1\({}^{\circ}\)C in insulated buildings and 1.4 \({}^{\circ}\)C for the radiant ceiling. In well-insulated masonry buildings the difference is 1.2 \(\div\) 1.5 \({}^{\circ}\)C compared to the existing standard temperature variation for the radiant floor and 1.2 \({}^{\circ}\)C for the radiant ceiling. In well-insulated buildings with light structures the difference is about 1.7 \({}^{\circ}\)C \(\div\) 2.0 \({}^{\circ}\)C for the radiant floor, as well as for the radiant ceiling. These values are conservative since the calculation has been limited in the period December-February which is the one which provided the lowest efficiencies in terms of losses and hence the greatest values of the temperature difference \(\Delta T_{i,emb}+\Delta T_{i,ctr}\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{3}{*}{**Type of Building**} & \multirow{3}{*}{
\begin{tabular}{c} **Type of Radiant** \\ **System** \\ \end{tabular} } & \multicolumn{3}{c}{\(\Delta T_{i,emb}\) + \(\Delta T_{i,ctr}\) [\({}^{\circ}\)C]} \\ \cline{3-5}  & & \multicolumn{3}{c}{**Simulations**} & \multicolumn{1}{c}{**EN ISO 15316-2**} \\ \cline{3-5}  & & \multicolumn{3}{c}{**Constant Supply**} & \multicolumn{1}{c}{**Climatic Control**} \\ \hline \multirow{3}{*}{N} & FW & 1.1 & 1.1 & 1.9 \\  & FD & 1.5 & 1.4 & 2.2 \\  & C & 0.7 & 0.7 & 2.2 \\ \hline \multirow{3}{*}{I-M} & FW & 0.7 & 0.9 & 1.9 \\  & FD & 1.2 & 1.1 & 2.2 \\  & C & 0.8 & 0.9 & 2.2 \\ \hline \multirow{3}{*}{I-E} & FW & 0.8 & 0.8 & 1.9 \\  & FD & 1.2 & 1.1 & 2.2 \\  & C & 0.7 & 0.6 & 2.2 \\ \hline \multirow{3}{*}{I-I} & FW & 0.7 & 0.9 & 1.9 \\  & FD & 1.1 & 1.1 & 2.2 \\  & C & 0.9 & 0.8 & 2.2 \\ \hline \multirow{3}{*}{WI-E} & FW & 0.8 & 0.7 & 1.9 \\  & FD & 0.7 & 0.6 & 2.2 \\ \hline \multirow{3}{*}{WI-I} & FW & 0.4 & 0.6 & 1.9 \\  & FD & 0.7 & 0.6 & 2.2 \\  & C & 0.7 & 0.7 & 2.2 \\ \hline \multirow{3}{*}{WI-X} & FW & 0.3 & 0.3 & 1.9 \\  & FD & 0.2 & 0.3 & 2.2 \\ \cline{1-1}  & C & 0.2 & 0.3 & 2.2 \\ \hline \multirow{3}{*}{WI-L} & FW & 0.4 & 0.3 & 1.9 \\ \cline{1-1}  & FD & 0.4 & 0.3 & 2.2 \\ \cline{1-1}  & C & 0.4 & 0.4 & 2.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Temperature variation values calculated from the results of the dynamic simulations with DIGITHON and values according to EN ISO 15316-2-2017.