## 5 Results and Discussion
### The Effect of Numerical Calculation of Thermal Bridges on the Energy Performance  
The energy performance results using the conservative thermal bridge approach (default \(U\)-value increase by \(\Delta U\)) are compared to the ones calculated using the \(\psi\)-values shown in Table 6 with respective lengths of thermal bridges together with \(U_{\mathit{eff}}\)-values of opaque envelope elements. The analysis was performed for the southern orientation of the main facade. Transmission heat losses \(H_{D}\) were the same for all climates (Table 7). It can be seen from Table 7 that the total \(H_{D}\) were 48.4% lower for the case when calculations were performed using the calculated \(\psi\)-values and \(U_{\mathit{eff}}\)-values. The \(H_{D}\) value for opaque building elements was 24.5% higher when using the default \(U\)-value increase, which is a consequence of adding \(\Delta U=0.05\) W/(m\({}^{2}\)K) to the \(U\)-values of the building envelope. As can be seen from Table 7, the contribution of thermal bridges to transmission heat losses is significant, where the negative value is due to the \(\psi\)-values calculation approach described above. Results indicate that using the default \(U\)-value increase can lead to unrealistically increased heat flow through building envelope elements, and, consequently, to increased energy demand on the whole building level. In such a way, the reliability of energy performance calculations can be questioned and lead to an increased energy performance gap (discrepancy between predicted and measured energy use), but this is out of the scope of this paper. On the other hand, applying \(U_{\mathit{eff}}\)-values and addressing 2D \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Units** & \begin{tabular}{c} **Approach Using the Default** \\ _U-Value Increase_ \\ _\(\Delta U\) = 0.05 W/(m\({}^{2}\)K)_ \\ \end{tabular} & \
\begin{tabular}{c} **Approach Using the \(U_{\mathit{eff}}\)** \\ _and Calculated_ \\ _\(\psi\)-Values_ \\ \end{tabular} &
\begin{tabular}{c} **Relative Difference** \\ **[\%]** \\ \end{tabular} \\ \hline Total \(\mathrm{H_{D}}\) & [W/K] & 33.977 & 17.530 & 48.4 \\ \hline \(\mathrm{H_{D}}\)—opaque building elements & [W/K] & 21.429 & 16.189 & 24.5 \\ \hline \(\mathrm{H_{D}}\)—transparent building elements & [W/K] & 12.548 & 12.548 & 0.0 \\ \hline \(\mathrm{H_{D}}\)—thermal bridges & [W/K] & 0 & \(-\)11.207 & / \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Transmission heat losses \(H_{D}\) for the case of the MUZA. heat flow more precisely describes the heat flow through the observed building envelope. Negative \(\psi\)-value has only a mathematical meaning; it does not represent an \"opposite\" heat flow direction. A negative \(\psi\)-value means that the actual heat flow is less than what was calculated using external measurements (external measurements are used to evaluate the whole thermal envelope). Figure 11 gives the heating and cooling energy need calculations depending on the thermal bridge calculation approach (default \(U\)-value increase or calculated \(\psi\)-values and \(U_{\mathit{eff}}\)) for different climate conditions. It can be seen from Figure 11 that a significant decrease in \(Q^{\prime\prime}{}_{H,nd}\) is achieved when calculated \(\psi\)-values and \(U_{\mathit{eff}}\)-values were used. This decrease was around 46% for the cooler climates of Gospic and Zagreb Maksimir, while for the warmer climates, the contribution was even higher (56.8% for Split Marjan and 58.5% for Hvar). On the other hand, as expected, the cooling energy need \(Q^{\prime\prime}{}_{C,nd}\) has increased for all climates, to 28.9% and 20.6% for the cooler climates of Gospic and Zagreb Maksimir, respectively and 8.7% and 13.4% for warmer climates of Split Marjan and Hvar, respectively. The total impact of thermal bridges on heating energy required is significant, while on the other hand, the impact on cooling energy, the relative conductive contribution of which is much smaller, is less significant.