## 4 A Case Study of a Low-Energy House in Bialystok (NE Poland)
* properly designed (with \(U\)-values of the building envelope much lower than the current Polish requirements),
* equipped with very efficient balanced ventilation with heat recovery (with 90% heat recovery efficiency) and a ground heat exchanger for pre-heating the ventilation air,
* constructed very precisely. Detailed solutions used in the building are presented in Figure 7. Windows are made of triple glassing two coated panes+ and Gealan Synergic frames installed in a layer of thermal insulation of walls (Figure 7c). An air source heat pump using energy stored in ambient air is used. A split system consists of one unit inside and one outside the building. The heat is distributed through the surface and the central water heating system (Figure 8d) and used for the heating of DHW. Sample photographs from the construction stage of the building are shown in Figure 8. The \(U\)-value of individual elements of the analyzed building (Table 2) is approximately 40% lower than the requirements for the NF15 standard. This difference is even greater in relation to the WT2021 standard (more than double for walls and doors, and even more than four times for a floor on the ground). Figure 7: Construction of the building envelope: (**a**) roof in connection with external walls; (**b**) connection of the wall with the floor slab; (**c**) installation the window in wall. Due to the requirements of the NFEP and WM, in order to evaluate detailed heat transfer losses through the building envelope, steady-state heat transfer numerical simulations were made for individual construction details in the analyzed building. The modelling was carried out in accordance with the procedures of the standard [136], by using the THERM 6.3 software [137], developed by the Lawrence Berkeley National Laboratory (LBNL). The simulation results are presented in Table 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{_U-Value for the_} & \multicolumn{2}{c}{**Maximum _U-Value for the Standards_**} \\ \cline{2-4}
**Building Elements** & \multicolumn{2}{c}{**Analyzed Building**} & **WT2021** & **NF15** \\ \cline{2-4}  & \multicolumn{2}{c}{**(W/m\({}^{2}\)K)**} \\ \hline External Walls & 0.075 & 0.20 & 0.12/0.10 (before 5 December 2015) \\ Roof & 0.077 & 0.15 & 0.12/0.10 (before 5 December 2015) \\ Ground floor & 0.071 & 0.30 & 0.12 \\ Windows (g = 0.50) & 0.55; 0.65 & 0.90 & 0.80 \\ Door 56 & 0.57 & 1.30 & 1.10/0.80 (before 5 December 2015) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Heat transfer coefficient (_U_-value) requirements for the WT2021 and NF15 standards [119, 123] and achieved for the analyzed building [135]. Figure 8: Photographs of the construction stage of the building: (**a**) Foundation wall insulation; (**b**) wall insulation; (**c**) installing the window; (**d**) underfloor heating installation. The obtained values of the linear heat transfer coefficient of all details in the analyzed case study met the requirements of the NF15 standard (\(\Psi<0.05\) W/(mK)) [134]. Unfortunately, the WT2021 standard does not specify such requirements [130]. Additionally, it can be noticed that according to the criterion of the Passive House Institute [138] a \"thermal bridge free design\" was achieved (\(\Psi<\)0.01 W/(mK)). Before the building was put into operation (in 2015), the computational energy demand of heating was determined with use of Audytor OZC version 6.8 Pro software (Sankom, Warsaw, Poland). The calculations were carried out in accordance with ISO 13,790 standards [139], which were then in force and indicated by the NFEP and WM [134] for the assessment of energy-efficient buildings. The statistical multi-year climatic conditions for Bialystok [140] were used in accordance with the building's location. The number of heating degree days for Bialystok was assumed to be 4095.4 Kd. The energy need of water heating was calculated on the basis of Polish regulations [141].