## 3 Results and Discussion
### Thermal Transmittance of the Test FaCdes  
It is now possible to determine the thermal transmittance (U-value) of the test facades in two different ways:  
1. Using the material properties: thermal conductivity of the materials [W/mK] and thickness of the materials [m],
2. Using the energy use data [kWh/m\({}^{2}\)] for the rooms behind the facades, combined with the degree hours [\(\Delta\)Kh]. Both methods were used, and a comparison could be made. **(i) U-value based on material properties**  
At the time of the construction of the facades, a total of 10 specimens per material (time render, hep-line render) were also produced. These specimens were cast in molds \(100\times 100\times 100\) mm by the same mason and in the same way as he had applied these materials to the walls. Also, some of the timber was saved when constructing the walls. This timber measured approximately \(27\times 49\) mm and was cut into specimens that were on average 86 mm long. These materials were used to determine thermal conductivity. Material specimens were stored in a climate chamber at \(20.4\pm 0.2\)\({}^{\circ}\)C and \(60.7\pm 1.1\%\)RH prior to measuring their thermal conductivity. The specimens were stored in the climate chamber for more than a year. The thermal conductivity of the building materials was determined using a Thermal Constants Analyser (TPS1500, Hot Disk(r)). Power and measurement time were adjusted to the material (see Table 3). For each material, a minimum of three measurements were made. For the timber, the measurements were made in the same direction as the timber was situated in the wall, which was perpendicular to the fiber direction. The measured values for thermal conductivity are shown in Table 4.  
The U-value of both facades could then be calculated, using the thickness of the materials (d) and their thermal conductivity (\(\lambda\)). It was assumed that the indoor surface thermal resistance (R\({}_{\text{in}}\)) was 0.13 m\({}^{2}\)K/W and the outdoor surface thermal resistance (R\({}_{\text{out}}\)) was 0.04 m\({}^{2}\)K/W. Both facades had wooden slats embedded in the (hemp-) lime render (see Figures 6 and 7). The slats comprised approximately 12% of the rendered material. This means that 88% consisted of lime render (room A) and hep-line render (room B), respectively. Thermal transmittance (U) for the facade was then determined as follows:  
\[\sum_{i=1}R=\sum_{i=1}\frac{d}{\lambda} \tag{4}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Material** & **Thermal Conductivity [W/mK]** \\ \hline Timber plank (perpendicular to fibre direction) & 0.18 \\ Hemp- lime render & 0.14 \\ Air lime render & 0.87 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Thermal conductivity of the materials used in the walls, measured with TPS1500, Hot Disk®. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Material** & **Power [W]** & **Measurement Time [s]** \\ \hline Timber & 0.05 & 160 \\ Hemp- lime & 0.03 & 320 \\ Air lime render & 0.20 & 80 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Power and measurement time for the measurements of thermal conductivity using TPS1500, Hot Disk®. \[U_{facade}=\frac{1}{\sum R} \tag{5}\]  
The thermal resistance for the lime facade could then be calculated as follows:  
\[ \begin{array}{l}R_{A}=\frac{d_{timider}}{\lambda_{timider}}+\left(0.88\cdot\frac{ d_{time}}{\lambda_{timider}}+0.12\cdot\frac{d_{timider}}{\lambda_{timider}}\right)+\frac{d_{ time~{}readr}}{\lambda_{timider}}+R_{in}+R_{out}\\ =0.61~{}m^{2}K/W\end{array} \]  
Additionally, the U-value of the lime facade was determined as:  
\[ \begin{array}{l}U_{A}=\frac{1}{\sum R}=1.64~{}W/m^{2}K\end{array} \]  
The thermal transmittance for the hemp-line facade was determined as follows;  
\[ \begin{array}{l}R_{B}=\frac{d_{timider}}{\lambda_{timider}}+\left(0.88\cdot \frac{d_{humiler}}{\lambda_{humiler}}+0.12\cdot\frac{d_{timider}}{\lambda_{timider }}\right)+\frac{d_{time~{}readr}}{\lambda_{time~{}readr}}+R_{in}+R_{out}\\ =1.10~{}m^{2}K/W\end{array}