## 2 Materials and Methods
### Thermophysical Analysis  
Based on the experimental results obtained from the samples, in terms of flexural and compressive strengths, the 30% cork mortar had higher compressive strength than the 15% cork mortar, as well as higher than expected values. It was decided that thermophysical tests would be carried out only on the 30% cork samples. This decision was also based on studies conducted by other authors who obtained lower strength values than those obtained in the present study. Therefore, in this section, the results of the thermophysical properties of the designed matrix were summarized on natural lime mortar with 30% cork granules. Tests for measuring thermal conductivity were conducted using thermal flow meters (HFMs) to measure steady heat transfer through flat materials according to the following codes: ASTM Standard C518-17 and EN 12667 [34; 35]. For the test measuring thermal conductivity, the FOX 314 TM and FOX 50 TM apparatuses were utilized, as shown in Figure 6[36]. A preliminary test run (Test Run 1) was conducted using the Fox 314 instrument for the evaluation of the thermophysical properties of the lime-cork mortar 300 \(\times\) 300 \(\times\) 30 mm\({}^{3}\) specimen (S1), while the homogeneity of the specimen was estimated on two circular specimens (S2 and S3) extracted from the specimen of Test Run 1 using a drilling procedure (diameter d = 50 mm and depth de = 30 mm). The first phase of the thermophysical test was conducted on a 300 \(\times\) 300 \(\times\) 30 mm\({}^{3}\) (S1) specimen using the Fox 314 instrument (see Figure 7a). \begin{table}
\begin{tabular}{c c c c} \hline
**Specimen** & **Mass** & **Fc** & **Rc** \\
**Code** & **[g]** & **[N]** & **[MPa]** \\ \hline M15-C1\({}^{1}\) & 254 & 3900 & 2.76 \\ M15-C1\({}^{2}\) & 258 & 4050 & 2.83 \\ M15-C2\({}^{1}\) & 258 & 3800 & 2.16 \\ M15-C2\({}^{2}\) & 261 & 3920 & 2.25 \\ M15-C3\({}^{1}\) & 253 & 3750 & 2.44 \\ M15-C3\({}^{2}\) & 257 & 3900 & 3.35 \\ \hline \end{tabular}
\end{table} 
Table 6: Results of the compressive tests of the matrix with 15% cork after 28 days. \begin{table}
\begin{tabular}{c c c c} \hline
**Specimen** & **Mass** & **Fc** & **Rc** \\
**Code** & **[g]** & **[N]** & **[MPa]** \\ \hline M30-C1\({}^{1}\) & 250 & 4100 & 2.56 \\ M30-C1\({}^{2}\) & 253 & 4300 & 2.69 \\ M30-C2\({}^{1}\) & 252 & 3800 & 2.38 \\ M30-C2\({}^{2}\) & 254 & 4000 & 2.50 \\ M30-C3\({}^{1}\) & 250 & 3900 & 2.44 \\ M30-C3\({}^{2}\) & 260 & 4000 & 3.19 \\ \hline \end{tabular}
\end{table} 
Table 7: Results of the compressive tests of the matrix with 30% cork after 28 days. Figure 6: Thermophysical analysis apparatuses used for the tests: (a) FOX 314 TM; (b) FOX 50 TM. The results of this analysis, along with the set temperatures, are presented in Table 8.  
It is worth noting that, although the thermal gradient across the specimens was set to 20 \({}^{\circ}\)C in accordance with the requirements of the relevant technical codes [37], each measurement run involved several average temperatures to examine the parameter's influence on thermal conductivity. The second phase of the experimental procedures, as mentioned above, aimed to measure the homogeneity of the specimens. Specifically, specimen 2 (S2) was taken from the edge, while specimen 3 (S3) was obtained from the core (Figure 7b). The Fox 50 TM apparatus was used for the measurements. The results of the second phase of experimental procedures are reported in Tables 9 and 10. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Measure ID** & \(\mathbf{t_{low}}\) (\({}^{\circ}\)C) & \(\mathbf{t_{up}}\) (\({}^{\circ}\)C) & \(\mathbf{ta_{vg}}\) (\({}^{\circ}\)C) & **k** \\  & (\({}^{\circ}\)C) & (\({}^{\circ}\)C) & (\({}^{\circ}\)C) & **W/mk** \\ \hline
1 & 5 & 25 & 15 & 0.4459 \\
2 & 15 & 35 & 25 & 0.4455 \\
3 & 25 & 45 & 35 & 0.4455 \\  & & & Average & 0.4456 \\  & & & Standard Deviation & 0.0002 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Results of Test Run C—specimen S3.