## 3 Results and Discussion
### Thermal Conductivity Measurement Results  
Table 3 shows the declared thermal conductivities as a function of the temperature and density. As can be observed, the thermal conductivities varied between 0.029 and 0.092 as a function of temperature and density. The tested materials were loose-filled and lightweight insulation; therefore, they were very compressible. [PERSON] equipment enables measuring the thermal conductivity of the samples under various loads of heat plates applied on the samples, as well as allows measurement without any load. However, here it must be emphasized that the default setting for the applied load was about 2 kPa. Moreover, by using this equipment, the thermal conductivity could also be measured at different mean temperatures. First, to observe the effects of compression and the resultant change in density on the thermal conductivity, three measurements were performed on each sample at a mean temperature of 30 \({}^{\circ}\)C, and the results are highlighted in Figure 4. Black squares show the measured thermal conductivities without any load. With an increasing density, a decreasing thermal conductivity was reached. Then, the samples were compressed manually with the equipment by 20%, and their thermal conductivities were measured again. Here, the results presented the same order as above: the highest value was attained for the pink sample, while the lowest value was measured for the orange. The phenomenon that the increasing density reduces the thermal conductivity was also presented by others \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Gaussian Model**} \\ \hline  & **Pink** & **st. Err.** & **Yellow** & **st. Err.** & **Green** & **st. Err.** & **Orange** & **st. Err.** \\ \hline Adj. R-squared & 0.986 & & 0.88 & & 0.879 & & 0.765 & \\ \hline xc & 2.37 & 0.025 & 2.25 & 0.093 & 2.66 & 0.0944 & 2.23 & 0.125 \\ \hline sigma & 0.66 & 0.029 & 0.86 & 0.11 & 0.87 & 0.123 & 0.742 & 0.15 \\ \hline Calculated mean & 2.36 & 0.725 & 2.47 & 1.02 & 2.87 & 1.18 & 2.8 & 1.27 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The results of the fitted Gaussian model on each sample. Figure 3: The fiber diameter vs. as-received density. for fibrous insulations, although notably, the thermal conductivity decreased to a local minimum [16; 42]. In order to see the effect of the compression load on the thermal conductivity, samples were pressed with the plates applying 2 kPa pressure, resulting in about an 80 N force. This compression could happen in real cases, where the insulation material is placed between two layers, or it is compressed by another layer inside the structure. In this case (indicated with red circles), the density of the pink insulation changed the most due to the compression and reached the lowest thermal conductivity. Here, it must be mentioned that due to the compression, the resultant thermal conductivity and thickness decrease might also result in a decrease in the calculated thermal resistance. However, these results supported the case that increasing density decreases the thermal conductivity. In Table 4, thicknesses measured during the thermal conductivities in the case of the 20% compression and under 2 kPa load are displayed. One can see that in the last case, where 2 kPa load was exerted on the materials, the thicknesses was less than 1 cm, where the measurement limit of the equipment was reached. Therefore, these results should be treated with care, and no significant conclusions should be drawn from this. Additionally, from the results presented in Figure 4, it can be stated that the best choice for the thermal conductivity measurements was the setup where the compression was fixed at 20%. The reason for this was because these materials are loose-filled and compressible. For exact measurements of the thermal conductivities, the heat plates had to be in good contact with the surface, and we found that this was the best solution for the thermal conductivity measurements.