## 5 Results, Analysis, and Discussion
### Attenuation Coefficient  
According to the literature [39; 40], the thermal stability of a building envelope can be typically characterized by the decrement factor. Since the fluctuations of outdoor air temperature are the cause of fluctuations in the temperature of the building envelope, the decrement factor is calculated as the ratio of amplitude of external temperature fluctuations to internal surface temperature fluctuations. In most theoretical considerations, it is assumed that temperature fluctuations are harmonic, i.e., they follow the sine wave within a 24 h period. For the purpose of this study--analysis of the external active layer performance, the attenuation coefficient was proposed, as (Figure 7):  
\[\mathrm{AC}=\frac{\Delta\mathrm{T6}^{x}}{\Delta\mathrm{T7}^{x}}=\frac{\mathrm{ T6}_{\mathrm{max}}^{x}-\mathrm{T6}_{\mathrm{min}}^{x}}{\mathrm{T7}_{\mathrm{ max}}^{x}-\mathrm{T7}_{\mathrm{min}}^{x}} \tag{2}\]  
where:  
\(x\)--number of analyzed test section (PCM/REF)  
T6--readout from temperature sensor 6 (according to Figure 4)  
T7--readout from temperature sensor 7 (according to Figure 4)  
Figure 7: Example values used for attenuation coefficient calculation. The attenuation coefficient (AC) was introduced to quantitatively describe and compare the ability of an externally positioned layer of material to attenuate the temperature fluctuations on the external boundary of the partition. Considering a single day of the analysis, it can be stated that the higher value of attenuation coefficient causes the bigger daily temperature amplitude on an external surface. Comparing results for analyzed sections, it can be concluded that lower values of attenuation coefficient means a greater ability of the layer to decrease the temperature fluctuations. The analyzed one-year period of measurement was divided into two seasons:  
* Heat loss season (HLS)--days when maximum daily temperature on external surface of the wall was higher than maximum daily temperature in the ventilated cavity of the facade,
* Heat gain season (HGS)--days when maximum daily temperature on external surface of the wall was lower than maximum daily temperature in the ventilated cavity of the facade. Values of attenuation coefficients were calculated for each day of the analyzed one-year period of time. Nevertheless, since the aim of comparative analysis was to determine the effect of latent heat storage on thermal performance of the wall, it was stated that analysis should be proceeded only for the days when phase change occurred in the PCM-perlite composite (P4). It was assumed that latent heat accumulation could have occurred when maximum daily temperature measured in the point T7 (Figure 4) was greater than 25 \({}^{\circ}\)C, and minimum daily temperature measured in the point T4 was lower than 25 \({}^{\circ}\)C. In Figure 8, the values of AC calculated for the period of the whole year for the test section (P4) were presented. It can be observed that during the winter months (X-II) phase change did not occur, and due to the assumption of HLS length, only HGS was further analyzed (164 days from 352). Results obtained for the panels with PCM-perlite composite (P4) and reference one (P6) are presented in Figure 9. In the further analysis values measured by two sensors--T6 and T7 were used. As was proved before, temperatures registered by sensor T7 were almost equal for all sections; thus the differences revealed in attenuation coefficient came from the different temperatures registered on the external surface of the wall. Figure 8: The attenuation coefficient (AC) values calculated for test section modified with PCM (PT—results for these days when phase transition occurs, noPT—results for the days without phase transitions). Based on the results presented in Figure 9 it can be clearly noticed that the values of AC calculated for the reference test section (P6 = REF) are much higher than for PCM-perlite composite (P4 = PCM). The mean value obtained for P4 was almost two-fold lower than for P6 (0.36 and 0.66 respectively).