## 3 Results
### Practical Application of the Results  
In order to see the practical applications of the revealed effects of both thermal annealing and sorption properties, as well as freezing, on thermal conductivity, overall thermal transmittance values were calculated for two hypothetical cases. Firstly, a suspected wall structure was created with 0.4 cm of brick and another with 0.4 cm of concrete, having 0.72 and 0.70 W/mK thermal conductivities, respectively. For calculating the U-value (m\({}^{2}\)K/W), the following equation was used:  
\[\mathrm{U}=1/((1/\alpha_{\mathrm{i}})+\Sigma(\mathrm{d}/\lambda)+(1/\alpha_{ \mathrm{e}})) \tag{5}\]  
where d is the layer thickness, \(\lambda\) is the thermal conductivity and \(\alpha_{\mathrm{i}}\) and \(\alpha_{\mathrm{e}}\) are the surface heat transfer coefficients. In our case, these were 8 and 24 m\({}^{2}\)K/W, respectively. Moreover, plasters were also counted on both sides, with 2.5 cm thicknesses and having thermal conductivities of 0.9 W/mK. For these hypothetical constructions, the initial value for the thermal transmittance U\({}_{\mathrm{o}}\) for the brick was 1.29, while for the concrete it was 1.26 W/m\({}^{2}\)K without any insulation. For the first case, both wall structures (brick and concrete) were theoretically insulated with 1 cm thick aerogel insulation, starting with the initial 0.017 W/mK thermal conductivity. This thickness was chosen because the original as-received tested aerogel, provided by the manufacturer, had a thickness of 1 cm. Figure 4 presents the calculated thermal transmittances for the brick and concrete walls having 1 cm of aerogel insulation. Starting from Figure 3, presented above, we can observe salient peaks for Cases A5, B5 and B6, while A0, A1, A2 and B1 remained constant for both cases. A slight increase can be observed by A3, A4, B2, B3 and B4. These values mirror the thermal conductivity results well, too. As a base of those values, we can declare the following (trivial) phenomenon: increasing thermal conductivity increases the U-value. To go deeper into these energetics calculations, another structure pair was also investigated. Another calculation row was executed using the measured thermal conductivities, where the initial thermal transmittance was fixed at U = 0.24 W/m\({}^{2}\)K. These values were chosen because in Hungary, the building energetics requirement for the nearly zero buildings is 0.24 W/m\({}^{2}\)K (see Figure 5). Figure 4: The hypothetical structures of (**a**) brick with 1 cm of aerogel and (**b**) concrete with 1 cm of aerogel. One goal of this paper is to present a sensitivity analysis regarding the U-value. It was first calculated that, for a 40 cm brick or concrete system covered (theoretically) with 2.5 cm thick plaster on both sides, 6 cm of aerogel with (0.0171 W/mK) insulation would be needed to fulfill the requirement, since this thickness was fixed for the calculations. In Figure 5, this U = 0.24 W/m\({}^{2}\)K was highlighted with a red dashed line. Following Figure 3, as well as Figure 4a,b, one can observe the similar noticeable cases. The outstanding results belong to Cases A5, B5 and B6, while A3, A4 and B2, as well as B3 and B4, had only mild protrusion from the background (U = 0.24 W/m\({}^{2}\)K) value. After this, with a percentile calculation, we analyzed which case results exceeded U = 0.24 W/m\({}^{2}\)K. These changes are presented in Figure 6.  
From Figure 6, one can see that two cases, the values belonging to thermal annealing at 483 K for 1 day and for humidity treatment at 296 K and for 90% relative humidity, resulted in more than 10% increases (A5 and B6), in which B6 belonged to the wetted sample, causing a high moisture load and increasing the U-value by about 15%. A1 and A2 (sample annealed at 343 K for 1 day and annealed at 373 K for 1 day) kept the requirement. however, A3 and A4 broke it, belonging to the heat treatment  
Figure 5: The structure with U = 0.24 W/m\({}^{2}\)K thermal transmittance. (**a**) Brick with 6 cm of aerogel and (**b**) concrete with 6 cm of aerogel.