*5.6. Validation of the Model by Using Fragmented Temperature Measurements*

In order to assess the compliance of the adopted calculation methodology with the actual conditions, fragmentary temperature measurements were performed. Measurements were made in a real facility in a single-family residential building, on an external brick wall with the following parameters:


Following temperatures measurements were taken:


The purpose of the measurements is to show the effect of thermal inertia of the partitions on the changes in internal temperature. The measure of the influence of inertia is the amplitude of changes in the internal temperature and the temperature of the internal surface of the external partition as a function of the amplitude of changes in the external air temperature.

Measurements were taken continuously and the values were averaged over an hourly period for analysis.

This impact was initially analyzed on the basis of measurements conducted from 20–29 February 2020 and from 18–20 July 2020. The results presented in the table below were obtained for these cases. Results of calculations and measurements have been presented in Table 4.



Exemplary results for several hours in the heating season (February) are shown in Figure 15 as a function of successive hours throughout the year. The graph also shows the corresponding temperatures for these hours obtained from calculations (Tio, Twio, Teo).

On the horizontal axes of the graphs (Figure 15 and following), the time is defined as successive hours of the year. Such a system was adopted for the purpose of comparing the results of measurements and calculations, because the calculations used climatic data for the following hours of the year. The hours for calculations and measurements were kept consistent.

Supplementary markings:


During the heating season with variable outside air temperature, there are small changes in the temperature of the inner surface of the outer wall. The temperature value is comparable with the value calculated according to the adopted method.

In the summer, we can observe a similar tendency. A detailed comparison will be the purpose of further research. We initially present sample measurement results for summer season. We presented obtained results of researches in the Figure 16.

In order to verify the correctness of the adopted methodology, the amplitudes of differences in temperature between the internal air and the internal surface of the external wall were determined and presented in the Table 5.

During the measurement period, there were significant fluctuations in the outside temperature and due to this there were also changes in the internal temperature, despite the regulation of the heating with a thermostatic valve. For this reason, there was a change in the temperature difference between the inside air and the wall surface. The course of amplitude changes during the period from 20 to 29 February 2020 is shown in Figure 17.

**Table 5.** The amplitudes of temperature differences between the internal air and the internal surface of the external wall.


**Figure 16.** Variability of the measurement and calculation temperatures during the time from 18 to 20 July 2020.

**Figure 17.** Difference in temperature of internal air and internal wall surface during the time from 20 to 29 February 2020.

Analogically, the course of amplitude changes during the time from 18 to 20 July 2020 is presented in Figure 18.

**Figure 18.** Difference in temperature of internal air and internal wall surface during the time from 18 to 20 July 2020.

In order to verify the correctness of the adopted methodology, additional, more precise temperature measurements were made for the period from 9 to 17 November 2020. The measurement results are shown in Figures 19 and 20.

**Figure 19.** Variability of the temperature during the time from 9 to 17 November 2020.

**Figure 20.** Variability of internal surface temperature for the period from 9 to 17 November 2020.

The measurement results were compared with the values used in the calculations in the adopted model and are presented in Table 6.


**Table 6.** Results of calculations and measurements for the period from 9 to 17 November 2020.

The influence of the thermal inertia of partitions on changes in internal temperature was analyzed. The results of measurements and calculations are shown in Figure 20.

Changes in the temperature of the outside air cause slight changes in the temperature of the inside surface of the outside wall. The value of the wall surface temperature is comparable with the value calculated in accordance with the adopted method, which is shown in Figure 20.

In order to better visualize the compliance of the measurement results with the calculations, relative deviations calculated on the basis of the differences in the measurement and calculation results were determined. The deviations were applied to the temperature of the inner surface of the outer wall, because this temperature determines the transfer of heat for all three analyzed measurement series.

$$\delta = 100 \cdot \frac{\text{T}\_{\text{wi}} - \text{T}\_{\text{wio}}}{\text{T}\_{\text{wi}}} \, [\%] \tag{28}$$

when:

δ—relative deviation of the measured and calculated internal surface temperature.

The changes of the relative deviations of the values measured for the period from 9 to 17 November 2020 is shown in Figure 21. The relative deviations for all three measurement series are presented in Table 7.

**Figure 21.** Relative measurement deviations for the period from 9 to 17 November 2020.


**Table 7.** Relative deviations of the measured and calculated internal surface temperature.

A small value of the average deviation of the measurement and calculation results during the heating season indicates the correctness of the adopted analysis method. The big difference in July is caused by very large changes in outside air temperatures, deviating from typical meteorological years. It should be emphasized that such a result is obtained from measurements of a real object (not in a laboratory) under very variable climatic conditions. Moreover, the temperature of the indoor air in the summer with no air conditioning is directly related to the temperature of the outdoor air and is not regulated.

Furthermore, complete measurements are planned to fully assess the compliance of the calculation model.

The presented data show the following conclusions:

