## 4 Numerical Analyzes
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **Unit** & **Teriva Panel 160** & **Teriva Panel 180** & **Teriva Panel 200** \\ \hline \(R_{T}\) flow upwards & (m\({}^{2}\)\(\cdot\)K)/W & 0.199 & 0.220 & 0.241 \\ \(R_{T}\) flow downwards & (m\({}^{2}\)\(\cdot\)K)/W & 0.213 & 0.222 & 0.241 \\ \(R_{U}\) flow upwards & (m\({}^{2}\)\(\cdot\)K)/W & 0.339 & 0.360 & 0.381 \\ \(R_{U}\) flow downwards & (m\({}^{2}\)\(\cdot\)K)/W & 0.413 & 0.432 & 0.451 \\ \(U\) flow upwards & W/(m\({}^{2}\)\(\cdot\)K) & 2.947 & 2.775 & 2.623 \\ \(U\) flow downwards & W/(m\({}^{2}\)\(\cdot\)K) & 2.420 & 2.317 & 2.219 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Values of thermal parameters of various Teriva Panel ceiling variants. Figure 12: Results of Teriva Termo ceiling calculations: (**a**) flow upwards, (**b**) flow downwards. Comparing the results of numerical calculations with the calculations carried out in accordance with EN ISO 6946:2017 [28], it can be stated that the heat transfer coefficients obtained on the basis of numerical calculations are higher than those obtained on the basis of standard calculations. The smallest difference of almost 12% was obtained for the Teriva Panel ceiling with a height of 200 mm. The biggest difference between the results of the calculations occurred in the case of the Smart ceiling, where the numerical simulations showed a \(U\) factor 39% higher than in the calculations carried out in accordance with EN ISO 6946:2017 [28]. The percentage differences between the values of the heat transfer coefficient U, calculated in accordance with the standard and obtained from numerical analyses, are given in Table 15.  
Numerical calculations have always resulted in higher \(U\) values. Greater differences in the results of standard and numerical calculations were observed at downward flow than at upward flow. This is due to different heat transfer resistance values used in traditional and numerical calculations. When calculating the thermal characteristics of building partitions, the EN ISO 6946:2017 standard is most often used [28]. The heat exchange through ceilings takes place by conduction, convection and radiation. In the case of air-filled spaces in the ceiling, the mathematical description of free convection in free spaces consists in providing a system of equations that includes the equation of continuity, the momentum equation, and the energy conservation equation with boundary conditions. If the spaces have a regular shape, it is possible to replace the complicated description of the phenomenon by assuming that the heat transport in the cavity is one-dimensional heat conduction with a modified air conductivity coefficient. The intensity of air circulation as a result of convection depends on the geometries of the free space (its height and width) and the difference in temperature of the surrounding walls. This phenomenon can be characterized by an equivalent thermal conductivity coefficient, which was adopted for calculations on the basis of nomograms given in the paper [22]. For the numerical calculations of the airspace, the actual geometries of the voids were given. The thermal conductivity coefficient was selected from the program's material database. A different way of taking convection into account in the ceiling spaces that are filled with air indicated the expected possibility of obtaining various results of numerical simulations and normative calculations with the additional taking account of the equivalent air heat conductivity coefficient. In the case of Teriva Panel ceilings, where there are no air voids, the differences at upward flow of 12%-14.9% are not too great. With a downward flow, the differences are 25.8%-28.2%. For cases of ceilings with air hollow blocks, the results obtained from the numerical calculations differ significantly from the results. With an