## 3 Traditional Calculations
Most of the discussed ceilings contain free spaces filled with air in their structure. The thermal resistance of these parts of the ceilings was determined by treating them as unventilated air layers. The value of this parameter depending on the heat flow direction and layer thickness is selected from the table data [22]. After determining thermal resistance, heat transfer resistance was calculated. \(R_{U}\) resistance was calculated as a series connection of the ceiling thermal resistance and heat transfer resistance:  
\[R_{U}=R_{si}+R_{T}+R_{se}, \tag{6}\]  
where: \(R_{si},\ R_{so}\)--resistance to heat transfer on the internal and external surfaces of the ceiling. The values of these resistances, depending on the type of partition (external or internal) and the direction of the heat flow, are presented in Table 6.  
The last of the analyzed parameters, i.e., the heat transfer coefficient \(U\), was calculated as the inverse of the heat transfer resistance:  
\[U=\frac{1}{R_{U}}, \tag{7}\]  
The methodology for determining these thermal parameters is presented in detail in one of the ceilings in publication [22]. Performing the relevant calculations, two directions of heat flow (downwards and upwards) were considered for each ceiling system when treating them as internal partitions. The values of thermal conductivity coefficients \(k\) adopted for individual materials occurring in the analyzed ceilings are summarized in Table 7. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Type of Surface**} & \multicolumn{2}{c}{**Heat Flow Direction**} \\ \cline{2-3}  & **Upwards** & **Downwards** \\ \hline internal & 0.10 & 0.17 \\ external & 0.04 & 0.04 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Heat transfer resistance according to EN ISO 6946 [28] in m\({}^{2}\)K/W. In the case of the Teriva Panel system, calculations were made for three construction variants differing in the thickness of the concrete overlay layer: Teriva Panel 160 (concrete overlay layer 40 mm), Teriva Panel 180 (concrete overlay layer 60 mm) and Teriva Panel 200 (concrete overlay layer 80 mm). The calculation results were compared in Tables 8 and 9. Table 8 presents the results obtained for individual Teriva Panel ceiling variants, while Table 9 contains the results obtained for the Smart system and three Teriva systems: Base, Plus and Termo. Among the calculated parameters, the heat transfer resistance obtained for the heat flow downwards should be considered the most important from a practical point of view. The comparison of the values of this parameter shows that increasing the thickness of the concrete overlay from 40 mm (Teriva Panel 160) to 60 mm (Teriva Panel 180) and 80 mm (Teriva Panel 200) increases the heat transfer resistance of these systems by 3.6% and 7%, respectively. The lowest value of penetration resistance is found in the Smart ceiling, for which this parameter is 0.459 (m\({}^{2}\)-K)/W. This result is caused by two factors. First of all, this ceiling has the lowest height (only 15 cm), and as it results from Equation (5), the thermal resistance of the layer is greater the larger its size. The second factor in this respect is the relatively high height of the air ducts, which contributes to the intensification of heat exchange due to convection. In turn, the best insulating properties are characterized by the Teriva Termo ceiling, for which the analyzed parameter is 0.874 (m\({}^{2}\)-K)/W. This result is due to the ceiling height, which in this case is 30 cm, and the relatively small size of the air chambers within the hollow blocks. The latter factor significantly reduces air convection. For a more detailed analysis of the results obtained, the percentage excess of heat transfer resistance was determined in relation to the value obtained for the Smart ceiling. This parameter was calculated according to the relationship:  
\[\delta R=\frac{R_{x}-R_{0}}{R_{0}}\cdot 100\%\, \tag{8}\]