# Thermal Impact of 5G Antenna Systems in Sandwich Walls
## 3 Results and Discussion
### Signal-Transmissive Walls  
When using the parallel path and isothermal planes methods to compute the U-values of the signal-transmissive walls, the two-arm spirals were omitted due to their extremely small thickness (0.035 mm) and high thermal conductivity of copper (400 W/mK), resulting in an insignificant thermal resistance. Table 2 shows the comparison of U-values between the analytical and numerical approaches for the signal-transmissive walls. Copper is the most used connector material in coaxial cables, while other materials are not widely available. This is why we compare both copper and stainless-steel conductors in this work. The 3D thermal finite element simulations in the steady state produced U-values of 1.56 W/m\({}^{2}\)K and 0.3 W/m\({}^{2}\)K for the current design (using stainless steel as connector materials) and previous design (using copper as connector materials), respectively, compared to the U-value of 0.1496 W/m\({}^{2}\)K for the sandwich wall. The previous work [15] reported a U-value of 0.16 W/m\({}^{2}\)K for a signal-transmissive wall with stainless-steel connectors, which is very similar to the current design discussed in this paper. This U-value was obtained through numerical modeling in a master's thesis. The difference between the U-value reported in the previous work [15] and the U-value calculated in this study is only approximately +0.003 W/m\({}^{2}\)K, which is small and likely due to differences in thermal conductivity values for the same materials and differences in the internal convective heat transfer coefficient value. Furthermore, the U-values obtained from all three analytical methods employed in this study, namely the parallel path, isothermal planes, and ISO 6946 combined methods, were comparable to the U-value derived from numerical modeling for the current design, as demonstrated in Table 2. Most importantly, according to ASHRAE [24], the actual U-value for a building component containing inhomogeneous layers generally is some value between the U-values obtained using the parallel path and isothermal planes methods. For the current design, the actual U-value is expected to be between 1.53 and 1.57 W/m\({}^{2}\)K, and our estimation of U = 1.56 W/m\({}^{2}\)K using COMSOL Multiphysics falls exactly within this range, providing further validation for our numerical models of signal-transmissive walls. In designing the signal-transmissive walls, copper was initially used as the connector material, but was later replaced by stainless steel in an effort to reduce thermal bridging effects caused by the 5G antenna. The results in Table 2 confirm the success of this change, as the U-value decreased to 0.156 W/m\({}^{2}\)K, which is below the maximum U-value recommended by the National Building Code of Finland (i.e., U = 0.17) [34] for external walls. The increase in U-value is a small amount, 0.0064 W/m\({}^{2}\)K (=0.156-0.1496). The heating degree day (HDD) method (as described in Equation (9)) was used to calculate the heat loss and cost associated with this increase in U-value (i.e., 0.0064 W/m\({}^{2}\)K). \begin{table}
\begin{tabular}{l l l} \hline \hline  & **Materials of Connectors** & **U-Value (W/m\({}^{2}\)K)** \\ \hline \multirow{2}{*}{COMSOL Multiphysics} & Stainless steel (current design) * & 0.156 \\  & Copper (previous design) ** & 0.3 \\ \multirow{2}{*}{Parallel path} & Stainless steel (current design) * & 0.153 \\  & Copper (previous design) ** & 0.173 \\ \multirow{2}{*}{Isothermal planes} & Stainless steel (current design) * & 0.157 \\  & Copper (previous design) ** & 0.32 \\ \multirow{2}{*}{ISO 6946 combined} & Stainless steel (current design) * & 0.155 \\  & Copper (previous design) ** & 0.225 \\ \hline \hline \end{tabular}
* Center and outer connectors were composed of stainless steel (Figure 4b). ** Center and outer connectors were composed of copper (Figure 4b).  
\end{table} 
Table 2: Calculated U-values for signal-transmissive walls.