# Thermal Impact of 5G Antenna Systems in Sandwich Walls
## 3 Results and Discussion
### Signal-Transmissive Walls
\[Q_{wall\_heat\_loss}=(U.24.HDD)/1000 \tag{9}\]  
where \(Q_{wall\_heat\_loss}\) is the heat loss through the wall per year (KWh/m\({}^{2}\)), U is the U-value (W/m\({}^{2}\)K), 24 is the conversion factor (h/d), and \(HDD\) are the heating degree days a year (Kd/a). Annual heating degree days and district heating price in Helsinki were assumed to be 3547 \({}^{\circ}\)C d/a (averaged value from 2008 to 2022; the effective indoor temperature is 17 \({}^{\circ}\)C) [35] and 11.35 cents/KWh [36]. The simulation results indicated that the current design requires only an additional 0.545 KWh/m\({}^{2}\) of heating energy per year, resulting in a cost of approximately 0.062 EUR/m\({}^{2}\) per year. This cost is considered negligible. On the other hand, the previous design had an additional heat loss of 12.8 KWh/m\({}^{2}\) per year and a cost of 1.45 euros/m\({}^{2}\) per year, which was 23.5 times greater than the current design. The current design has greatly reduced thermal bridging effects. Figures 11 and 12 display the results of heat flow lines and temperature distributions of signal-transmissive walls in COMSOL Multiphysics. Compared to the heat flow lines in the sandwich wall (as shown in Figure 10), the observations from Figures 11 and 12 are as follows:  
* In the current design, it can be assumed that the heat flows perpendicular to the planes of the building elements. However, in the previous design, the heat flow direction was no longer perpendicular to the planes of the building elements. * Unlike the current design, in the previous design (Figure 12), the distribution of heat flow lines varied between different layers. For instance, in the insulation layer, the heat flow lines are distributed closer to the dual coaxial cable compared to other layers. This is because the thermal resistance of rockwood is much higher than that of the dual coaxial cable, which used copper as a center connector material. The above observations further confirm the previous conclusion that the current design minimizes the thermal bridging effect. Furthermore, the observations also suggest that the isothermal planes method is more appropriate than the parallel path method for determining the U-values of signal-transmissive walls. In an inhomogeneous layer, there can be significant changes in heat transfer paths if the thermal conductivity contrast between its materials is much higher than that of its adjacent layers (e.g., for the previous design). The parallel path method does not take this fact into account, while the isothermal planes method does. In the isothermal planes method, heat transfer paths are reallocated layer by layer. If the U-values estimated by COMSOL Multiphysics are taken as target values, the percentage errors generated by the three analytical methods are as follows (=(calculated U-value by analytical approach--U-value by COMSOL) * 100/U-value by COMSOL):  
* For the current design (Table 2): \(-1.9\%\) (parallel path), +0.64% (isothermal planes), and \(-0.64\%\) (ISO 6946 combined). * For the previous design (Table 2): \(-42.3\%\) (parallel path), +6.7% (isothermal planes), and \(-25\%\) (ISO 6946 combined). For the current design, all three analytical methods produced good accuracies, with the isothermal planes and ISO 6946 combined methods slightly outperforming the parallel path method. However, for the previous design, the isothermal planes method significantly outperformed the other two methods. The National Building Code of Finland [34] employs the isothermal planes method in calculating the thermal resistances of inhomogeneous layers. Additionally, ASHRAE [24] and the National Building Code of Finland [34] provided more complex methods for situations where thermal bridging effects were substantial.