# Thermal Impact of 5G Antenna Systems in Sandwich Walls
## 3 Results and Discussion
### Three by Three Signal-Transmissive Walls  
Figure 13 shows heat flow lines and temperature distributions of \(3\times 3\) signal-transmissive walls in COMSOL Multiphysics.  
Figure 12: Heat flow lines generated by numerical modeling (COMSOL Multiphysics) for the signal-transmissive wall with copper as connector materials (previous design).  
The heat flow patterns in 3 \(\times\) 3 signal-transmissive walls exhibit comparable trends to those depicted in Figures 11 and 12 for standalone signal-transmissive walls. Specifically, for the current design, heat flows in a direction almost perpendicular to the building element planes, unlike the previous design. Moreover, the results revealed that the heat flow patterns of individual cells (a cell is a signal-transmissive wall depicted in Figure 3) within 3 \(\times\) 3 signal-transmissive walls remain consistent with those observed in standalone signal-transmissive walls. Using the numerical approach, the overall U-values for the 3 \(\times\) 3 signal-transmissive walls, including all cells, were determined to be identical to those presented in Table 2, which were 0.156 and 0.3 W/m\({}^{2}\)K for the current and previous designs, respectively. The U-values calculated via theoretical approaches were also the same as those listed in Table 2. The average (normal) conductive heat fluxes on the interior surfaces of the nine cells ranged from 4.68 to 4.73 W/m for the current design, and from 8.83 to 8.90 W/m for the previous design, indicating proximity between the nine cells.  
Figures 11-13 do not display a temperature profile for any plane inside the walls, so to address this concern, we selected a cut plane that is situated 20 mm from the exterior surface of a wall to showcase the temperature profiles for signal-transmissive and 3 \(\times\) 3 signal-transmissive walls (refer to Figures 14 and 15). This cut-plane is positioned in the outer concrete layer. As evidenced by Figures 12 and 13, the heat flow in the concrete layers is more disorderly than that in the insulation layer.  
Some observations have been made from Figures 14 and 15, as well as from analyzing temperature profiles from various cut planes situated in different layers (not shown here due to space limitations):  
* The current design (shown in Figure 14) has an insignificant thermal bridging effect, as the maximum temperature difference is less than 0.04 \({}^{\circ}\)C. However, the previous design exhibits clear thermal bridging effects with a maximum temperature difference of approximately 0.4 \({}^{\circ}\)C, as presented in Figure 15.
* The thermal bridging effect, as depicted in Figure 15, affects an area larger than that of a dual coaxial cable but smaller than the cell size of 150 mm \(\times\) 150 mm. This observation is probably applicable to all planes that are perpendicular to the building elements.
* The thermal bridging effect, although small, cannot be disregarded in some planes of the current design.  
Figure 13: Heat flow lines generated by numerical modeling (COMSOL Multiphysics) for (**a**) the 3 \(\times\) 3 signal-transmissive wall with stainless steel as connector materials (current design), and (**b**) the 3 \(\times\) 3 signal-transmissive wall with copper as connector materials (previous design).  
* There is no evidence to suggest that the thermal behavior of a cell is dependent on its location in the 3 \(\times\) 3 signal-transmissive wall. This is supported by the fact that all nine cells in a 3 \(\times\) 3 signal-transmissive wall were found to have similar average surface conductive heat fluxes (Figure 13), and their temperature profiles for cut planes are also very similar and closely resemble those of standalone signal-transmissive walls (as demonstrated in Figure 15). However, more investigation is necessary to validate these findings (see Section 4 for future work).