# Thermal Impact of 5G Antenna Systems in Sandwich Walls
## 2 Materials and Methods
### Numerical Approach  
COMSOL Multiphysics 6.1 was used to perform 3D thermal finite element simulations [33]. The \"3D Heat Transfer in Solids\" module was chosen to construct steady-state models for the sandwich wall (as shown in Figure 1) and the signal-transmissive walls (as shown in Figure 3, including both the current and previous designs). The boundary conditions were applied as depicted in Figure 8.  
Convective heat transfer was selected for the exterior and interior surfaces, with outdoor and indoor temperatures set at \(-10\)\({}^{\circ}\)C and \(20\)\({}^{\circ}\)C, respectively. In the U-value calculation for a wall sample, it is generally assumed that a steady-state condition exists [22]. Therefore, convective heat transfer coefficients were maintained constant in this study (see Figure 8). The edge faces (total of four) were treated as insulated. For each wall examined, the U-value was calculated, which is independent of the type of heat transfer and the temperature setting for the exterior and interior surfaces. The choice of convective heat transfer and \(\Delta\)T = 30 \({}^{\circ}\)C (=20 \({}^{\circ}\)C-(\(-10\)\({}^{\circ}\)C)) was for convenience. Equations (1) and (2) were utilized to compute the U-values of the walls. Swept meshing was used for meshing the two-arm spirals in the signal-transmissive walls, as their thickness was too small for traditional meshing methods [33]. The triangular meshes for the remaining elements in the signal-transmissive walls were created manually with different element size settings to accommodate thin areas. Automatic meshing with triangular elements was carried out for the sandwich wall. COMSOL provides a feature of adaptive mesh refinement, which  
Figure 8: Boundary conditions for 3D thermal finite element simulations (left: the sandwich wall: right: signal-transmissive wall). T\({}_{\text{o}}\) and T\({}_{\text{i}}\) are outdoor and indoor temperatures, while \(h_{se}\) and \(h_{si}\) are indoor and outdoor heat transfer coefficients.  
enhances the mesh during simulation to minimize the global error in the model [33]. We utilized this feature for numerical modeling in this work.  
In practice, a signal-transmissive wall (as illustrated in Figure 3) can be regarded as a cell of a 5G antenna external wall, and a 5G antenna external wall consists of numerous such cells. Apart from the three wall models examined in this paper (Section 2.1), we present an additional wall model to broaden our investigation to walls with multiple antennas. The additional wall model is a 5G antenna external wall made up of nine cells arranged in a 3 \(\times\) 3 grid, as illustrated in Figure 9. We refer to this specific 5G antenna wall as a 3 \(\times\) 3 signal-transmissive wall throughout this paper. On the other hand, a sandwich wall that features only one 5G antenna is commonly known as a \"signal-transmissive wall\" and is illustrated in Figure 3.  
The boundary conditions applied to the 3 \(\times\) 3 signal-transmissive walls in numerical modeling are identical to those used for sandwich and signal-transmissive walls.