# Thermal Impact of 5G Antenna Systems in Sandwich Walls
## 1 Introduction
It requires proficiency in using simulation software. The simplest method of determining the U-values of building components that contain inhomogeneous layers is to use analytical formulas. Several formulas have been introduced, including the ISO 6946 combined method [22], the parallel path method [23], the isothermal planes method [24], and the ASHRAE zone method [24]. Although these formulas are only applicable to simpler configurations and steady-state one-dimensional heat transfer [24], they still offer a straightforward and efficient way of evaluating the U-values of building components. In the existing research, the majority of thermal studies on building components with inhomogeneous layers focus on wood- and steel-framed walls. For example, [PERSON] [25] used CosmosWorks 2008 to conduct three-dimensional thermal finite element simulations to estimate the thermal resistances of a series of wood-framed walls with framing factors ranging from 6% to 30%. The study aimed to evaluate the thermal effects of fasteners, including drywall screws and siding nails. The results showed that these fasteners had a considerable thermal impact on the overall thermal resistance of the walls, reducing them from 3.3% to 12%. This thermal impact became increasingly significant as the framing factor increased. Additionally, the study found that the calculated overall thermal resistances using the parallel path method required an adjustment factor to match the simulation results obtained by CosmosWorks [26]. [PERSON] et al. [27] evaluated six different analytical approaches for calculating the U-values of 80 different lightweight steel-framed wall models. The analytical U-values obtained were then compared with numerical simulations using the THERM finite element method software. The results showed that all the evaluated analytical methods had good accuracy. The ISO 6946 combined method had better average precision than the ASHRAE modified zone method and the Gorgolewski Method 2, which were specifically developed for lightweight steel-framed walls. [PERSON] et al. [28] used the isothermal planes method to calculate the thermal resistance and U-value of a lightweight steel-framed wall consisting of an outer layer of 10 mm of thick cement board, an inner layer of gypsum board with a thickness of 12.5 mm, interspersed by fiber glass and air, and a galvanized steel C-section profile (90 \(\times\) 40) with a thickness of 0.95 mm. The obtained thermal resistance and U-value were then compared with numerical simulations conducted using ANSYS 15. The results showed that the isothermal planes method provided reliable results, and the difference between the results obtained using the isothermal planes and numerical solution methods was only 9% for the thermal resistance. Other similar works include references [20; 21; 23; 29; 30; 31]. However, there is a scarcity of studies examining the thermal impact of 5G passive antenna systems embedded in building walls. This study aims to address this gap. The objectives of this study are:  
* To conduct 3D numerical modeling to determine the U-values of the developed signal-transmissive walls with stainless steel and copper used as connector materials. * To compare the calculated U-values of the signal-transmissive walls with the same wall without a 5G passive antenna and to determine the additional heat loss and cost per year under Finnish weather conditions. * To utilize analytical formulas to evaluate the U-values of the signal-transmissive walls, in order to identify a suitable and practical tool for future thermal studies of signal-transmissive walls. This paper only focuses on thermal issues, and the study of the electromagnetic aspects of signal-transmissive walls is beyond the scope of this study and is covered in [15]. Hence, this paper can be seen as a continuation of [15] with respect to thermal issues.