## 1 Introduction  
Thermal comfort and reduction of energy consumption are consolidated topics in scientific literature. Currently, an increasing interest in these fields is related to the benefits of adaptive technologies. These technologies, when applied to building envelopes, allow buildings to adjust their characteristics, in a reversible way, in response to external stimuli. As a result, an adaptation of their behavior to climate fluctuations is achieved, and, consequently, users' comfort requirements can be more efficiently met [1, 2]. Currently, the most promising results of adaptive envelopes [3] are related to wall-integrated PCMs [4, 5], switchable glazing [6, 7, 8, 9], adaptive solar shadings [10, 11, 12], dynamic insulation [13, 14], and multifunctional facades [15, 16]. Among this wide range of technologies, PCMs have constantly grown their importance in recent years, thanks to broad experimentation and diffusion in different scientific fields [17, 18]. These include mainly the aerospace industry [19], the design of low-energy buildings [20], the preservation of products [21], the electronic industry [22], and waste heat recovery systems [5]. The spread of PCMs in all these fields is related to the advantages of latent heat storage (LHS), which allows the storage and release of naturally available heat in low-volume elements, increasing, therefore, the energy storage density of the material [23]. In the building design domain, the importance of PCMs is related mainly to two different topics usually investigated in scientific literature: the reduction of HVAC energy consumption (i.e., active strategies) and the reduction of local and global thermal discomfort (i.e., passive strategies). Many studies have highlighted that PCMs can reduce the energy demand of HVAC systems by up to 30% if applied as a retrofit solution in residential buildings located in cold climates [24]. Moreover, thanks to the stabilization of the indoor radiant temperature, a significant reduction of thermal discomfort can be obtained [25]. Starting from these two important results, the aim of this paper is to merge and generalize these studies by considering: (i) a broader range of climates, (ii) both passive and active strategies, (iii) different building types, and (iv) different thicknesses of PCMs. Therefore, the benefits of PCM implementation are assessed through numerical analyses. To design and model a PCM-integrated building element correctly and maximize its benefits, it is fundamental to understand the functioning of this technology and the different products available. The functioning is strictly related to the different ways in which materials can store or release heat: sensible heat storage (SHS), latent heat storage (LHS), and thermochemical heat storage. While SHS and LHS are applicable to buildings, thermochemical heat storage technologies are currently not applied in the civil field [23]. Regarding SHS, the heat absorbed/released is related to the increase/decrease of temperature in relation to the mass of the body (\(m\)), the specific heat (\(c\)), and the variation of temperature (\(dT\)), as described in Equation (1). \[Q_{S}=\int_{T1}^{T2}m\ c\ dT \tag{1}\]  
During LHS, the heat absorbed or released leads to a change of phase--for example, a melting from solid to liquid--without changing the temperature of the body. In this case, the heat stored depends on the mass, the fraction melted (\(f_{m}\)), and the variation of enthalpy of fusion per unit mass (\(\Delta h_{m}\)) (Equation (2)).