## 1 Introduction
\[Q_{L}=mf_{m}\Delta h_{m} \tag{2}\]  
Therefore, generalizing a phenomenon with SHS and LHS for a gypsum-PCM board, the heat exchanged corresponds to the total enthalpy variation \(\Delta H_{tot}\) that depends on the enthalpy variation of each material contained in the board, according to Equations (3)-(5) [26]:  
\[\Delta H_{tot}=m\cdot\left[(1-f)\cdot\Delta h_{gypsum}+f\cdot\Delta h_{PCM}\right] \tag{3}\]  
where, considering the complete melting of the PCM (\(f_{m}=1\)), the partial enthalpies are:  
\[\Delta h_{gypsum}=(1-f)\int_{T1}^{T2}mc_{S}\ dT \tag{4}\]  
\[\Delta h_{PCM}=f\left(\int_{T1}^{Tm}c_{S}\ dT+\Delta h_{m}+\int_{T\pi m}^{T2} c_{L}\ dT\right) \tag{5}\]  
with \(f\) being the mass fraction of the PCMs in gypsum, \(c_{S}\) and \(c_{L}\) representing, respectively, the specific heat of the solid state and the liquid state, and \(T_{m}\) the melting temperature of the PCMs. For this reason, in building applications, a PCM with a melting range within the thermal comfort range (20 \({}^{\circ}\)C-30 \({}^{\circ}\)C) can take advantage of LHS [27]. This is due to the storage of a good amount of heat in low-volume elements without increasing the surface temperature and therefore, without affecting thermal comfort. While, theoretically, PCMs work on four different possible changes of phase for building applications, namely, solid-solid, solid-liquid, gas-liquid, gas-solid [28], solid-liquid PCMs are usually considered. PCMs can be classified into three main categories: organic, inorganic, and eutectic. Organic PCMs are composed of paraffins, fatty acids, fatty-acid esters, and sugar alcohols and, in general, can be classified as paraffin or non-paraffin. One of the main advantages of organic PCMs is that repeated melting-freezing does not lead to phase segregation; moreover, they are slightly affected by supercooling. Nevertheless, considering that paraffinic PCMs are derived from oil refining, organic PCMs have low ignition resistance, and, for this reason, envelope applications can be problematic. Organic PCMs can have a broad range of possible melting temperatures (\(-57\)\({}^{\circ}\)C; \(+187\)\({}^{\circ}\)C) with melting latent heat ranging from 85 to 300 J/g [29; 30; 31]; therefore, they should be accurately chosen to optimize their functioning. Inorganic PCMs are classified as salt-hydrates or metallic, and, despite having an enthalpy per mass similar to organic PCMs, they can reach higher melting latent heat per unit volume thanks to their higher density. Moreover, they have higher conductivity, can reach higher melting points, and are less expensive and less flammable than organic PCMs. However, inorganic PCMs present some limitations, such as supercooling, phase segregation, and corrosion. Lastly, eutectic PCMs are composed of at least two PCMs with the same melting point and can be classified as organic-organic, inorganic-inorganic, and organic-inorganic, depending on the types of PCMs used. Often PCMs are encapsulated, primarily to hold both solid and liquid phases and to protect the PCMs from harmful interactions with the environment and other building materials. Encapsulation can also reduce phase segregation and corrosion, provide easier handling, and increase the heat transfer area [32; 33]. Encapsulations can be classified, depending on capsule size, into macroencapsulation (d \(>\) 1 mm), microencapsulation (1 \(\upmu\)m \(<\) d \(<\) 1 mm), or nanoencapsulation (d \(<\) 1 \(\upmu\)m). Moreover, they can be made of different materials, e.g., aluminum, plastic, polyolefin, rubber, polymers, in different containers, such as balls, tubes, plates, and boxes [33]. Many studies have been performed to deepen the possible applications of PCMs to buildings, mainly classified into active storage systems and passive storage systems. Active systems are characterized by heat exchangers and forced convection and can be, in turn, classified into direct and indirect systems.