## 4 Case Study  
The investigated case study regards residential building blocks located in Naples, Southern Italy, with the typical thermophysical proprieties of residential buildings constructed during the 1960s and 1980s, as shown in Table 1. Specifically, this table identifies two types of buildings, referred to as Building 1 and Building 2. Building 1 features external tuff walls and single-glazed windows with wooden frames, while Building 2 has external empty box walls and double-glazed windows with aluminum frames without thermal break. This distinction arises because buildings with similar shapes and geometries are sometimes constructed using different opaque elements. According to the 2001 ISTAT data, the buildings in the municipality represent a heterogeneous building heritage regarding the construction period. ISTAT (Istituto Nazionale di Statistica) is the Italian National Institute of Statistics, responsible for collecting and analyzing data related to various aspects of Italian society, including demographics, economy, and housing. These data are essential for understanding the characteristics of the building stock in different regions [32]. The thermo-ignrometric features of the stratigraphy of the buildings, both in the case of external tuff walls and empty box walls, have been reported in Tables 2 and 3, respectively. Thermal insulation was applied to both the outside and inside surfaces. The simulations performed take into account the heat absorbed by the walls, as the building model considers the thermal mass of the walls themselves. The walls are modeled according to the transfer function relationships of Mitalas and Arseneault [33; 34; 35]. The dynamic energy balance of each wall accounts for the radiation heat flux absorbed at both the inside and outside surfaces, the radiative heat transfer with all other surfaces within the zone, and the conduction and convection heat fluxes. According to ISTAT data, 34,206 buildings belong to the Naples municipality. However, the analysis was conducted only for 2940 buildings, representing 21% of condominium buildings with four or more floors and equipped with centralized heating systems. It was assumed that these centralized heating systems were based on traditional natural gas-fired boilers with a generation efficiency (\(\eta_{th}\)) of 0.80. Seven different building typologies were identified in terms of shape, orientation, and si \begin{table}
\begin{tabular}{c c c} \hline
**Building** & **Component** & **U [W/m2K]** \\ \hline \multirow{4}{*}{1 (external tuff walls)} & External tuff wall & 1.169 \\  & Single-glazed wooden windows & 5.35 \\  & External roof & 1.268 \\  & Adjacent ceiling & 1.445 \\  & Ground floor & 1.322 \\ \hline \multirow{4}{*}{2 (external empty box walls)} & External empty box wall & 1.135 \\  & Aluminium double-glazed windows & 2.82 \\ \cline{1-1}  & without thermal separation & 1.268 \\ \cline{1-1}  & External roof & 1.445 \\ \cline{1-1}  & Ground floor & 1.322 \\ \hline \end{tabular}
\end{table} 
Table 1: Features of opaque and transparent components. \begin{table}
\begin{tabular}{c c c c c} \hline
**Layer** & **Thickness [M]** & **Conductivity** & **Specific Heat** & **Density [kg/M3]** & **U [W/M2K]** \\  & **[KJ/HMK]** & **Capacity [KJ/KGK]** & **Density [kg/M3]** & **U [W/M2K]** \\ \hline \begin{tabular}{c} Lime and gypsum plaster \\ Tuff masonry \\ Cement, sand, lime plaster \\ \end{tabular} & 0.020 & 2.520 & 1.000 & 1400 & \\ \
\begin{tabular}{c} Tuff masonry \\ Cement, sand, lime plaster \\ \end{tabular} & 0.400 & 2.268 & 0.700 & 1500 & 1.169 \\
\begin{tabular}{c} Cement, sand, lime plaster \\ \end{tabular} & 0.020 & 3.240 & 0.910 & 1800 & \\ \hline \end{tabular}
\end{table} 
Table 2: Stratigraphy of the external tuff walls. borhoods/municipalities (Figure 1). These typologies include block building (A), closed courtyard building (B), open courtyard building (C), four-floor line building (D), six-floor line building (E), eight-floor tower building (F), and ten-floor tower building (G).