## 4 Case Study
Regarding the lighting, considering that the average surface area of the apartment is about 90 m\({}^{2}\), it was assumed that the living room and kitchen were equipped with five LED lights of 14 W each, and the other rooms were equipped with six fluorescent lights for a total of 82 W. For all types of users, the lights are turned on from 7:00 to 23:30 if the total solar radiation on the horizontal surface is lower than 120 W/m\({}^{2}\), and in particular:  
* For 60% of the total lights, if four people are in the apartment;
* For 50% of the total lights, if three people are in the apartment;
* For 40% of the total lights, if two people are in the apartment;
* For 20% of the total lights, if one person is in the apartment. It is important to point out that for all residential units, the lights are switched off if no user is in the apartment. Naples belongs to climatic zone C according to the Italian Presidential Decree DPR 74/2013 [2]; therefore, the heating system is switched on from November 15 th to March 31 st. The centralized heating system is activated from 07:00 to 11:00 and from 17:00 to 21:00. An \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Age Classes (Years)** & **Number (-)** & **Amount on Total Users (\%)** \\ \hline Elderly & 65–100+ & 192,535 & 20.29 \\ Adults & 35–64 & 400,256 & 42.18 \\ Children and Teenagers & 0–19 & 186,746 & 19.68 \\ Youngs & 20–34 & 169,313 & 17.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Distribution of people inside the apartments. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Power (kW)** & **Heat Gain (kW)** & **Radiation Fraction (\%)** & **Convection Fraction (\%)** \\ \hline Fridge & 0.040 & 0.040 & 0 & 100 \\ Dishwasher & 1.820 & 0.364 & 51 & 34 \\ Oven & 0.870 & 0.522 & 14 & 49 \\ Cooktop & 1.500 & 0.900 & 24 & 16 \\ TV & 0.240 & 0.240 & 40 & 60 \\ PC 3.5 GHz processor 16 GB ram & 0.090 & 0.090 & 10 & 90 \\ Laptop & 0.059 & 0.059 & 25 & 75 \\ Washing machine & 1.270 & 0.254 & 40 & 60 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Power and heat gains due to the diverse appliances considered. Figure 2: Daily occupancy profile of the different types of users (from Monday to Friday). indoor set point temperature of 20 \({}^{\circ}\)C is considered for each thermal zone of the building, which is equipped with a suitable plant featured by a thermal flow rate of 80 W/m\({}^{2}\). A constant infiltration rate equal to 0.61/h was assumed, and a ventilation rate equal to 21/h was set to simulate the window opening in the early morning hours, from 07:00 to 08:00. The energy measures proposed in this work are the ones successfully implemented by the Italian funding policy, known as \"Superbonus 110%\" [10], namely:  
* The natural gas-fired traditional boilers are replaced by natural gas-fired condensing boilers, with a generation rated efficiency \(\eta_{th}\) equal to 0.98;
* The external tuff walls are insulated using 0.1 m of rock wool;
* The external empty box walls are insulated by 0.06 m of rigid polyurethane foam. The condensing boilers are modeled with a thermal efficiency of 0.98, reflecting the typical performance of modern condensing boilers under standard operating conditions. This efficiency aligns with the technical requirements of the Superbonus 110% incentive, which promotes the adoption of high-efficiency heating systems to achieve significant energy savings [10]. Other boiler efficiencies were not considered, as they either do not meet the incentive criteria or are not commonly used in the context of the residential buildings analyzed. The thermophysical properties of the thermal insulation in the proposed system are shown in Table 8.  
The thicknesses of the insulation materials of the external walls are selected in order to reduce the total transmittance of the external walls according to the limit values expected for the Superbonus incentive (Table 9).