# Energy Renovation of Residential Buildings in Hot and
## 2 Methodology
### Optimum Insulation Thickness for Walls, Roof, and FFF  
LCCA is used to determine the optimum insulation thickness of the thermal envelope of the building (walls, roof, and FFF) that achieves the maximum net savings in terms of the heating and cooling costs. The analysis considers the heating and cooling degree-days, the costs and properties of both the insulation materials and the fuels used, the main characteristics of the heating and cooling systems, the electricity costs, and the economic parameters, such as the interest rate, inflation rate, and lifetime [17]. To evaluate the total cost in the entire life cycle, one must take into account the manufacture stage cost, the transportation stage cost, the installation stage cost, the heating and cooling energy costs, the demolition stage cost, and the disposal stage cost [26]. However, in the present study, only the thermal insulation cost and the heating and cooling energy costs are considered. The thermal transmittance of an element \(e\) of the thermal envelope of a building, \(U_{e}\), in W/m\({}^{2}\cdot\)K, is calculated using the following equation:  
\[U_{e}=\frac{1}{R_{e}} \tag{1}\]  
where \(e\) corresponds to the walls, roof, and FFF; and \(R_{e}\) corresponds to the thermal resistance of element \(e\) of the building envelope, in m\({}^{2}\cdot\)K/W, and it is calculated using the following equations:  
\[R_{e}=R_{e}^{exist}+R_{e}^{insu} \tag{2}\]  
\[R_{e}^{exist}=R_{si,e}+\sum{}_{n}R_{n,e}+R_{se,e} \tag{3}\]  
\[R_{n,e}=\frac{x_{n,e}}{\lambda_{n,e}} \tag{4}\]  
\[R_{e}^{insu}=\frac{x_{e}}{\lambda} \tag{5}\]  
where \(R_{e}^{exist}\) is the thermal resistance of element \(e\) of the existing building, in m\({}^{2}\cdot\)K/W; \(R_{e}^{insu}\) is the thermal resistance of the insulation added to element \(e\) of the building, in m\({}^{2}\cdot\)K/W; \(R_{si,e}\) and \(R_{se,e}\) are the surface thermal resistance of element \(e\) of the thermal envelope of the building for indoor air and outdoor air, respectively, in m\({}^{2}\cdot\)K/W; \(R_{n,e}\) is the thermal resistance of layer \(n\) of element \(e\) of the thermal envelope of the existing building, in m\({}^{2}\cdot\)K/W; \(x_{n,e}\) is the thickness of layer \(n\) of element \(e\) of the thermal envelope of the existing building, in m; \(\lambda_{n,e}\) is the thermal conductivity of the material that makes up layer \(n\) of \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & **Unit** & **Value** & **References** \\ \hline \multirow{4}{*}{Thermal envelope} & EPS insulation (0.034 W/m\(\cdot\)K) & \(\xi\)/m\({}^{3}\) & 263.78 & [43] \\ \cline{2-5}  & MW insulation (0.034 W/m\(\cdot\)K) & \(\xi\)/m\({}^{3}\) & 181.50 & [43] \\ \cline{2-5}  & PUR insulation (0.025 W/m\(\cdot\)K) & \(\xi\)/m\({}^{3}\) & 302.50 & [43] \\ \cline{2-5}  & XPS insulation (0.034 W/m\(\cdot\)K) & \(\xi\)/m\({}^{3}\) & 267.00 & [43] \\ \cline{2-5}  & New openings (1.92 W/m\({}^{2}\cdot\)K) & \(\xi\)/m\({}^{2}\) & 282.63 & [43] \\ \hline \multirow{4}{*}{Energy carrier} & Heating oil & \(\xi\)/kWh & 0.0713 & [44,45] \\ \cline{2-5}  & Natural gas (20–200 GJ/year) & \(\xi\)/kWh & 0.0770 & [46] \\ \cline{2-5}  & Biomass (A1 certified pellet in bulk) & \(\xi\)/kWh & 0.0462 & [47] \\ \cline{2-5}  & Electricity 1 (2500–5000 kWh/year) & \(\xi\)/kWh & 0.2430 & [48] \\ \cline{2-5}  & Electricity 2 (5000–15,000 kWh/year) & \(\xi\)/kWh & 0.2042 & [48] \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The 2018 prices for insulation materials, new openings, and energy carriers. element \(e\) of the thermal envelope of the existing building, in W/m\(\cdot\)K; \(x_{e}\) is the insulation thickness added to element \(e\) of the building, in m; and \(\lambda\) is the thermal conductivity of the insulation material used, in W/m\(\cdot\)K.  
Equations (1)-(5) were adapted from [49]; \(R_{si,e}\) and \(R_{se,e}\) were obtained from [49]; and \(x_{n,e}\) and \(\lambda_{n,e}\) were obtained from [40].