## 3 Results  
In determining the optimum insulation thickness for provinces affected by the earthquake, an algorithm was developed using the heat transfer coefficient, the price of the insulation material, the degree-day value, the fuel price used for heating, relevant laws and regulations, and the cash value method for investment evaluation. By following the developed algorithm, optimum insulation thicknesses were calculated for different wall components, various insulation materials, and different fuels used for heating across three provinces with different degree-day values. These provinces are located in different climate zones and were affected by the earthquake, as outlined by TS 825, and the results are presented in tables. In the study, expanded polystyrene EPS, extruded polystyrene XPS, and rock wool were selected as insulation materials, and information about these insulation materials is given in Table 2.  
The main objective of the study is to promote insulation applications in uninsulated buildings and, consequently, achieve energy savings, thereby reducing the carbon footprint resulting from residential heating. The insulation investment in the study was calculated using the present value method, with an average interest rate of 53.11% and an inflation rate (CPI) of 53.86% for the year 2023 [26]. The economic life of the investment was considered to be 10 years. In the study, three distinct fuel types were selected for analysis: natural gas, electricity, and coal. Liquid fuels were not included due to their negative environmental impacts. Natural gas and electricity were chosen as they are the most suitable fuels for supporting the transition to green energy. Coal was selected because it is readily available in Turkey, despite its environmental drawbacks. Optimum insulation thicknesses and financial gains for 45 different situations (5 wall types \(\times\) 3 fuel types \(\times\) 3 insulation materials) for each city are calculated and compared with each other. Minitab V22.1 program, a statistical software, was used to compare the calculations made for a total of 135 different situations. To take into account uncertainties, interval plots drawn according to 95% confidence intervals are used. In Hatay province, which is located in the first degree-day (DD) region in Turkey, five different wall structures were analyzed using three different fuels (natural gas, electricity, and coal) and three different insulation materials (XPS, EPS, and rock wool). In the case where XPS is used as the insulation material and electricity, natural gas, and coal are used as fuels, the optimum insulation thicknesses and annual financial gains for five different wall structures are given in Figure 3. Optimum insulation thickness values (m) and annual financial gains (USD/m\({}^{2}\) year) with different insulation materials are given in Table 3 for Hatay. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **EPS** & **XPS** & **Rockwool** \\  & **(Expanded Polystyrene)** & **(Extruded Polystyrene)** & **Rockwool** \\ \hline Place of application & External wall & External wall & External wall \\ Purpose of insulation & Heat & Heat & Heat, sound, fire \\ Coefficient of heat conduction & 0.032 & 0.031 & 0.035 \\ (W/mK) & TS 7316 EN 13163 & TS 11989 EN 13164 & TS EN 12667/12939 \\ \multicolumn{1}{c}{Unit price} & 203 USD/m\({}^{3}\) & 339 USD/m\({}^{3}\) & 407 USD/m\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Information on the insulation materials used [25]. Figure 3: Interval plot of (**a**) optimum insulation thickness values (m) and (**b**) annual financial gains (USD/m\({}^{2}\)) with XPS insulation material for Hatay. According to Figure 3, the smallest insulation thickness was obtained when coal was used as a fuel. This thickness was 0.0224 m for a 15 cm concrete wall, while it decreased to 0.0000 m for Ytong and perforated brick wall types. The greatest value of the optimum insulation thickness was observed when electricity was used as the fuel for all wall types, except for the Ytong wall.