## 3 Results
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multicolumn{6}{c}{**Insulation Material: XPS**} & \multicolumn{6}{c}{**Insulation Material: EPS**} & \multicolumn{6}{c}{**Insulation Material: RW**} \\ \hline
**Wall** & **Fuel** & **Optimum** & **Financial** & **Wall** & **Fuel** & **Optimum** & **Financial** & **Wall** & **Fuel** & **Optimum** & **Financial** \\
**Type 1** & **Type 2** & **Thickness** & **Gain** & **Type 1** & **Type 2** & **Thickness** & **Gain** & **Type 1** & **Type 2** & **Thickness** & **Gain** \\ \hline
1 & 1 & 0.0157 & 3.86 & 1 & 1 & 0.0234 & 4.38 & 1 & 1 & 0.0136 & 3.46 \\
2 & 1 & 0.0059 & 0.72 & 2 & 1 & 0.0132 & 1.24 & 2 & 1 & 0.0026 & 0.32 \\
3 & 1 & 0.0099 & 1.53 & 3 & 1 & 0.0174 & 2.04 & 3 & 1 & 0.0071 & 1.13 \\
4 & 1 & 0.0147 & 3.27 & 4 & 1 & 0.0223 & 3.79 & 4 & 1 & 0.0125 & 2.87 \\
5 & 1 & 0.0000 & 0.00 & 5 & 1 & 0.0000 & 0.00 & 5 & 1 & 0.0000 & 0.00 \\
1 & 2 & 0.0394 & 18.69 & 1 & 2 & 0.0546 & 19.69 & 1 & 2 & 0.0367 & 17.92 \\
2 & 2 & 0.0296 & 7.04 & 2 & 2 & 0.0444 & 8.04 & 2 & 2 & 0.0256 & 6.27 \\
3 & 2 & 0.0336 & 10.02 & 3 & 2 & 0.0485 & 11.02 & 3 & 2 & 0.0301 & 9.25 \\
4 & 2 & 0.0384 & 16.49 & 4 & 2 & 0.0319 & 3.76 & 4 & 2 & 0.0355 & 15.72 \\
5 & 2 & 0.0169 & 2.44 & 5 & 2 & 0.0313 & 3.44 & 5 & 2 & 0.0112 & 1.67 \\
1 & 3 & 0.0399 & 19.04 & 1 & 3 & 0.0551 & 20.05 & 1 & 3 & 0.0371 & 18.27 \\
2 & 3 & 0.0300 & 7.20 & 2 & 3 & 0.0450 & 8.21 & 2 & 3 & 0.0260 & 6.42 \\
3 & 3 & 0.0340 & 10.23 & 3 & 3 & 0.0725 & 12.22 & 3 & 3 & 0.0305 & 9.45 \\
4 & 3 & 0.0388 & 16.81 & 4 & 3 & 0.0541 & 17.82 & 4 & 3 & 0.0359 & 16.04 \\
5 & 3 & 0.0173 & 2.52 & 5 & 3 & 0.0318 & 3.53 & 5 & 3 & 0.0116 & 1.74 \\ \hline \hline \end{tabular} \({}^{1}\) Wall types, 1: concrete wall (15 cm); 2: perforated brick (19 cm); 3: solid brick (22 cm); 4: stone wall (35 cm); 5: Strong wall (15 cm) (see Table 1 for specifications). 2 Fuel types, 1: coal; 2: natural gas; 3: electric.  
\end{table} 
Table 4: Optimum insulation thickness values (m) and annual financial gains (USD/m\({}^{2}\) year) with different insulation materials for Adhyaman. Figure 6: Interval plot of (**a**) optimum insulation thickness values (m) and (**b**) annual financial gains (USD/m\({}^{2}\)) with XPS insulation material for Adhyaman. and natural gas are used. When the wall type is changed to Ytong with the same thickness, these values are calculated as 0.0173 m, 0.00 m, and 0.0169 m, respectively. When XPS insulation material is used in concrete walls and stone walls, similar results are obtained. Annual financial gain varies in direct proportion to the optimum insulation thickness. In case EPS is used as the insulation material and electricity, natural gas, and coal are used as the fuel, optimum insulation thicknesses and annual financial gains for five different walls are given in Figure 7.  
According to Figure 7, the biggest insulation thickness was obtained when electricity was used as the fuel. This value was 0.0725 m for a 22 cm solid brick wall, while it decreased to 0.0318 m for the Ytong wall type. The smallest value of the optimum insulation thickness was obtained when coal was used as fuel in other wall types except the Ytong wall. In case rock wool is used as the insulation material and electricity, natural gas and coal are used as the fuel, optimum insulation thicknesses and annual financial gains for five different walls are given in Figure 8. According this graph, the smallest insulation thickness was obtained when coal was used as the fuel. This value was 0.0136 m for a 15 cm concrete wall, while it decreased to 0.00 m for the Ytong wall type. The biggest value of the optimum insulation thickness was obtained when electricity was used as fuel in other wall types except the Ytong wall. Figure 8: Interval plot of (**a**) optimum insulation thickness values (m) and (**b**) annual financial gains (USD/m\({}^{2}\)) with rock wool insulation material for Adyaman.