## 3 Results and Discussion
### Optimum Insulation Thicknesses for Different Directions and Seasonal Usages  
As an example, with respect to the applied insulation thickness, the variation of energy, insulation, and total cost for the north-facing wall is presented in Figure 8, considering the annual energy requirements. It is observed that when there is an augmentation in insulation thickness, the insulation cost follows a linear upward trend, while energy costs experience a decline. Accordingly, it is understood from the figure that there is an ideal insulation thickness that minimizes the total cost. Using this approach, optimum insulation thicknesses for the cardinal and intermediate directions are obtained for three scenarios, including cooling-only, heating-only, and both cooling and heating. Ideal insulation thicknesses for each scenario are determined for the cardinal and intermediate directions, taking into account cooling, heating, and annual energy demands, as shown in Figure 9. As seen from the visualized data, different patterns are obtained for each scenario. The analysis results reveal that depending on the wall orientation, ideal insulation thicknesses vary between 4.52 and 5.02 cm for heating, 1.56 and 2.09 cm for cooling, and 5.92 and 6.08 cm for annual energy requirements, respectively. Figure 9a illustrates the optimum insulation thickness required for various wall orientations when the primary goal is to minimize heating energy demand. It is evident that the north-facing wall requires the greatest insulation thickness of 5.02 cm due to receiving the least amount of solar radiation, which leads to higher heating requirements. Conversely, the south-facing wall, which receives more solar radiation during the heating season, necessitates the minimum insulation thickness of 4.52 cm. This variation in insulation requirements across different orientations highlights the impact of solar radiation and building orientation on heating energy demand. For insulation to be applied to a house intended for summer use (considering cooling energy requirement), it is understood from Figure 9b that the  
Figure 7: Variation of heating (**a**) and cooling (**b**) energy requirement for various directions. wall facing the south requires the thickest insulation. While the optimum insulation thickness calculated for the north-facing wall is 1.56 cm, the ideal insulation thickness for the south-facing wall is 2.09 cm (see Figure 9b). Figure 9c presents the optimum insulation thicknesses for different wall orientations when considering both heating and cooling demands throughout the year. The results indicate that the required insulation thicknesses are relatively similar across all orientations, ranging from 5.92 cm to 6.08 cm. The north-facing wall demands the highest thickness (6.08 cm), which is slightly more than the other directions due to its high heating demand and relatively low cooling requirement. However, the variation in thicknesses across all orientations is minimal, with only a 0.16 cm difference between the maximum and minimum values. This suggests that when a building is used year-round for both heating and cooling, the optimal insulation thickness is not significantly affected by wall orientation, and a uniform insulation strategy can be effectively applied. The optimum insulation thicknesses to be applied for all directions are presented in Table 2 for three scenarios of seasonal usage. When considering the purpose of use of the building and the wall directions, it is seen that there is a difference of approximately 4.52 cm between the minimum (1.56 cm) and maximum (6.08 cm) optimum insulation thicknesses. Furthermore, in cases where a building is used year-round, requiring both heating and cooling, it has been observed that the wall orientation does not significantly impact the insulation thickness. The calculated disparity between the wall necessitating the thickest insulation (6.08 cm) and the one demanding the thinnest (5.92 cm) is merely 0.16 cm.