## 1 Introduction  
Energy conservation is becoming an indispensable topic around the world. Especially in recent years, this issue has gained more importance due to the increase in energy unit prices. Several factors, notably the quick resurgence of the economy after the COVID pandemic contributed to the tightening of energy markets in 2021. Natural gas prices experienced sharp increases, reaching record highs in 2022, followed by significant fluctuations, as seen in Figure 1[1]. Because of these elevated and volatile prices, the cost of electricity generation is expected to remain unpredictable, making it crucial to improve energy efficiency [2]. Due to these adverse developments experienced worldwide, what needs to be done is to use the existing energy as efficiently as possible. Thermal insulation applications on buildings' external walls are frequently used for energy conservation. There are some studies on this topic in the literature. [PERSON] [3] conducted a study to investigate various factors affecting the determination of the optimal insulation thickness. These factors included cooling and heating loads, energy costs, discount and inflation rates, lifetime, and physical properties of the insulation material. The study utilized a comprehensive life cycle cost analysis approach to determine the most appropriate thickness. In the study by [PERSON] [4], an investigation was conductedin order to acquire the most suitable insulation thickness for a construction situated in a warm climatic region. The outcomes of the study, acquired through dynamic thermal assessments, were compared with those obtained from the degree-hour and degree-day approaches. The results show that in the summer season, the north-facing wall is found to be the most economical wall direction, which has an insulation thickness of 3 cm. [PERSON] et al. [5] carried out a detailed statistical analysis to obtain the optimal insulation thickness, considering factors, such as the insulation cost, present worth factor, electricity cost, fuel cost, coefficient of cooling system performance, heating system efficiency, and heating-cooling degree days, by using the Taguchi method. The study revealed that the key factors influencing the determination of the ideal insulation thickness were heating degree days, insulation cost, and the present worth factor. [PERSON] [6] conducted an examination to obtain the optimal insulation thicknesses for Turkiye's 81 provinces. Analyses were carried out for various fuels, which were LPG, fuel oil, coal, and natural gas. Furthermore, they examined five distinct insulation materials, including expanded polystyrene, rock wool, polyurethane, extruded polystyrene, and glass wool. According to the results of the study, the ideal insulation thickness for buildings that require both cooling and heating is typically higher than that for buildings that only require heating. While this difference is more pronounced in warm climates, it is a practically negligible degree in cold climates. [PERSON] [7] conducted a parametric study on the optimum insulation thickness under dynamic thermal conditions by changing the indoor design temperatures. The outcomes of this research demonstrate that the indoor design temperature and wall direction have an impact on cooling, heating, and annual transmission loads. [PERSON] [8] conducted a literature review on thermal insulation applications for buildings' external walls, with particular emphasis on establishing an economically viable insulation thickness. He summarized the insulation applications in the literature based on the purposes (emission reduction or cost reduction), methods for determining heating/cooling loads in buildings, financial analysis methods, types of insulation materials, fuel types, climate regions where insulation is applied, and optimum insulation thicknesses in tabular form. The study determined that insulation applications were conducted with a focus on either cost or environmental considerations.