## 4 Conclusions  
Energy conservation is increasingly important in countries where energy consumption is increasing astronomically, such as Saudi Arabia. This paper presents a novel method for optimizing external wall insulation, considering performance and economic factors. As a case study, the suggested method was implemented with different insulation materials for the five climatic zones of Saudi Arabia represented by five cities: Riyadh, Jeddah, Dhahran, Guriat, and Khamis Mushait. The cost of insulation materials and electricity in KSA and economic conditions representing the country's economy are used. A single-layer wall made of bricks is considered. In addition, the three commonly used insulation materials considered for this study are molded polystyrene, polyurethane board, and rock wool. Thermal and economic analyses are carried out for the base model to determine the annual heat gain and \(X_{opt}\) for each insulation material. The thermal heat gain was determined based on the cooling degree day's concept, and it was validated and adjusted based on an energy simulation, while the economic analysis is based on the net present value method. Based on the comparison with the energy simulation results, the model was adjusted by introducing a correction factor based on the average humidity in each city. The modified model resulted in a better estimation of the annual heat gain, \(X_{opt}\), and payback periods. The results show that the insulation of residential buildings in Saudi Arabia is economically feasible and should be implemented as it will provide higher rates of comfort accompanied by lower air conditioning energy costs. The main results are summarized as follows:  
1. In all the climatic zones, yearly cooling loads dominate over yearly heating loads. However, heating is absent for Jeddah, while yearly cooling loads are the highest;
2. The annual cooling loads proposed in the method are benchmarked against energy simulation;
3. Polystyrene gives the lowest total cost (C\({}_{t,\text{min}}\)) followed by rock wool and polyurethane for all climates. Therefore, polystyrene is the most economical insulation with the shortest payback period. In addition, polyurethane has the lowest thickness among the insulation materials in the five zones;
4. The optimal insulation values using molded polystyrene (MP), polyurethane board (PB), and rock wool (RW) as insulation materials were obtained for the five climatic zones of Saudi Arabia. The values of Riyadh, Jeddah, and Dhahran range between 3 and 8 cm, while Guriat and Khamis Mushait, with a moderate climate (i.e., low CDD), range between 2 and 5.5 cm;
5. C\({}_{t,\text{min}}\), and \(X_{opt}\) values for Dhahran and Riyadh are very close; those for Guriat and Khamis Mushait are almost equal and much smaller. Therefore, the moderate climate of Guriat and Khamis Mushait is much more cost-effective regarding energy consumption;
6. Payback periods calculated at \(X_{opt}\), considering inflation and cost of money, range from about 1 to 3 years, reflecting the high feasibility of applying thermal insulation;
7. The study's findings highlight the significant impact of climatic conditions on the optimal insulation thickness and the corresponding thermal performance metrics, R-value, and U-value. Unlike the Saudi Building Code (SBC 601 and SBC 602), which sets a single standard for maximum U-values and minimum R-values across all regions, our results demonstrate the need for climate-adaptive insulation strategies. The optimal insulation thickness varies considerably between cities, with locations experiencing higher cooling demand requiring thicker insulation to achieve lower U-values. These findings reinforce the necessity of incorporating both economic and climatic considerations when establishing insulation guidelines, ensuring energy-efficient and cost-effective building envelope designs tailored to specific regional conditions.