## 1 Introduction
[PERSON] and [PERSON] [32] examined the impact of wall orientation on optimal insulation thickness (\(X_{opt}\)) using climatic data from Riyadh. Additionally, they conducted parametric tests to evaluate the sensitivity of \(X_{opt}\) to variations in economic parameters. Their findings indicated that an increase in electricity costs, building lifespan, and inflation rate led to higher \(X_{opt}\) values, whereas a decrease in insulation material costs, air conditioning system coefficient of performance, and discount rate resulted in lower \(X_{opt}\) values. The study also demonstrated that while wall orientation significantly influenced transmission loads and thermal lag, its effect on \(X_{opt}\) was relatively minor. Among the insulation materials analyzed, polystyrene was identified as the most cost-effective option, with \(X_{opt}\) of 9.3 cm. In a separate study, [PERSON] et al. [33] determined optimal R-values for building walls under the climatic conditions of Riyadh, Jeddah, and Abha. Their methodology incorporated three different insulation materials and multiple wall configurations. The study employed a combination of thermal analysis, using the control-volume finite-difference implicit method, and economic evaluation, applying the net present value method, over a 30-year life cycle. The results indicated that at \(X_{opt}\), payback periods--accounting for inflation and financial costs--ranged between 3 and 10 years. The literature shows an increasing interest in using life-cycle cost and thermal analyses to estimate the optimum insulation thickness of residential building walls in different climatic zones. Therefore, various insulation materials, wall configurations, and economic and environmental parameter values were considered. This study aims to present an optimization model for selecting proper insulation material for external walls and determining the optimum insulation thickness under different desert climatic conditions satisfying both financial and performance requirements. The proposed model is validated by energy modeling, and it was applied to the desert climates of Saudi Arabia as a case study. Three locally used materials were considered: polyurethane board, rock wool, and molded polystyrene. This study will significantly contribute to effective practices for applying thermal insulation to buildings in Saudi Arabia and offers an accurate validated method that can be adopted anywhere to better use walls' thermal insulation. from [34], a recognized reference that aligns with the climatic and geographic characteristics of Saudi Arabia. The annual cooling energy and, consequently, the annual cooling cost could be estimated based on the determined annual heat gain. Then, the optimum insulation thickness is determined by applying economic analysis. The base model is then applied to Saudi Arabia as a case study for validation. The optimum insulation thicknesses of a unit's external wall, assuming electricity as the energy source, are calculated by examining three different insulation materials integrated into a specific external wall structure in five cities representing the five climatic zones of Saudi Arabia (Sections 2.1-2.4). Optimization of the insulation thickness is conducted using the LCC analysis. The thermal analysis involved is based on the degree-days concept in which transmission cooling loads are calculated as a baseline (Section 2.1). Then, energy modeling is used to validate and adjust the results obtained from the simplified calculation method (Section 2.6). The adjusted cooling loads are used to improve the annual cooling cost prediction and apply the economic analysis, adjusting the steps in Sections 2.1 and 2.2; therefore, determining a more accurate optimum insulation thickness. Based on the comparison between the heat gain obtained from the degree-days and energy modeling, a novel modified and verified model is developed and proposed for determining the optimum insulation thickness. Figure 2: Summary of the methodology.