## 4 Conclusions
This study provides a more precise methodology for determining the most effective insulation thickness, leading to enhanced energy savings and improved thermal performance in desert climates;
8. The effects of thermal bridging, external air film, shading effects, oversimplified thermal boundary conditions, thermal mass, and thermal lag were not explicitly considered in the optimization process. Additionally, the integration of other passive cooling strategies, such as shading devices, natural night ventilation, and roof overhangs, was beyond the scope of this study but holds significant potential for enhancing cooling efficiency. Future research should incorporate these parameters alongside insulation optimization for a more comprehensive evaluation of building energy performance, particularly under dynamic thermal conditions where these factors significantly impact heat transfer and overall energy savings. **Author Contributions:** Conceptualization, M.A.M. and A.A.E.F. ; methodology, M.A.M., W.A. and A.A.E.F. ; software, W.A. ; validation, M.A.M., W.A. and A.A.E.F. ; formal analysis, M.A.M. and A.A.E.F. ; investigation, M.A.M. ; resources, A.A.E.F. ; data curation, M.A.M., W.A. and A.A.E.F. ; writing--original draft preparation, M.A.M., W.A., H.S.K. and A.A.E.F. ; writing--review and editing, M.A.M., W.A. and A.A.E.F. ; visualization, M.A.M., W.A. and A.A.E.F. ; supervision, A.A.E.F. ; project administration, A.A.E.F. ; funding acquisition, A.A.E.F. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by IRC-CBM, grant number INCB2309 and the APC was funded by King Fahd University of Petroleum and Minerals. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author. **Acknowledgments:** The authors would like to express their gratitude to the support of King Fahd University of Petroleum and Minerals (KFUPM) (Dhahran 31261, Saudi Arabia) for using it's laboratory and research facilities. **Conflicts of Interest:** The authors declare no conflicts of interest. **Nomenclature**  
C. Cost (SAR)  
C.y. Cost of insulation (SAR/m\({}^{3}\))  
C.e. Cost of electricity (SAR/kWh)  
C.A.C. Annual cost of consumed energy (SAR/m\({}^{2}\))  
C.e. Pres-insulation cooling energy cost (SAR/m\({}^{2}\))  
C.t. Total cost of consumed energy and insulation costs (SAR/m\({}^{2}\))  
C.OP. Coefficient of performance of HVAC system (Dimensionless)  
\(\eta\). Efficiency of the combustion system (Dimensionless)  
Q.y.ar. Annual heat loss and gain (kWh/m\({}^{2}\))  
Q.eff (yar). Humidity-adjusted annual heat loss and gain  
E.yar. Annual cooling energy (kWh/m\({}^{2}\))  
k. Thermal conductivity (W/m.K)  
R. Thermal resistance (K.m\({}^{2}\)/W)  
R.opt. Thermal resistance for the optimum insulation thickness (m\({}^{2}\).K/W)  
U. Over all heat transfer coefficient (W/m\({}^{2}\).K)  
U.opt. Overall heat transfer coefficient for the optimum insulation thickness (W/m\({}^{2}\).K)  
X. Layer thickness (m)  
X.ins. Insulation thickness (m)  
N. Building lifetime (years)  
PP. Payback period (years)  
X.opt. Optimum insulation thickness (m)  
R.W. Wall layers heat transfer resistance (K.m\({}^{2}\)/W)  
R.o, R.i. Heat transfer coefficients of the outside and inside environments (K.m\({}^{2}\)/W)  
PVF. Present Value Factor (dimensionless)  
q.yar. Yearly transmission load (kWh/m\({}^{2}\).yr)  
q. Heat transfer rate (W/m\({}^{2}\))  
i,f. Interest and inflation rates (%)  
r. Actual interest rate  
SAR. Saudi Riyal (1 US dollar = 3.75 SAR)  
T. Temperature (\({}^{\circ}\)C)