The leakage of compressed gas from various systems and devices not only results in high economic costs but also leads to various technical and safety issues. In many instances, compressed gas leaks are not visible or audible, making them challenging to detect promptly. The research in this field is are based on analyzing the thermal irreversibility of a solidified layer of nano-enhanced phase change material (NePCM) above narrow thermally isolated leak holes through which heated gas leaks. The diameter of the leak holes diameters varied by 0.15 and 0.3 mm, while the gas temperature was adjusted to 65 and 80 °C. As the heated gas passed through the NePCM, it created an exit hole. The established heat transfer between the gas and the solidified NePCM layer altered its temperature field, leading to liquefaction and a change in the emissivity of its outer surface. The nanoparticles used in this study are Al2O3 and SiO2 in volumetric ratios of 1.5 and 3% which were dispersedly added to the base PCM, sodium acetate trihydrate (C2H3O2Na). Mathematical modeling was used to establish the relationship between the temperature field of the annular liquefied NePCM and the thermal entropy, considering characteristic geometric and process parameters. The methodology established in this study enables the optimization of the geometric and physical parameters of the NePCM layer based on minimizing thermal entropy. The experimental analysis conducted in this work includes qualitative infrared thermographic analysis as well as direct measurements of characteristic physical quantities.