## 1 Introduction
Heat transfer linked with sky longwave radiation is associated with an effective sky temperature and today the simulation of buildings' energy performance involves models capable of estimating the temperature of the sky. The exchange of the sky longwave radiation is a function of the effective sky temperature. In the context of buildings, radiative cooling is caused by lost heat through the emission of longwave radiation in the direction of the sky, where the sky can be considered as a heat sink for outdoor services. Radiative cooling peaks at night when there are clear skies and reduced humidity [6]. It is widely acknowledged that electromagnetic radiation is emitted by all bodies in a wavelength range that is a function of their temperature and, in ambient conditions, the majority of the energy release occurs in the infrared range. The radiative cooling approach is aimed at establishing a cooling net balance between the thermal radiation emitted by ground level surfaces and the atmosphere. With regard to buildings, radiative cooling is a passive approach to cooling that exploits thermal radiation attributes to cool an object or areas of a building that face a colder surface, like the sky [7]. Such observations are purely linked with the construction sector, where nearly half of the energy demands of buildings are attributed to the need to air-condition living spaces. Additionally, the energy needs of buildings are growing, particularly in developing nations [8; 9; 10]. The construction industries of numerous countries need significant reform [11], and engineers and researchers deal with complex codes for the purpose of simulating the energy demands of buildings, analysing the manner in which the building interacts with internal and external environments [12], one aspect of which is represented by radiative heat exchange between the surfaces of the building and the sky vault. For such heat transfers to be evaluated, it is necessary to assess sky emissivity and temperature. From the beginning of the 20 th century onwards, numerous researchers have focused on sky temperature models with studies proposing distinct relationships [13]. Sky models are associated with local weather patterns and particular locations. Hence, the extant differences between the models have been critical in the development of new models for various sites over the years [14; 15]. Generally, large areas of the world are not covered by the existing sky models. Researchers have suggested various relationships in the literature and the majority of these models have been approximated because of insufficient accurate measured data. The form and degree of complexity of the current models differ considerably. More data and research are required to include additional variables and facilitate improved predictions of sky temperature, accounting for factors like daily cycles or hourly fluctuations that occur independent of location and that can explain phenomena like dust storms or smog that exceeds cloudiness. Considering the effect of distinct relationships when simulating the energy performance of buildings, it was determined that the yearly energy demands from heating and cooling can be influenced by high percentage differences, which range between \(-10\%\) and \(19\%\) for tropical environments, \(-10\%\) and \(13\%\) for dry climatic environments, \(-19\%\) and \(28\%\) for mild temperature environments and, lastly, between \(-43\%\) and \(83\%\) for snowy environments (the latter percentage range is significantly higher than the others as it denotes virtually negligible energy demands for cooling) [16]. The universe is a perfect heat sink as its temperature is about 3 kelvin. However, at night, objects on the ground cool down due to the radiative emission to space. At daytime, the effect is negligible because solar irradiation heats up surfaces much more [17]. When radiation hits a surface it is partly reflected, partly absorbed (or transmitted). The absorbed radiation induces heat into the material.