## 1 Introduction
### Analyses Based Only on Modelling of Heat Transfer Through Window  
A similar type of study was conducted by [PERSON] et al. [16] in three different Mexican locations: Merida, Yucatan, Mexico. However, in this case no specific building was considered, but only heat transfer through single-pane, double-pane and triple-pane window configurations was taken into account. The calculations were performed based on computer code written and validated by the authors. Based on the analysis of the simulation results, it was found that triple-glazed windows reduced energy consumption by up to 33% and 15.5% compared to single- and double-glazed windows, respectively. Windows consisting of six panes were constructed and tested by [PERSON] et al. [17]. The analysed structure was composed of four chambers containing argon and one open chamber filled with air. Two panes (outer and inner) were 8 mm thick, three panes were 2.1 mm thick and one was 4 mm thick. The interior panes were sprayed with low-emission filters. This type of technical solution was characterised by a very low U-value of 0.24 W/(m\({}^{2}\)-K), a direct solar energy transmittance coefficient of 0.17 and an SHGC value of 0.24. The case study glazing was used to renovate the Wergelandsveien 7 building located in Oslo (Norway). It turned out that replacing the existing triple-pane glazing with a 6-pane glazing system resulted in a significant reduction in annual energy consumption per m\({}^{2}\) from 220 kWh to 110 kWh. The issues of the evaluation and selection of optimal building glazing using the Pareto optimal frontier method were considered by [PERSON] et al. [18]. This research study included estimating the investment costs and environmental life cycle of various window systems and was performed for 32 variants, taking into account eight types of glazing and four types of frames. The reference object [8] was a window measuring 1.23 m \(\times\) 1.48 m installed in the front wall, with dimensions of 3.60 m \(\times\) 2.80 m, of an office room with a total area of 19.8 m\({}^{2}\). The general conclusion of the analysis was that in the case of warm climate conditions, windows should be characterised by the lowest possible solar gains. The optimal solution for glazing installed in buildings located in cold climate zones should be the highest possible thermal resistance. An evaluation of thermal and optical characteristics of windows consisting of three and four panes was carried out by [PERSON] and [PERSON] [19]. They developed a new mathematical method to investigate the effect of blinds and shutters on the thermal performance of the glazing. Various inter-pane spacings, louvre angles and gas fill types were subjected to parametric analysis. The results of numerical simulations indicated that the convective heat transfer coefficient is largely dependent on the angle of the blinds. When the blinds were fully open, the value of the window's heat transfer coefficient was the highest. A numerical simulation of the heat transfer phenomenon occurring in double-, triple- and quadruple-glazed windows was carried out by [PERSON] et al. [20]. Multivariate calculations, taking into account a change in the gap width between the panes from 6 mm to 21 mm and a change in outside temperature from \(-28\)\({}^{\circ}\)C to 5.2 \({}^{\circ}\)C, were performed. A window height of 1 m and an air temperature in the room of 20 \({}^{\circ}\)C were assumed as constant parameters. Based on the simulation results, it was estimated that the energy savings resulting from replacing a double-glazed window with a triple-glazed or quadruple-glazed window were approximately 50% and 67%, respectively. The authors of this numerical simulation recommended the use of multi-glazed windows in regions of Turkey that are characterised by cold climatic conditions. Transparent facade elements have a significant influence on the energy efficiency of buildings, as well as on aesthetics. [PERSON] et al.