## 1 Introduction
Currently, the energy efficiency of buildings occupies a high priority in the construction industry. When designing and operating residential buildings to ensure their energy efficiency by increasing the thermal insulation characteristics of external walls and reducing the costs of heating, ventilation, and air conditioning, optimal engineering solutions should be sought. The possibility of optimizing fence designs from the point of view of reducing heating costs lies in the fact that fences should have maximum thermal protection at minimal cost [26]. Firstly, this is possible through the use of less expensive thermal insulation materials, secondly through the rational choice of their thickness, and thirdly by the selection of a cost-effective design and technological and organizational solutions for thermal insulation of the facades using modeling [27; 28; 29]. It is known [13; 14; 20] that external thermal insulation composite systems finished with plaster with glued and mechanically fastened insulation are most often used in the mass construction of buildings with various structural schemes. This choice of facade insulation technology is due to one of the main reasons for its use--lower price compared with ventilated facades. However, despite the rather long period of their use, due attention is not always paid to the thermal insulation of protruding parts of floors, for example, balconies and bay windows (Figure 1) [30]. This figure clearly shows that the reinforced concrete floor slabs protruding beyond the facade in the form of balconies and bay windows were not insulated at all, which led to significant heat losses. They are \"cold bridges\" that reduce the energy efficiency of the building, worsen the thermal comfort in the premises, and force their users to spend more money on heating. \"Cold bridges\" can lead to the appearance of fungi and mold in the corners of rooms and disruption of the microclimate of a room as a whole. The design and development of energy-efficient node connections are also carried out abroad. The experience of German scientists at the Dortmund Passive House Institute (Passiv HausInstitut) indicates that by the European Energy Saving Directive, passive houses are designed by DIN 4108. One solution is to use thermal inserts. According to numerical modeling, with thermal conductivity of walls from 0.13 to 0.21 W/(mK), in the case of using thermal liners with thermal conductivity of less than 0.05 W/(mK), negative values of linear heat transfer coefficients are obtained, as shown in Figure 2[31]. The negative values of the linear coefficients shown in Figure 2 show that due to the placement of thermal inserts, the reduced heat transfer resistance can exceed the value of the heat transfer resistance along the main field. From the review, it is clear that nodal connections are among the places with the greatest heat loss of external enclosing structures. To increase the heat transfer value of building envelopes, including in node connections,  
Figure 1: A house with insulation: (**a**) a thermogram of a house with bay windows without insulation. (**b**) Ambient air temperature. Figure 2: Dependence of the linear heat transfer coefficient of the wall on the thermal conductivity of the thermal liner [31]. changes in the thickness and type of insulation are used [7; 32; 33; 34]. By installing additional insulation, heat transfer resistance and temperature in the inner corner increase [33]. It should be noted that, despite the numerous achievements of scientists in the field of energy efficiency of construction projects, the problem of heat-conducting inclusions remains poorly understood. It is known that almost every building insulated by current codes contains heat-conducting inclusions that disrupt the thermal uniformity of the insulating shell and are a source of significant heat loss.