## 1 Introduction  
Ensuring proper electrical insulation and heat dissipation out of devices are the main tasks for electro-insulating liquids which are used in electrical power equipment [1; 2]. In the case of transformers, heat transport takes place along the heat source (core, windings), insulation system (paper impregnated with electro-insulating liquid and electro-insulating liquid), tank, and air. The fact that the electro-insulating liquid has the largest volume in the transformer cooling system makes it essential in heat transport. The heat generated in the windings arises as a result of Joule's losses, while the heat generated in the core is related to magnetic hysteresis and eddy currents. The electro-insulating liquid that flows through the oil channels cools the windings and core, taking away the heat from them. The heat generated by the core and the winding through the liquid is transferred to the ladle, from where it goes to the surroundings. The main purpose of the cooling system is to prevent excessive temperature increases in the windings. The areas characterized by the highest temperature occur in places where windings are in contact with solid insulation (paper impregnated with electro-insulating liquid). Due to the fact that this insulation is very sensitive to temperature (elevated temperature accelerates the aging processes [3; 4; 5] and causes its degradation [6; 7]), it is necessary to use materials that ensure an adequate level of cooling, thus reducing the risk of sudden transformer damage [8; 9; 10]. At present, the most commonly used electro-insulating liquid in transformers around the world is mineral oil. The key success of mineral oil is primarily due to its three advantages: good dielectric properties, low costs associated with its availability, and very good recognition of this liquid [11; 12]. However, the growing requirements regarding fire safety and environmental protection, as well as extending the lifetime of transformers, has forced their producers and users to search for alternative electro-insulating liquids for mineral oil [13; 14]. To a large extent, the alternative to mineral oil is considered to be natural and synthetic esters. So far, these liquids have been used mainly in distribution transformers. Recently, however, they are increasingly being used in power transformers [15; 16; 17; 18; 19]. This is mainly due to the properties of esters, such as high biodegradability [20; 21; 22], low toxicity [15; 23], and high flash-point and fire-point values [24; 25; 26; 27; 28]. These properties allow for the use of esters in places where, previously, they were only used in dry transformers--in densely populated areas, near water reservoirs, or in petrochemical plants or mines [29; 30]. Recently, an increasing amount of research related to the search for alternative electro-insulating liquids has focused on the use of nanotechnology [31]. By dispersing nanometric materials (nanoparticles, nanofibers, nanotubes, nonowires, nanorods, nanosheets) in base fluids, a new class of dielectric liquids called nanofluids can be obtained [32; 33]. [PERSON] invented this term in 1995 [34]. Nanofluids can be defined as nanoscale colloidal suspensions containing concentrated nanomaterials. They are therefore two-phase systems, with one phase (solid phase) being suspended in the other (liquid phase) [32]. Currently, it is believed that nanofluids are next-generation fluids, which, compared to ordinary liquids, offer greater possibilities, both in terms of dielectric properties and improved heat-exchange efficiency [35]. The area of potential application of nanofluids is very wide and covers many important areas, such as electronics, medicine, and electrical power engineering [36; 37; 38; 39]. In the case of nanofluids' applications in transformers, the main research is related to the improvement of the dielectric properties of the base liquids.