## 1 Introduction
There are many publications confirming the positive influence of electro-insulating liquids' modifications, with nanomaterials on their dielectric properties and phenomena such as breakdown voltage [40; 41; 42; 43], streamer propagation [44], electrical conductivity, and the dissipation factor [45; 46; 47; 48; 49]. In addition, as reported in the literature [50; 51], fullerene C\({}_{60}\) can also be used to absorb free radicals arising from the aging of vegetable oils. Bearing in mind that the electro-insulating liquid fills the transformer's interior, in addition to ensuring adequate electrical insulation, it also has the task of cooling the device, and seems fully justified in that the use of nanotechnology can also contribute to the improvement of heat transport and thus the reliability of transformers. As is well-known in the context of the general improvement of cooling efficiency, liquids' properties, such as thermal conductivity, viscosity, density, specific heat, and thermal expansion, are important. Therefore, in many scientific publications, scientists are improving these properties by dispersing nanomaterials in the base liquids (water, oils, ethanol). It was observed that the improvement of thermal properties of the resulting nanofluids, in relation to the base liquids, occurs in most cases of the applied nanomaterials [52; 53; 54; 55; 56; 57; 58; 59; 60]. [PERSON] et al. [53] observed that the thermal conductivity of nanofluids based on water and nanoparticles Al\({}_{2}\)O\({}_{3}\) and CuO increased by about 30% compared to base liquids. However, such a large increase was observed only in the case where the concentration of nanoparticles ranged from 4-10% of the volume. In the case of concentrations below 2% of the volume, the low thermal conductivity of the analyzed nanoparticles resulted in low thermal conductivity of the analyzed nanofluids. The same authors have also observed that in the case of ethylene glycol and CuO nanoparticles, the thermal conductivity of the resulting nanofluids, in which the concentration of nanoparticles is 10-15% by volume, increases by about 40-50% relative to the base liquids. In turn, [PERSON] et al. in [54] presented the results of studies that showed that the thermal conductivity of nanofluids based on Al\({}_{2}\)O\({}_{3}\), CuO, Cu, SiO\({}_{2}\), and TiO\({}_{2}\) nanoparticles increased with decreasing thermal conductivity of the base liquid. In [58], [PERSON] et al. presented the results of studies in which they applied Newtonian nanoparticles using functionalized nanodiamonds (NDs). The authors observed that NDs were a good type of nanofiller, because without the deterioration of electro-insulating properties and viscosity (viscosity increased by about 1% in relation to the base liquid), they improve the thermal conductivity of the oil by about 14.5%. [PERSON] et al. in [59] found that doping vegetable oil with nanoparticles of boron nitride resulted in a significant improvement in heat transfer with respect to the base liquid. In turn, [PERSON] et al. in [60] showed that, depending on the type of nanoparticles used, they had different (both positive and negative) effects on the viscosity of the analyzed nanofluids. On this basis, it can be concluded that the effect of nanoparticles on the thermal properties of liquids is not linear and requires detailed testing for each potential nanofluid. As can be seen from the literature, in the case of electro-insulating nanofluids, their dielectric properties are more important. Only few papers concern the thermal properties of nanofluids for applications in the transformer insulation system. Therefore, in this paper, the authors decided to analyze the impact of nanoparticles modification of the most commonly used insulating liquids on the efficiency of the transformer cooling system. Modifying the base liquids with fullerene C\({}_{60}\) and titanium dioxide TiO\({}_{2}\) nanoparticles was what made the insulating nanofluids.