## 7 Mathematical Calculations  
In this study, the calculation of the maximum heating power transferred by the cooling device from the interior of the electric enclosure to the surroundings was performed. The purpose of the mathematical calculation was to find a simple method to theoretically determine the heating power transferred through the phase change of the working substance which occurs inside the loop thermosiphon at loaded heat. The calculation was performed on the basis of the theoretical relationships of convective heat transfer inside the tube and on the outside of the finned tube. The calculation was based on the theory of thermal equilibrium of a heat pipe, where it is assumed that the amount of heat received in the evaporating part of the device is equal to the amount of heat dissipated by the condensing part to the surroundings. The computational relations were applied in ideal conditions. The values of the physical quantities used in the relationships were determined from the tables on the basis of the measured temperatures and pressures of the electrical enclosure interior, the outside environment, and the cooling device obtained during the measurement [39,40]. \[\dot{Q}_{c}=\dot{Q}_{e} \tag{1}\]  
Due to the thermal balance, it was sufficient to create a model for calculating the total heating power removed by the cooling device for only one part of the device. The calculation was performed for the condenser part according to the equation:  
\[\dot{Q}=k\Delta t_{avg}A_{1} \tag{2}\]  
Equation (2) depends on the inner surface of condenser tubes \(A_{1}\) (m\({}^{2}\)), average logarithmic temperature difference \(\Delta t_{avg}\) (K) and overall heat transfer coefficient \(k\) (W/m\({}^{2}\cdot\)K). The overall heat transfer coefficient depends mainly on \(\alpha_{1}\) (W/m\({}^{2}\cdot\)K), the condensation heat transfer coefficient inside the tube, and \(\alpha_{2}\) (W/m\({}^{2}\cdot\)K), the convective heat transfer coefficient on the outside tube of the condenser, and is defined by the equation:  
\[k=\frac{1}{\frac{1}{\frac{1}{\alpha_{1}}+\frac{A_{1}^{\prime}}{\alpha_{2}}\frac {1}{\alpha_{2}}}} \tag{3}\]  
The calculation of heat transfer coefficients inside the pipe and on the surface depends on the density, thermal conductivity, dynamic and kinematic viscosity, surface tension, thermal conductivity, and latent heat. The efficiency of the fins and the size of the heat exchange surface are also important factors in heat exchange. The values of these physical quantities depend on temperature and change over time. It follows that the heat transfer coefficient is within a certain interval. The calculation of the condensation heat transfer coefficient inside the horizontal tubes of the condenser, in which the condensation of water vapour to the liquid took place, was performed according to the following equation [41]:  
\[\alpha_{1}=0.56\sqrt[4]{(gl_{v}\varrho^{2}\lambda^{3})/(v\Delta\theta d_{i})} \tag{4}\]  
where \(g\) (m/s\({}^{2}\)) is the gravitational acceleration, \(l_{v}\) (J/kg) is the latent heat of vaporization, \(\varrho\) (kg/m\({}^{3}\)) is the air density, \(\lambda\) (W/m\(\cdot\)K) is the thermal conductivity, \(\
u\) (m\({}^{2}\)/s) is the kinematic viscosity, \(\Delta\theta\) (K) is the temperature difference of the tube wall and media, and \(d_{i}\) (m) is the inner tube diameter. In the range of our investigated temperatures, the values of the heat transfer coefficient during condensation in the range of 330-520 W/m\({}^{2}\cdot\)K were calculated. On the outside of the condenser tubes, heat was transferred to the surroundings by forced air convection due to the forced air flow from the external fan.