## 4 Results and Discussion
### Results of Analytical Thermal Modeling  
The diagrams in Figure 4a,b show the volume power of heat sources \(\mathrm{Q_{tg,v}}\) as a function of the vibration amplitude \(\mathrm{X}\) for rectangular bus bars installed horizontally with a vertical and horizontal major axis (according to Figure 1), respectively. All these volume powers of heat sources are obtained for a vibration frequency of 120 Hz. The results obtained for \(\mathrm{X}=0\) m correspond to stationary bus bars (Figure 1a,c), while all other results correspond to vibrating bus bars (Figure 1b,d). According to Figure 4a,b, the volume power of heat sources increases with an increase in the vibration amplitude, and also with a decrease in the cross-sectional area of the bus bars. In the first case, the dependencies \(\mathrm{Q_{tg,v}}=\mathrm{f(X)}\) are almost linear, while in the second, they are non-linear. The resulting nonlinearities are a consequence of the approach to modeling the vibration-assisted convection from the top and bottom surfaces of the bus bars using empirical correlations for forced convection. In particular, the diagrams in  
Figure 4: Volume power of heat sources as a function of vibration amplitude at a vibration frequency of 120 Hz for different rectangular bus bars: (**a**) Bus bars installed horizontally with a vertical major axis; (**b**) Bus bars installed horizontally with a horizontal major axis. \begin{table}
\begin{tabular}{c c c c c} \hline
**FE Mesh** & **Number of Nodes** & **Number of Elements** & \(\mathbf{(\Gamma^{\prime}_{s}-T_{a})}\) (\({}^{\circ}\)C) a & \(\mathbf{(T_{s}-T_{a})}\) (\({}^{\circ}\)C) b & \(\mathbf{(\Gamma^{\prime}_{s}-T_{s})}\) (\({}^{\circ}\)C) c \\ \hline Automatically generated & & & & \\ (Figure 3a) & 92 & 30.004153 & 30.0 & 0.004153 \\ Generated after the & & & & \\ first refinement & & & & \\ Generated after the & & & & \\ second refinement & & & & \\ \hline \end{tabular}  
* Values of the temperature difference \(\mathrm{(\Gamma^{\prime}_{s}-T_{a})}\) obtained for different densities of the FE mesh using COMSOL 4.3, where \(\mathrm{\Gamma^{\prime}_{s}}\) stands for the maximum value of the bus bar temperature. b The reference value of the temperature difference \(\mathrm{(T_{s}-T_{a})}\) taken from the experiments performed in [21]. c Differences between the simulated and measured values of the bus bar temperature obtained as \(\mathrm{(T_{s}-T_{s})}=\mathrm{(\Gamma^{\prime}_{s}-T_{a})}-\mathrm{(T_{s}-T_{ a})}\).  
\end{table} 
Table 3: Details on the FE meshes generated within the two-dimensional domain in Figure 3a and results of the corresponding mesh independence tests performed for the case of rectangular bus bar 0.0004 m \(\times\) 0.025 m and vibration class B. Figure 4a,b show that as the vibration amplitude increases, more electricity (i.e., a higher current) can flow through the same bus bar. As for the heat transfer coefficient due to radiation, the value \(\mathrm{h_{r}}=2.812\) W\(\cdot\)m\({}^{-2}\cdot\)K\({}^{-1}\) is obtained in each simulation performed by the BUSBAR.m program. This is the expected result, which can also be obtained by the calculation method described in [25]. The diagrams in Figure 5a,b show the normalized Nusselt number \(\mathrm{N_{USV}}/\mathrm{N_{US}}\) as a function of the velocity ratio \(\frac{2\pi\mathrm{f_{V}}\chi\mathrm{H}}{\omega\omega\mathrm{Au_{S}^{2}}}\) for different rectangular bus bars installed horizontally with a vertical and horizontal major axis, respectively. These normalized Nusselt numbers are generated for different vibration amplitudes at a vibration frequency of 120 Hz. The normalized Nusselt numbers obtained for X = 0 m correspond to stationary bus bars (Figure 1a,c), while all other normalized Nusselt numbers correspond to bus bars affected by horizontal transverse vibrations (Figure 1b,d). In this regard, the definition of the velocity ratio used here can be found in [21].