## 4 Results and Discussion
### Results of Analytical Thermal Modeling
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & & \(\mathbf{I_{cp}}\) for & \(\mathbf{I_{cp}}\) for & \(\mathbf{I_{cp}}\) for & \(\mathbf{I_{cp}}\) for & \(\mathbf{I_{cp}}\) for & \(\mathbf{I_{cp}}\) for & \(\mathbf{I_{cp}}\) for & \(\mathbf{I_{cp}}\) for & \(\mathbf{I_{cp}}\) for \\ \multirow{2}{*}{**W**} & \multirow{2}{*}{**H**} & \multirow{2}{*}{**60 Hz \(\mathbf{k_{c}}\) at**} & \multirow{2}{*}{**X = 0 m**} & \(\mathbf{\mu}\)m & \(\mathbf{X}\) = 1 mm & \(\mathbf{X}\) = 1.6 mm & \(\mathbf{X}\) = 3 mm & \(\mathbf{X}\) = 4 mm & \(\mathbf{X}\) = 5 mm \\ \cline{3-10}  & & & **70 \({}^{\circ}\)C** & & **BUSBAR \({}^{\circ}\)** & **BUSBAR \({}^{\circ}\)** & **BUSBAR \({}^{\circ}\)** & **BUSBAR \({}^{\circ}\)** & **BUSBAR \({}^{\circ}\)** \\ \cline{2-10}  & & & & & & & & & & \\ \hline
**m** & **m** & **–** & **A** & **A** & **A** & **A** & **A** & **A** & **A** \\ \hline \multicolumn{10}{l}{Bus bars installed horizontally with a vertical major axis} \\ \hline
0.0004 \({}^{\mathrm{a}}\) & 0.02 & 1.000 & 44.3 & 44.4 & 51.3 & 55.0 & 62.9 & 68.0 & 72.7 \\ \hline
0.0004 \({}^{\mathrm{a}}\) & 0.025 & 1.000 & 53.9 & 53.9 & 61.6 & 65.7 & 74.6 & 80.4 & 85.8 \\ \hline
0.0005 \({}^{\mathrm{a}}\) & 0.02 & 1.000 & 49.7 & 49.8 & 57.4 & 61.6 & 70.4 & 76.1 & 81.3 \\ \hline \end{tabular}
\end{table} 
Table 4: Bus bar ampacity as a function of vibration amplitude at a vibration frequency of 120 Hz for bus bars in an indoor environment. Figure 8: Heat transfer coefficient due to convection from the bottom surfaces of different rectangular bus bars as a function of vibration amplitude at a vibration frequency of 120 Hz: (**a**) Bus bars installed horizontally with a vertical major axis; (**b**) Bus bars installed horizontally with a horizontal major axis. According to Table 4, the bus bar ampacity increases with an increase in the vibration amplitude. Compared to the case corresponding to free convection (X = 0), this increase amounts to 0-0.226%--for X = 8.541 \(\mu\)m; 1.039-15.801%--for X = 1 mm (vibration class A); 1.663-24.154%--for X = 1.6 mm (vibration class B); 6.445-41.986%--for X = 3 mm (vibration class C); 10.811-53.499%--for X = 4 mm; and 14.969-64.108%--for X = 5 mm. For all the vibration amplitudes considered, the minimum increases correspond to a bus bar with a cross-section of 0.025 m \(\times\) 0.0004 m, while the maximum increases correspond to a bus bar with a cross-section of 0.0004 m \(\times\) 0.02 m.  
The volume power of heat sources \(\mathrm{Q_{tg,v}}\) as a function of the vibration frequency \(\mathrm{f_{V}}\) for rectangular bus bars installed horizontally with a vertical and horizontal major axis is presented in Figure 9a,b, respectively. The volume powers of heat sources are calculated for a vibration amplitude of 3 mm (vibration class C). The volume powers of heat sources obtained for \(\mathrm{f_{V}}=0\) Hz correspond to stationary bus bars (Figure 1a,c), while the volume powers of heat sources obtained for all other vibration frequencies correspond to vibrating bus bars (Figure 1b,d). From Figure 9a,b, it can be observed that the volume power of heat sources increases with an increase in the vibration frequency, and also with a decrease in the cross-sectional area of the bus bars. In the case shown in Figure 9a, the dependencies \(Q_{\text{tg,v}}=f(f_{\text{v}})\) are almost linear, while in the case shown in Figure 9b, they are non-linear. As in the case of Figure 4b, 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. Specifically, the diagrams in Figure 9a,b show that as the vibration frequency increases, a higher current can flow through the same bus bar. Therefore, for the considered ranges of values, the effect of the vibration frequency on heat generation enhancement is significantly greater than the effect of vibration amplitude.