## 4 Results and Discussion  
### Experimental Validation of the Proposed Analytical Model  
The proposed analytical model of steady-state heat transfer in and around the rectangular bus bars needs to be compared against relevant experimental data. These comparisons are required to validate that the proposed analytical model indeed represents the actual thermal behavior of the bus bars at steady-state conditions. For this purpose, the experimentally determined dependency of the normalized Nusselt number \(\rm Nu_{SV}/Nu_{S}\) on the velocity ratio \(\rm\frac{2\pi ft_{V}XH}{\alpha_{c}n_{N}^{2}}\) from [21] is used. This dependency in its discrete form was generated for four different plate fins and different vibration amplitudes at natural frequencies of 50, 29, 59, and 40 Hz, assuming no heat transfer from the top and bottom surfaces of the plate fins (the so-called adiabatic assumption). According to [21], the natural frequencies of 50, 29, 59, and 40 Hz refer to plate fins with cross-sections of 0.0004 m \(\times\) 0.02 m, 0.0004 m \(\times\) 0.025 m, 0.0005 m \(\times\) 0.02 m, and 0.0005 m \(\times\) 0.025 m, respectively. In addition, for the purpose of this validation, a series of simulations was performed with bus bars having cross-sections identical to the cross-sections of plate fins from [21]. The data were generated using the BUSBAR.m program for different vibration amplitudes (ranging from 0 to 5 mm) at the same frequencies as those of the experiments, assuming that the top and bottom surfaces of the bus bars are non-adiabatic. Finally, the simulated data are correlated using Equation (10) and compared with the corresponding experimental data from [21]. This comparison is shown in Figure 2.  
Figure 2: Normalized Nusselt number versus velocity ratio generated for different vibration amplitudes at natural frequencies of 50, 29, 59, and 40 Hz. The discrete representations correspond to the plate fins considered in [21] assuming that their top and bottom surfaces are adiabatic. The continuous representation, i.e., Equation (10), refers to the rectangular bus bars considered here assuming that their top and bottom surfaces are non-adiabatic.  
According to Figure 2, the normalized Nusselt number represented by Equation (10) agrees well with the experimental data from [21], where the discrepancy is only in two cases beyond the \(\pm\)10% limits. According to [21], Equation (10) should be valid for vibration frequencies from 29 to 59 Hz and for velocity ratios from 0 to 20, i.e., for the ranges for which the experiments were carried out. In this study, according to Figure 2, these ranges of values are logically exceeded. Compared to the corresponding diagram from [21] that refers to the adiabatic assumption, there is practically no difference. Accordingly, the introduction of the non-adiabatic assumption for the top and bottom surfaces of the bus bars did not introduce any significant change in the thermal sense. Therefore, it can be considered that the proposed analytical model has been successfully validated through this comparison with experimental results.  
Quantification of the effect of the non-adiabatic assumption on the bus bar ampacity for cases corresponding to the experiments from [21] is also performed. Table 2 outlines the ampacity values obtained for different amplitudes at frequencies of 50, 29, 59, and 40 Hz, assuming that the bus bars are installed horizontally with a vertical major axis.  
The first four rows of Table 2 are generated for the adiabatic assumption from [21], while the remaining results are generated for the non-adiabatic assumption proposed in this paper. According to Table 2, the largest difference between these results is 0.4 A. This agrees with the results shown in Figure 2.