## 4 Results and Discussion
### Results of Analytical Thermal Modeling
The normalized Nusselt number \(\text{Nu}_{\text{SV}}/\text{Nu}_{\text{S}}\) as a function of the velocity ratio \(\frac{2\pi f_{\text{v}}\times\text{XH}}{\alpha_{\text{ta}}\text{Nu}_{\text{S}} ^{3}}\) for different rectangular bus bars installed horizontally with a vertical and horizontal major axis is provided in Figure 10a,b, respectively. These normalized Nusselt numbers are calculated for different vibration frequencies at a vibration amplitude of 3 mm. The normalized Nusselt numbers obtained for \(f_{\text{v}}=0\) Hz correspond to free convection (Figure 1a,c), while all other normalized Nusselt numbers correspond to vibration-assisted convection (Figure 1b,d). From Figure 10a,b, it is clear that the normalized Nusselt number increases with an increase in the velocity ratio. Thus, the normalized Nusselt number increases with an increase in the vibration frequency at \(X=3\) mm, and in this particular case, the Nusselt number is higher for bus bars installed with a horizontal major axis (Figure 10b). Convection heat transfer coefficients for the surfaces of different rectangular bus bars as functions of vibration frequency are presented in Figures 11-13. The coefficients are generated for a vibration amplitude of 3 mm. Figure 11 refers to the two side surfaces, Figure 12 to the top surface, and Figure 13 to the bottom surface. The heat transfer coefficients obtained for \(f_{\text{v}}=0\) Hz refer to free convection (Figure 1a,c), while all other heat transfer coefficients refer to vibration-assisted convection (Figure 1b,d). Figure 9: Volume power of heat sources as a function of vibration frequency at a vibration amplitude of 3 mm 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. Figure 11: Heat transfer coefficient due to convection from the side surfaces of different rectangular bus bars as a function of vibration frequency at a vibration amplitude of 3 mm: (**a**) Bus bars installed horizontally with a vertical major axis; (**b**) Bus bars installed horizontally with a horizontal major axis. Figure 10: Normalized Nusselt number as a function of velocity ratio for different rectangular bus bars and different vibration frequencies at a vibration amplitude of 3 mm: (**a**) Bus bars installed horizontally with a vertical major axis; (**b**) Bus bars installed horizontally with a horizontal major axis. From Figures 11-13, it is clear that the vibration-assisted convection heat transfer coefficients from all the surfaces of the rectangular bus bars increase with an increase in the  
Figure 12: Heat transfer coefficient due to convection from the top surfaces of different rectangular bus bars as a function of vibration frequency at a vibration amplitude of 3 mm: (**a**) Bus bars installed horizontally with a vertical major axis; (**b**) Bus bars installed horizontally with a horizontal major axis. Figure 13: Heat transfer coefficient due to convection from the bottom surfaces of different rectangular bus bars as a function of vibration frequency at a vibration amplitude of 3 mm: (**a**) Bus bars installed horizontally with a vertical major axis; (**b**) Bus bars installed horizontally with a horizontal major axis. vibration frequency at \(X=3\) mm (vibration class C), and, in general, with a decrease in the corresponding characteristic length. According to Figure 11a,b, the vibration-assisted convection coefficients from the side surfaces of the bus bars are almost linear. Furthermore, according to Figures 12 and 13, the vibration-assisted convection coefficients from the top and bottom surfaces are non-linear. The presence of nonlinearities in Figures 12 and 13 is once again caused by the approach to modeling the effect of horizontal transverse vibrations on free convection using empirical correlations for forced convection.