## 2 Geometry, Material Properties, and Assumptions  
In general, the steady-state heat conduction equation follows from the law of conservation of energy in the volume of a rectangular bus bur of unit length (L = 1 m). Such volume elements of rectangular bus burs having width W (in m), height H (in m), and length L (in m) are shown in Figure 1. The unit length of the bus bars was chosen because the process of solving two-dimensional heat transfer problems in COMSOL implies that the default length of any geometric model (i.e., default depth when an object or solid is displayed on a two-dimensional computer screen) is L = 1 m. Thus, the representations of the problems in Figure 1 are three-dimensional, and the problems solved in COMSOL are two-dimensional with a length of 1 m.  
The remaining symbols appearing in Figure 1 are as follows: T\({}_{\text{a}}\) is the ambient air temperature in K; Q\({}_{\text{tg,v}}\) is the volume power of heat sources in W\(\cdot\)m\({}^{-3}\); T\({}_{\text{s}}\) is the bus bar temperature in K, h\({}_{\text{CS}}\) is the heat transfer coefficient due to free or vibration-assisted  
Figure 1: Three-dimensional representation of heat transfer in and around rectangular bus bars installed horizontally in an indoor environment: (**a**) A stationary bus bar installed with a vertical major axis; (**b**) A vibrating bus bar installed with a vertical major axis; (**c**) A stationary bus bar installed with a horizontal major axis; (**d**) A vibrating bus bar installed with a horizontal major axis. convection from the two side surfaces in W\(\cdot\)m\({}^{-2}\)\(\cdot\)K\({}^{-1}\); h\({}_{\rm cT}\) is the heat transfer coefficient due to free or vibration-assisted convection from the top surface in W\(\cdot\)m\({}^{-2}\)\(\cdot\)K\({}^{-1}\); h\({}_{\rm cB}\) is the heat transfer coefficient due to free or vibration-assisted convection from the bottom surface in W\(\cdot\)m\({}^{-2}\)\(\cdot\)K\({}^{-1}\); and \(\varepsilon\) is the thermal emissivity of the bus bar surfaces. Specifically, the effect of vibration parameters (vibration amplitude X in m or/and vibration frequency f\({}_{\rm V}\) in Hz) on free convection from the side, top, or bottom surface of a rectangular bus bar is included based on the coefficient h\({}_{\rm cS}\), h\({}_{\rm cT}\), or h\({}_{\rm cB}\), respectively. In the introduction, it is already provided that the considered bus bars are made of aluminum alloys 5052-O and 6101-T61. The thermal and electrical properties of these aluminum alloys are taken from [21; 22; 24] and outlined in Table 1. In Table 1, k\({}_{\rm t}\) is the thermal conductivity in W\(\cdot\)m\({}^{-1}\)\(\cdot\)K\({}^{-1}\), \(\rho_{\rm e20}\) is the direct current (or d.c.) resistivity at 293.157 K (or 20 \({}^{\circ}\)C) in \(\Omega\)\(\cdot\)m, and \(\alpha_{\rho}\) is the temperature coefficient of resistivity in K\({}^{-1}\). For the materials used, it is assumed that they are homogenous and isotropic, and that there is only radial heat conduction within them. It is also assumed that the volume powers of heat sources existing within those materials together with the corresponding thermal and electrical properties, and surface radiation properties (thermal emissivity \(\varepsilon\) and solar absorptivity \(\alpha\)) are constant. For the indoor environment, it is assumed that the ampacity values are determined under the following service conditions [22]: (i) still air conditions; (ii) T\({}_{\rm a}\) = 40 \({}^{\circ}\)C; (iii) continuously permissible temperature of bus bars T\({}_{\rm cp}\) = 70 \({}^{\circ}\)C; (iv) \(\varepsilon\) = 0.35; (v) \(\alpha\) = 0; (vi) frequency of the power system f = 60 Hz; and (vii) extra loss coefficient for the proximity effect k\({}_{\rm p}\) = 1. Still air means that the wind velocity is 0 m\(\cdot\)s\({}^{-1}\), solar absorptivity of \(\alpha\) = 0 means that there is no thermal effect of the sun, while k\({}_{\rm p}\) = 1 means that the phase bus bar conductors are installed so that they do not affect each other thermally.