# Development of Wireless Power Transmission System for Transfer Cart with Shortened Track
## 3 Thermal Analysis and Pickup Module Fabrication
### Thermal Analysis
The geometrical configuration used in the simulation is represented in [22] for the WPT system and the ducts for inserting cables. The basic thermal analysis considers a rectangular duct filled with a cable with a diameter of 15 mm. Calculations were performed for all test cases using the commercial CFD (Computational fluid dynamics) package of ANSYS FLUENT 14.2. All simulations were performed using an Intel Core i7-5930K 3.5 GHz processor, and a typ  
Figure 2: Pickup module prototype fabrication concept: (**a**) Front section view, (**b**) inside view of the rear part, and (**c**) three-dimensional view. The uppercase English alphabet represents design improvements to ensure mass production and reliability, and detailed descriptions of design improvements are described in the main text. time of about 1.5 h. The momentum and heat fluxes were assumed to be laminar and the energy equation was solved under the condition of steady-state. At the surfaces of the duct, the heat flux was used as the thermal boundary condition. However, radiation heat transfer between the surfaces was neglected. No-slip boundary conditions were imposed for all solid surfaces. The Boussinesq approximation was used to specify the air density variation due to temperature [28]. The resulting relative variation in the air density was less than 2% inside the enclosure. We generated about a 2.66 million tetra grid and approximately 7.6 million nodes. For analytical accuracy, the grid size was created by using a sizing function with a growth rate of 1.2 and a non-uniform grid distribution from 0.35 to 70.83 mm. The enclosure condition assumed that the WPT system was exposed to 20 \({}^{\circ}\)C air, and convergence conditions were conducted until the remaining conditions for energy conservation were satisfied with the requirements of 10\({}^{-6}\). The simulation result shows that the maximum temperature, \(T_{\text{max}}\), is 46 \({}^{\circ}\)C, which is about 4 \({}^{\circ}\)C lower (about 8% error) than that of the experimental data [23]. If we consider the existence of uncertainty in the system or the environment (for example, elusive effects such as interfacial thermal resistance, convective surface film coefficient, and complex geometries), it can be concluded that the temperature contours agree well with each other with a deviation of less than 10%. In this study, all temperature measurements were performed using a thermographic camera (model: FLIR i5, max. 250 \({}^{\circ}\)C, every 0.1 \({}^{\circ}\)C). Although \(T_{\text{max}}\) is underestimated for the case of thermal analysis, our method to obtain values of \(\delta\) and \(r_{\text{e}}\) is reasonable because the experimental conditions and the analytical conditions cannot be exactly the same, due to the computational limitations, as discussed above. Further investigation would yield additional insight into the skin effect dependence of the electric flow mechanism. For the convenience of thermal analysis, the effective property values are used because the exterior of the module is composed of a bakelite and ferrite core. The material properties of the exterior of the pickup module used in the analysis are listed in Table 1. The effective values (\(X_{\text{eff}}\)) are calculated by using the volume fraction of the bakelite (\(\varphi\)): \(X_{\text{eff}}=\varphi X_{\text{Bakelite}}+(1-\varphi)X_{\text{Ferritic core}}\). From the result, we also identified the physical properties of the external case of the module.