## 2 Methodology and Validation
### Experimental Measurement  
The planar moving induction heating experimental platform is established, as shown in Figure 9. The workpiece Inconel 718 is fixed on a moving platform apparatus and the velocity can be precisely controlled. The experimental system mainly includes induction heating power supply, frequency conversion voltage regulator, strengthening sensor (including concentrator MPB-MFC) and cooling device. The cooling device can circulate water inside the coil to prevent overheating of the coil and reduce energy consumption during heating. The validation experimental parameters are presented in Table 1, which mainly contains the MFC model, heating distance \(d\), current intensity \(I\), current frequency \(f\) and the moving velocity \(v\). The heating distance \(d\) is set as 1 mm because the distance between the induction coil and the workpiece should be no more than 2 mm in order to concentrate the magnetic flux more efficiently. The frequency conversion regulator can realize the frequency regulation range from 10 kHz to 50 kHz, and the intensity of the induction coil current is controlled from 0 to 1200 A. The levels of \(I\) and \(f\) are listed in Table 1 according to the former induction heating experimental analysis [10; 15]. As to the velocity of the workpiece, it is verified that the velocity should be controlled at a low level, due to its negative effect on the induction heating [10]. In addition, the experimental system includes a temperature acquisition and analysis device. The surface temperature of the workpiece is obtained by infrared thermal imager (NEC R300W2-NNU). At the same time, the temperature history of the workpiece surface and internal points is measured by the semi-natural artificial thermocouple, as shown in Figure 9. By simultaneously measuring the surface temperature with a thermocouple and an infrared camera, the thermal imager can be calibrated, and the accuracy of the temperature measurement can be improved. Figure 8: Electrical resistivity of Inconel 718. Figure 9: Experiment apparatus of the planar moving induction heating. The power density then is extracted and used to calculate the final temperature distribution. Figure 13 presents the temperature profile obtained from the analytical model in this paper, in which the input parameters are respectively set as \(I=430\) A,\(f=37.6\) kHz, \(v=5\) mm/s. Under these input parameters, the power density in the surface is 14e10 W/m\({}^{3}\) and the corresponding power applied into the analytical model is 70 W. Figure 14 is the temperature profile calculated by the finite element simulation model. It is shown that in the analytical calculation the most of heat is concentrated on the surface of the workpiece and the maximum temperature is in the surface, due to the skin effect in the induction heating, which is similar with the finite element simulation result. The temperature is mainly distributed in the surface and sub-surface region of the workpiece, due to the skin effect in the induction heating process, which is commonly realized and validated [2,10]. In order to verify the analytical computational results, several finite element simulations and the corresponding validation experiments are conducted under various input parameters of the planar moving induction heating process. The experimental parameters and the corresponding results are listed in Table 2. Figure 15 shows the maximum temperature in the workpiece while the velocity is 5 mm/s, while Figure 16 shows the Maximum temperature in the workpiece while the velocity is 8 mm/s. Figure 17 shows the Maximum temperature in the workpiece at four different velocity levels. It is observed that the maximum temperature by analytical calculation is higher than the simulation results and the experimental results. The main reason causing this situation is that the simulation model has taken into consideration of the surface heat transfer effect while the analytical model ignores it, which varies with the temperature [10,22].