## 2 Methodology and Validation
### Experimental Measurement
Moreover, the experimental data has a measurement error, due to the emissivity parameter of the infrared thermal imager, which is only set as a constant and in fact varies with the temperature. In addition, it is investigated that the higher input current intensity \(I\) of the coil, the higher temperature is acquired (Test 1 vs. Test 3, Test 2 vs. Test 4), which has a good agreement with the finite element simulation results and the experiment results [10]. Similarly, the heated temperature rises as the frequency \(f\) increases at the same level as the current intensity \(I\) (Test 1 vs. Test 2, Test 3 vs. Test 4). The same conclusion can be drawn when the moving velocity becomes 8 mm/s, as shown in Figure 17. By compared with Figures 15 and 16, it is found that temperature obtained will experience a drop while the moving velocity changes from 5 mm/s to 8 mm/s. It is proved in Figure 17 that the moving velocity also plays a vital rule in the temperature control in the planar induction heating process, besides the current intensity \(I\) and the current frequency \(f\)[15]. The relative errors of the analytical calculation and the finite element simulation are listed in Table 2. It is clear shown that the relative errors between the analytical maximum temperature and the corresponding experimental data are lower than 25%, especially there is a low error level when the temperature is higher than 200 \({}^{\circ}\)C. This result is matched with the fact that the convective heat transfer coefficient decreases with the temperature rises in reality and the difference in the analytical model will drop when the heated temperature rises than 200 \({}^{\circ}\)C [22]. It is also true in Table 2 that the finite element simulation possesses a lower relative error than the analytical calculation in this work. However, the computation efficiency of the analytical model is much higher than the finite element simulation model. The calculation time of the analytical model in this work just needs several seconds while the finite element simulation model requires much more time, which is verified in other applications [17]. Thus considering the indispensable simplification during the analytical modeling and the difficult precise calculation and control of the induction coil during the planar moving induction experiment system, it is believable that the relative errors of these validation experiments listed in Table 2 are considered to be in an acceptable level. Thus it is believed that the established analytical model in this work can be used to predict the temperature evolution in the heated workpiece by the planar moving induction heating. Moreover, in order to obtain more accurate results, the next research work needs to consider the heat exchange coefficient in the analytical modeling. Figure 16: Maximum temperature validation in the surface of the workpiece (\(v=8\) mm/s). Figure 14: Temperature profile calculated by finite element simulation. Figure 13: Temperature profile calculated by the analytical method. Figure 9.0 Maximum temperature validation in the surface of the workpiece (\(v=5\) mm/s).