# Energy Consumption Characteristics for Design Parameters of Permanent Magnet-Based Al Billet Heater
## 4 Heating Characteristic Effects on Design Parameters
### Heating Effect for Magnetic Polarity Direction  
The polarity direction of the magnetic field of the induction heating system using permanent magnets can be arranged in the normal or tangential direction. Therefore, in this study, the effects of the two forms of magnet arrangement were analyzed, as shown in Figure 8, to examine the effects of the changes in the magnetic polarity direction. The tangential model in Figure 8a was configured in such a manner that each pair of permanent magnets with the same pole were placed to face each other, whereas the normal model in Figure 8b was configured in such a manner that the magnet poles would be formed toward the center axis of the circle and the N and S poles would be placed alternately.  
Figure 7: Comparison of analysis and experiment results: (**a**) RPM–time curve; and (**b**) temperature–time graph.  
The numerical analysis of the billet heater using permanent magnets was performed with the same conditions as the analysis method of the base model, and the results are shown in Figure 9. The results in Figure 9 are listed in the order of magnetic flux density, vector potential, active power density, current density, and temperature. The results of the electromagnetic-thermal analysis according to the polarity direction of the billet heater using permanent magnets confirmed that due to the surface effect, the magnetic flux density is concentrated in the outside of the billet in both models, as shown in Figure 9. It can be observed that in the tangential model, the magnetic flux density on the billet surface is concentrated at four points around the center of the magnet, whereas, in the normal model, it is concentrated in eight areas on the edge of the magnet. This indicates that different magnetic fields are formed according to the polarity direction even when permanent magnets with the same flux density are used, and that although the range of the maximum and minimum magnetic flux density is not wide enough, the area of the concentrated magnetic field is larger in the normal direction. As a result, in the normal model, a high eddy current occurs inside the billet, and the current density and power density values are also higher. Hence, it can be observed that power density is determined by the flux penetration of the billet surface due to the magnetic flux density and surface effect, and the normal model is advantageous for heating over the tangential model among the four permanent magnet models.  
The temperature result according to the changes in the permanent magnet flux direction showed that the temperature increased the heating time. As shown in Figure 9, in the case of the tangential model for the flux direction, the heating time and energy consumption at which the temperature of the billet reached 450 \({}^{\circ}\)C were approximately 260 s and 302.57 kWh/ton, and in the normal model, they were approximately 70 s and 287.01 kWh/ton, respectively. Thus, the normal model for the flux direction improves the heating time by approximately 73% and the energy consumption by approximately 5% compared to the tangential mode.