# Energy Consumption Characteristics for Design Parameters of Permanent Magnet-Based Al Billet Heater
## 4 Heating Characteristic Effects on Design Parameters
### Heating Effect Based on Number of Magnets  
In this study, the effects of the increasing number of permanent magnets from 4 to 16 in the tangential and normal models, as mentioned above, were analyzed. All the permanent magnets were arranged with the same clearance, and the same flux direction arrangements of tangential and normal models were applied to the analysis.  
Figure 8: Permanent magnet polarity direction change model: (**a**) tangential direction model; (**b**) normal direction model.  
Figure 9: Analysis result according to permanent magnet flux direction change: **(a)** tangential direction result; **(b)** normal direction result; **(c)** temperature result.  
The results of electromagnetic-thermal analysis based on the increased number of permanent magnets are shown in Figures 10 and 11. In the normal model, the power loss of the billet gradually decreased as the number of magnets increased. In the normal model, the hourly power loss of the billet gradually decreased as the number of magnets increased. This is because the magnetic force transmitted into the billet decreased despite the increase in the number of magnets and the decrease in the spacing. The biggest difference between the normal and tangential models is the difference in the form of the magnetic flux penetrating into the billet depending on the polarity direction; the normal model shows a deeper penetration into the billet than the tangential model. In contrast, it can be observed that the power loss gradually increased with the number of magnets for the tangential model, and an inflection point was reached when the number of permanent magnets was 12. Furthermore, the same phenomenon appears in the graphs of the time to reach 450 \({}^{\circ}\)C and the number of magnets. As described in the four cases above, this is due to the interference between permanent magnets. The narrower the clearance was, the lower the heating efficiency was as the magnetic flux, which should penetrate the billet, flows into the adjacent permanent magnet.  
Furthermore, when the temperature distribution with the increasing number of magnets was examined, as shown in Figure 9, the temperature distribution inside the billet of the tangential model showed a temperature difference of approximately 20 \({}^{\circ}\)C between the surface and center. In contrast, the normal model showed a temperature difference of approximately 5 \({}^{\circ}\)C.  
In this section, the effects of the increasing number of permanent magnets were analyzed using electromagnetic-thermal analysis, and the clearance between the permanent magnets was found to be a major parameter that influenced the heating efficiency. As the number of tangential direction magnets increased, flux density and current density increased and then decreased. This was because, as the number of magnets increased, as the poles of the magnets became closer, the amount of flux and current generated by the Al ingot by the interference of flux decreased. In addition, the required torque increased due to the increase in the number of magnets, and the increased torque became a factor to reduce the power loss. In Figure 10, the conversion capacity to heat is high in the 12 magnets, with the maximum power loss and a short heating time. Energy consumption  
Figure 10: Result graph showing temperature rise to 450 \({}^{\circ}\)C according to the change in the number of permanent magnets: (**a**) number of magnets–heating value graph; and (**b**) number of magnets–heating time graph.  
was the most efficient when the power loss was large and the heating time was short. Energy consumption according to the number of magnets is shown in Table 3. As shown in the table, the tangential model with 12 permanent magnets showed the best heating efficiency in consideration of the clearance between the permanent magnets.  
Figure 11: Cont.