# Energy Consumption Characteristics for Design Parameters of Permanent Magnet-Based Al Billet Heater
## 1 Introduction
Regarding the preheating structure using permanent magnets that convert mechanical energy into thermal energy, methods to achieve equal or higher efficiency, as compared to HTS DC induction, through permanent magnets and electric motors without using an expensive superconducting system have been studied [23; 24]. The permanent magnet heating method consists of a stator with various numbers of magnets assembled and a billet rotor with high electrical conductivity. When the billet is rotated, the magnetic field starts to fluctuate in the rotor. Then, the closed circles of eddy currents are induced on the rotor based on [PERSON]'s law, which opposes the direction of the magnetic field on the rotor. Therefore, the induced eddy current loops resist against the direction of the motion of the rotor and generate heat (heat is produced in accordance with the Joule-Lenz Law and hysteresis losses) [25]. Such studies on structures using permanent magnets have included the analyses of the effects of the changes in design parameters, such as the materials, shapes, directions, and number of magnets [26; 27; 28; 29; 30; 31; 32; 33; 34]. On this basis, it is generally known that high energy efficiency of 78-85% can be maintained by preheating with a magnetic field created in the system using permanent magnets [23]. However, such studies have conducted analytic verification by selecting a specific object rather than performing a systematic review about the characteristics of the design factors. As a result, studies on the effect of the characteristics on performance, on elucidating the relationships among them, and on the systematic comparisons of the optimization processes using them are insufficient. [PERSON] et al. reported a study result showing that the peel strength of the intermetallic compound (IMC) layer and the thickness of the intermetallic layer increased after heat treatment between 400 \({}^{\circ}\)C and 500 \({}^{\circ}\)C. That is, since the thickness of the intermetallic compound layer increases with temperature, it has been shown that the IMC layer thickness increases above 300 \({}^{\circ}\)C to increase the peel strength [35; 36]. In addition, an oxide film occurs above 500 \({}^{\circ}\)C, and [PERSON] et al. reported that the ultimate strength of the material decreased sharply from 200 \({}^{\circ}\)C in the case of Al and converges to about 10 MPa at 450 \({}^{\circ}\)C and above [37]. Therefore, in this study, the influence of the change in the design parameters of a billet heater that uses permanent magnets was numerically analyzed, and its design direction was examined. The numerical analysis model was verified by comparing the analysis of the base model with the experimental results to establish its reliability. We numerically analyzed the effects of the design parameters, including the magnetic force direction of the permanent magnet, the number of permanent magnets, and the clearance and eccentricity between the permanent magnet and billet. In addition, the characteristics of billet heating were analyzed for various factors using the numerical results. The electromagnetic field characteristics, such as current density, power loss, and energy consumption according to the change in the design parameters of the billet heater were analyzed, and the heating performances of the billet were verified according to the internal heating characteristics. Furthermore, the characteristics of the basic design factors were obtained so that they can be used in the design of billet heaters to achieve effective heating performance.