# Energy Consumption Characteristics for Design Parameters of Permanent Magnet-Based Al Billet Heater
## 1 Introduction  
Recently, there has been a tendency toward using green energy with high efficiency in various industries requiring high energy consumption, given the adverse environmental effects of fossil fuel energy. Under these circumstances, research on weight reduction, such as via structural design change, the application of new construction methods, and the development of new materials is being actively conducted [1, 2]. Furthermore, there has been a trend to switch from the conventional ferrous materials to non-ferrous materials to achieve weight reduction. As part of such a trend, substantial research is underway on manufacturing methods using various types of non-ferrous metals according to the environment of use; the most commonly used non-ferrous metal is aluminum. Aluminum is effective in weight reduction because its specific gravity is only a third of that of iron. Moreover, aluminum has excellent corrosion resistance, thermal and electrical conductivity, and recyclability, and it does not cause brittle fracture at low temperatures. Hence, it can be used in the form of sheets, for extrusion, and as a casting material. However, pure aluminum materials have process disadvantages, such as low rigidity, high cost, and welding-related problems. To overcome such problems, cladding extrusion technology has been studied [3]. Cladding is a method using strong metallurgical bonding and minimalsubstrate dilution, and various techniques of solid-state bonding are used [4; 5]. Solid-state bonding and manufacturing processes are considered to be quite mature, including friction stir welding, friction stir riveting, ultrasonic welding, roll bonding, extrusion bonding, and so on, and have been used extensively in the industry for decades [6; 7; 8; 9]. In addition, solid-state bonding includes the cold bonding process and heat bonding. The cold bonding process is defined by the processing temperature being less than the recrystallization temperature [10]. The heat bonding process is when the processing temperature is greater than the recrystallization temperature [11]. As such, solid-state bonding and manufacturing processes require pre-heating. Likewise, cladding extrusion requires preheating as a preprocessing step. Preheating methods include gas combustion, high-temperature superconducting using coils, and the use of mechanical power with permanent magnets. The billet heating method using a gas furnace is known to transmit 40-60% of the total gas heating energy in general. To increase the efficiency of gas heating, energy recovery methods using a heat exchanger to increase the efficiency of the billet heating process and of the entire system have been researched [12]. The heating method using coils is used to heat a billet by arranging a copper coil surrounding a heating object with a certain clearance in a direction parallel to its axis and applying an electric current to change the surrounding magnetic and electric fields. The heating method using a copper coil uses approximately 60% of the power supplied in heating, and the remaining energy is dissipated to the external environment [13; 14]. High-temperature superconductor DC induction heating has been introduced to alleviate this problem, and a method of achieving the same efficiency of the heater as that of the motor by minimizing energy consumption has been researched [15; 16; 17]. Accordingly, optimization research concerning the electromagnetic field and heat-related effects of commercial HTS DC motors has been conducted via numerical analysis of various motor design changes [18; 19; 20]. Increasing the efficiency by simultaneously heating multiple billets by arranging double HTS coils such that the changes in both the external and internal magnetic fields due to the coil are utilized [21; 22].