# Design and Numerical Study of Induction-Heating Graphitization Furnace Based on Graphene Coils
## 1 Introduction  
Graphitization is the process of converting initially non-graphitic carbon into graphitic carbon after high-temperature heat treatment [1]. Graphitized carbon materials have excellent thermal conductivity, electrical conductivity, and chemical stability [2], and they are indispensable in the chemical, metallurgical, automotive, and electronic industries. Graphitization requires heating temperatures typically up to 2800 \({}^{\circ}\)C or higher, which is an energy-intensive process requiring 3-8 MWh per ton of graphite product produced [3], with the energy consumption accounting for more than 50% of the total cost [4]. Therefore, there are significant environmental and economic incentives to reduce the energy consumption. Graphitization furnaces are basic equipment in the carbon industry, and they can be classified based on the heating method used, such as Acheson furnaces [5], lengthwise furnaces [6], and induction-heating graphitization furnaces (IHGFs) [7]. The Acheson furnace utilizes the Joule heating of resistive materials to indirectly heat and graphitize baked products. Its design is simple, robust, and easy to maintain, making it widely used in carbon plants. However, it has problems with low energy efficiency, uneven heating, and long production cycles [8; 9]. The use of induction-heating technology in IHGFs is nowadays chosen in many industrial, domestic, and medical applications due to its highheating rate, high-limit temperatures, flexible furnace chamber layout, safety, cleanliness, and precise control [10]. The induction-heating system is the central component of the IHGF. It comprises an alternating-current (AC) power supply, an induction coil, and a heater. The AC power supply delivers the alternating current to the induction coil, which generates an alternating magnetic field. The heater, exposed to the magnetic-field radiation, is rapidly heated by the ohmic heating of eddy currents. The induction coil is a crucial component of the induction-heating system, as it transmits induced electrical energy, directly impacting the heating rate and efficiency. The conductors used for induction coils usually play a key role in the design of the induction coils, and copper conductors are now widely used due to their excellent high electrical conductivity and moderate cost. During the operation of an induction furnace, the copper coils carrying the alternating current (AC) generate heat due to AC losses (coil losses) [11], and, in order to prevent heat buildup and coils overheating, a common industrial practice is to pass cooling water inside the copper coils. The cooling water absorbs the heat generated by the coil losses as well as the heat conducted from the heater and converts itself into warm water of 40-50 \({}^{\circ}\)C, which has a very low industrial use value. This process causes a large amount of energy waste [12]. For induction-heating furnaces, the energy loss due to cooling water is about 70% of the total energy loss [13]. The energy efficiency of an induction furnace is the product of its electrical efficiency (\(\eta_{\text{d}}\)) and thermal efficiency (\(\eta_{\text{r}}\)). Refs. [14; 15; 16] show that the electrical efficiency is related to the distance between the induction coil and heater, the number of turns of the coil, the depth of the current penetration, etc. The thermal efficiency mainly depends on the insulation performance of the induction furnace, which is related to the selection of the furnace lining material, the thickness of the insulation layer, and so on. The induction coil structure based on copper pipes plus cooling water occasionally leads to a contradiction between the electrical efficiency and thermal efficiency: increasing the thickness of the insulation layer is conducive to improving the thermal efficiency, but the increase in the coupling distance between the coil and the heater leads to a decrease in the electrical efficiency [17].