# Design and Numerical Study of Induction-Heating Graphitization Furnace Based on Graphene Coils
## 3 Results and Analysis
### Comparison of Energy Efficiency
#### 3.1.2 Energy Efficiency Comparison Experiment  
This paper describes a simulation of the heating processes of two furnaces. To facilitate the comparison, we applied different constant powers to the two furnaces and compared the amount of power required to reach the target temperature of 3100 \({}^{\circ}\)C after 20 h of heating. The induction furnace with the copper coil has a heating power of 201 kW, while the induction furnace with the graphene coil has a heating power of 135 kW. To study the heating rate, a temperature measurement point is selected inside the furnace. Figure 4a shows the relationship between the temperature and heating time at the selected points for the different types of furnaces. The figure shows that the copper-coil furnace initially heats the charge faster due to its higher heating power. However, around 2000 \({}^{\circ}\)C, the heating rate slows down significantly. In contrast, the graphene-coil furnace has a more stable heating rate, and there is no significant decrease in the heating rate in the high-temperature region.  
Figure 4b shows the curves of the heat flux versus time at the heater/insulation interfaces for both furnaces. The heat dissipation of the graphene-coil furnace is significantly reduced compared to that of the original furnace. As shown in Equation (14), the graphene-coil furnace has no in-coil cooling water and is further away from the cooling source (\(\mathrm{T_{0}}\)), so the heat dissipation power is lower for the same temperature difference, which allows it to maintain a higher heating rate in the high-temperature region.  
Figure 5a,b show the temperature variation in each part of the two furnaces during the heating process. The energy absorbed by each part during the heating process was calculated, and the energy efficiency performance parameters were derived according to Equation (13); the results are shown in Table 2. In terms of the electrical efficiency, the graphene coil is closer to the heater and the coupling distance between the two is short, which has a higher electrical efficiency compared to the copper coil. In terms of the thermal efficiency, the cold source of the copper-coil furnace is mainly located in the coil (coil  
cooling water), closer to the heater, while the cold source of the graphene coil is located at the far end of the furnace shell. In addition, the ohmic heat of the graphene coil is also used in the heat insulation of the heater, and thus the insulation performance is better. Taken together, only 12.02% of the coil input energy is absorbed by the heated charge in a conventional copper-coil induction furnace, while the graphene-coil furnace has an energy efficiency of 17.67%. As shown in Figure 5c, to heat the same mass of charge, the energy absorbed by the cooling water in the former furnace is 1506 kWh higher than that in the latter furnace, which has a higher temperature at the end of heating the insulation layer and absorbs 314 kWh more energy.  
Due to the advantages in the electrical and thermal efficiencies, the graphene-coil furnace has a higher energy efficiency compared to the copper-coil furnace, and for heating the same mass of charge, the energy consumption of the graphene-coil furnace can be reduced by 33.34%. It can be concluded that the graphene-coil furnace is more efficient than the copper-coil heating furnace in terms of energy utilization.  
Figure 4: (**a**) Temperature rise curves of two furnaces; (**b**) heat dissipation powers of two furnaces.  
Figure 5: _Cont_.