# Design and Numerical Study of Induction-Heating Graphitization Furnace Based on Graphene Coils
## 3 Results and Analysis
### Effect of Coil Parameters
#### 3.4.1 Effect of Coil Conductor Conductivity  
Given that the electrical conductivity of GCMs is still lower than that of copper, it is important to pay special attention to the coil losses. The ohmic heating of the current can be calculated using Equation (11), which takes into account the skin loss and the neighbor loss of the high-frequency current. The effects of the coil size and conductivity on the coil losses are discussed in this study. The side length of the square coil was varied from 60 mm to 100 mm, while the conductivity of the graphene coil was varied from 1 to 7 \(\times\) 10\({}^{6}\) S/m. It is clear from Figure 10a that the coil losses are not uniformly concentrated in the interior of the conductor. For coils of the same cross-sectional area, the area of coil losses decreases as the conductivity of the coil material increases. For the same coil with a conductivity of 1 \(\times\) 10\({}^{6}\) S/m, increasing the cross-sectional area shrinks the region of high losses. It should be noted, however, that because the distance between the coils is fixed, the proximity effect is enhanced as the distance between the coils decreases with the increasing coil area. Therefore, increasing the tube radius will reduce the skin effect while increasing the proximity effect.  
Figure 10: (**a**) Distributions of coil losses for different coil conductor conductivities and coil cross sections. (**b**) Effects of coil area and conductivity on coil losses.  
Figure 10b summarizes the coil losses for different coil conductor conductivities and different coil cross sections. For coils of the same cross-sectional area, the variation in the conductivity of the coil conductor significantly affects the magnitude of the coil loss. When the conductivity of the conductor material is varied from 1 \(\times\) 10\({}^{6}\) S/m to 7 \(\times\) 10\({}^{6}\) S/m, the total coil loss decreases from 18.13 kW to 6.67 kW for the same magnitude of alternating current (AC), while increasing the cross-sectional area of the coil has no significant effect on the coil loss.  
The effect of variations in the coil conductivity on the temperature distribution of induction furnace coils was investigated, as shown in Figure 11. It was observed that as the conductivity of the conductor material increased from 1 \(\times\) 10\({}^{6}\) S/m to 7 \(\times\) 10\({}^{6}\) S/m, the temperature of the coil decreased from 2561 \({}^{\circ}\)C to 2502 \({}^{\circ}\)C, and the energy efficiency of the induction furnace improved from 17.76% to 18.11%. This improvement is attributed to the reduction in coil losses as the conductivity of the conductor material increases, which, in turn, reduces self-heating and allows more energy to be used for induction heating, thereby increasing the energy efficiency of the induction furnace. It is evident that increasing the conductivity of the coil materials is beneficial for improving the energy efficiency and durability of induction furnaces.  
Figure 11: (**a**) Temperature distributions of induction furnace for different coil conductivities. (**b**) Temperature distributions along r-axis. (**c**) Effect of coil conductivity on energy efficiency.