## 6 Results and Discussion  
Figure 5 demonstrates the contours of \(A_{0r}\) of rz cross section and the iso-surface for axisymmetric coil and spiral coil at \(I\) = 1250 A and \(F\) = 16 kHz. Axisymmetric \(A_{0r}\) are illustrated in Figure 5a for the axisymmetric coil, and it can be seen that it is meaningful 2D axisymmetric model substitute for 3D model for axisymmetric coils. However, it also can be found obviously that \(A_{0r}\) is non-axisymmetric as shown in Figure 5b. In addition, as presented in Figure 6, the profile of \(A_{0r}\) and \(A_{0i}\) in r-direction for axisymmetric and spiral coil also can prove the above viewpoint. Therefore, it demonstrates that the coil structure has a great effect on the electromagnetic field. Figure 4: \(A_{0}\) and \(T\) profiles in r-direction for different meshes. (**a**) real part of magnetic potential, \(A_{0r}\); (**b**) imaginary part of magnetic potential, \(A_{0i}\); (**c**) temperature, \(T\). Figure 5: Contours of \(A_{0r}\) for axisymmetric and spiral coils at \(I\) = 1250 A and \(F\) = 16 kHz. (**a**) axisymmetric coil; (**b**) spiral coil. In SiC growth chamber, SiC powder surface, graphite crucible inner surface, and SiC crystal surface radiate strongly. To study the relationship between radiation and conduction heat transfer quantitatively, Figure 7 presents the radiation heat flux (\(q_{r}\)) and conduction heat flux (\(q_{cz}\)) of SiC powder surface and SiC crystal surface along with radius. It can be seen that: (1) both \(q_{r}\) and \(q_{cz}\) on SiC powder surface are bigger than 0 as shown in Figure 7a, which illustrates that the surface owns higher temperature and release heat; (2) both \(q_{r}\) and \(q_{cz}\) on SiC crystal surface are less than 0 as shown in Figure 7b, which illustrates that the surface owns lower temperature and absorption heat; (3) the temperature in the furnace is non-axisymmetric which can be demonstrated by the non-axisymmetric profile of \(q_{r}\) and \(q_{cz}\) on both surfaces; (4) \(q_{r}\) = 160\(-\)260 KJ/m\({}^{2}\) and \(q_{cz}\) = 240\(-\)390 J/m\({}^{2}\) on powder surface, \(q_{r}\) = \(-\)160\(-\)\(-\)80 KJ/m\({}^{2}\) and \(q_{cz}\) = \(-\)270\(-\)\(-\)240 J/m\({}^{2}\) on crystal surface, so \(q_{r}\) is about 2\(-\)3 orders of magnitude greater than \(q_{cz}\). Figure 8 shows profiles of temperature of powder surface and crystal surface along with r axis with and without radiation heat transfer, respectively. It can be found that: (1) the average temperature at \(-\)0.9 < r/R < 0.9 is 3247.9 K without radiation and it decreases to 2651.7 K with radiation on powder surface; (2) the average temperature is 2212.6 K without radiation and it increases to 2555.3 K with radiation on powder surface; (3) the temperature gradient is 373.1 K/cm without radiation, while it decreases to 34.76 K/cm, which in the suitable temperature ranges (1-50 K/cm) for SiC crystal growth introduced in reference [14]. The above simulation results illustrate that the reasonable temperature  
Figure 6: Profiles of \(A_{0r}\) and \(A_{0i}\) in r-direction for axisymmetric and spiral coil at \(I\) = 1250 A and \(F\) = 16 kHz. (**a**) \(A_{0r}\); (**b**) \(A_{0i}\). Figure 7: Radiation and conduction heat flux on surfaces of SiC powder and crystal. (**a**) SiC powder surface; (**b**) SiC crystal surface. difference can be gotten if radiation heat transfer is considered [7] and the radiation is helpful to uniform the temperature field in the chamber. Figure 9 shows temperature fields of both axisymmetric coil and spiral coil in the furnace at x = 0 cross section, and some similar results with two dimensional axisymmetric model [7; 14; 18] are obtained: (1) SiC powder and graphite crucible regions own the highest temperature (about 2700-2980 K) which is helpful for SiC to sublimate steadily, this is because the induction coil and induction heat locate in the areas surrounding graphite crucible.