Square billet induction heating simulation

The aim of the simulation is to calculate the temperature distribution in a square billet during continuous heating. Because the length of the inductor is several times larger than its diameter, it can be considered infinitely long and the case can be solved only in transverse cross section. Because 2D software normally only calculates sections where current flows perpendicular to this section (e.g. longitudinal section through an inductor), 3D software must be used. The cross section is modeled as a thin slice. On its walls the conditions of symmetry are defined. Because the square billet is symmetrical, only one-eighth of this slice can be calculated. This significantly reduces the computational time.

Fig. 2 shows the distribution of Joule heat in the non-magnetic heating phase. Less heat is generated in the corners because the current shortens the path over the corner so there is lower current density. The distribution of Joule heat depends significantly on the skin depth. In the magnetic phase when the skin depth is small the billet is heated up almost homogenously over the surface. However, this phase does not last long.

Fig. 3 shows the final temperature distribution. The coldest places are in the corners. Two phenomena contribute to this: less heat generated by induction and a larger surface area of the corner which losses heat by radiation.

Fig. 2 - Joule heat, arrows indicate the current

Fig. 3 - Temperature