Analytical Solutions of Electromagnetic Field and the Heat Generation Rate during Induction Heating of the Semi-infinite Body

The electromagnetic field and the heat generation rate distribution in the semi-infinite body which is heated by the induction coil, are obtained by solving the Maxwell equations through the analytical method. The impacts of the air gap width, induction coil width, current density and current frequency on the heat generation rate distribution in the workpiece are studied. The results show that the heat generation rate in the workpiece is in direct proportion to the square of the eddy current density and the square of the induction coil width. The heat generation rate follows the exponential attenuation law with the increase of the air gap width. The current density has effects on both the maximum heat generation and the heat generation distribution. When the effect of the air gap is neglected, the higher the current frequency, the larger the maximum heat generation rate. However, when the effect of the air gap is considered, the maximum heat generation rate will increase with the augment of the frequency when the frequency is less than the critical frequency and decrease with the augment of the frequency when the frequency is larger than the critical frequency, which is firstly reported in the paper. Moreover, the higher the current frequency, the heavier the heat generation rate attenuation in the workpiece.