Boundary element solution of 2-D thermal problem with a ferromagnetic conductor moving inside an induction coil

In induction heating and surface hardening applications, the calculations of the power density distribution tor Z-D terromagnenc billets moving through an induction coil are important, especially in designing the induction coil. In practice, the motion of the billet in and out the coil is necessary to obtain either a uniform heating process or a local heating process. These processes are usually required for a wide range of industrial applications such as: (a) uniform heating for surface hardening applications, and (b) local heating for welding applications. Previously, the thermal effects and the noniinearity of the conductor material were considered in developing an iterative algorithm for the calculations of the surface power density distributions for conductors having rotational symmetry. In the present work, this algorithm is modified to take into consideration the effects of the conductor motion. The algorithm is based on an Impedance Boundary Condition formulation derived for the semi-infinite conducting space problem combined with the time dependence temperature rise equation.