Induction heating for case hardening applications

It is observed that the equations describing induction heating in ferromagnetic materials are rather nonlinear. Although the thermal properties are nonlinear, the greatest nonlinearity arises from the ferromagnetic behavior of the material. A way of circumventing this difficulty while retaining the important magnetization curve is presented. A numerical solution accounting for temperature variations in the saturation magnetization, electrical and thermal conductivities, and specific heat is presented. It is found for case hardening applications that only a narrow near surface region heats to the vicinity of the Curie temperature, and a simple theory describing this region is derived. Just beyond the near surface region a sharp temperature gradient results which is of importance in case hardening. A simple expression for the gradient is developed. These expressions, verified by a complete numerical analysis, aid in the choice of an induction heating excitation system for case hardening applications.