# How to calculate the energy transfer between working coil and working piece and dissipated energy of working piece in induction heating?

For who don't know how does induction heating work, a short description can be found here.

However, my question is about physics. Assume I have a coil inductor calculated carefully 50 uH as below: the inductors Diameter is 20 mm and length is 1.8 * 40 = 72 mm.

9.4 A AC current is applied to the inductor at 33 Khz.

Now that I know how my inductor works, assume I placed an iron stick (1 cm diameter and 20 cm length) into the center of the inductor as below: How can I calculate the dissipated energy as heat on the iron stick? How can I calculate in how much time this system can heat the iron stick up to 500° celsius?

What kinds of calculations are involved here? Could you explain them step by step?

edit:

this is schematic: This is the power graph of the coil inductor: • Have you measured inductance with the iron stick? – user115350 May 22 '16 at 15:38
• No? I believe it won't do much effect since it is assumed to have infinite resistance. It is considered as open loop. – Alper91 May 22 '16 at 15:39
• I was thinking that changes permeability and thus changes inductance. Resistance inside the iron stick has limited value. That, with eddy current, is the source of heat. The quickest way to get the time is to measure the power input to the coil and, with certain efficiency 9(~90%), mass of iron stick and heat capacity, you may find the time by integral. However, this assumes there is no heat loss. – user115350 May 22 '16 at 16:40
• Correction! Inductance changes with the magnetic material inside of it. It increase with magnetic conductor presense. – Alper91 May 22 '16 at 16:41
• @user115350 Inductance changes and it leads current to decrease. Also the frequency decrease a little. But, it oscillates anyway. Power input to coil changes, its awarage power is like zero. How should I calculate the power? I added the graphs to the question. – Alper91 May 22 '16 at 16:59