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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:

inductor calculation

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.

AC current Frequency

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:

induction heating

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:

schematic

This is the power graph of the coil inductor:

power graph

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  • $\begingroup$ Have you measured inductance with the iron stick? $\endgroup$
    – user115350
    Commented May 22, 2016 at 15:38
  • $\begingroup$ No? I believe it won't do much effect since it is assumed to have infinite resistance. It is considered as open loop. $\endgroup$
    – Alper91
    Commented May 22, 2016 at 15:39
  • $\begingroup$ 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. $\endgroup$
    – user115350
    Commented May 22, 2016 at 16:40
  • $\begingroup$ Correction! Inductance changes with the magnetic material inside of it. It increase with magnetic conductor presense. $\endgroup$
    – Alper91
    Commented May 22, 2016 at 16:41
  • $\begingroup$ @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. $\endgroup$
    – Alper91
    Commented May 22, 2016 at 16:59

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