Transformer frequency contradiction on induction heating

[abdulbadii]

TL;DR

Help solve tangled transformer freq contradiction over induction heating

As a transformer freq bet higher, inside induction get more efficient i.e. less loss:

1. Hysteresis loss = η * Bmax^n * f * V.
2. Eddy current loss( proportional to B2mf2Bm2f2 )Now it seems that losses increases with increase in efficiency...
But the above equations are valid when max flux density Bmax remains constant.

The gist is that when increasing the frequency flux density does not remain constant, it actually decreases with increase in frequency, as

V = 4.44 . Bmax . A . f . Tp

Now how is it on Induction_heating, as it's read more, the more contradiction is to above

 

[Tom.G]

Yeah, seems counter intuitive doesn't it?

But it sounds like the Skin Effect is the important missing element here.

For DC and a solid conductor, current flow is evenly distributed throughout the cross section.

For AC, the current tends to concentrate towards the outer surface of the conductor. The higher the frequency, the thinner this conductive layer is, and the thinner the layer the higher the resistance.

For more details see:
https://www.google.com/search?q=electrical+skin+effect
https://www.google.com/search?q=inductive+heating
https://en.wikipedia.org/wiki/Induction_heating

Cheers,
Tom

 

[berkeman]

TL;DR Summary: Help solve tangled transformer freq contradiction over induction heating

As a transformer freq bet higher, inside induction get more efficient i.e. less loss:

1. Hysteresis loss = η * Bmax^n * f * V.
2. Eddy current loss( proportional to B2mf2Bm2f2 )Now it seems that losses increases with increase in efficiency...
But the above equations are valid when max flux density Bmax remains constant.

Can you please post a reference for your equations? And the 2nd equation is pretty unreadable, IMO. Please learn to post equations using LaTeX (see the LaTeX Guide link below the Edit box). Thank you.

 

[Rive]

when increasing the frequency flux density does not remain constant

That equation is about the flux density in a given transformer, driven at different frequencies.
In reality, a transformer (the energy transfer type) is built for one frequency: to have the maximal permissible flux density at that frequency. And so (after rearrangement) that equation is what gives you the required turn count when you design for specific frequency / parameters.