Induction heating / cooking - and where to get low ESR high VAR caps.

this is

right choice

ordinary steel case

Perhaps.

It's not so much containing it that's worrying me - it's losses in the case.

Somewhat pulling this out of thin air - just thoughts.

Winding differently may be interesting for a number of reasons, but has some issues. You really want the pan to be in the very near field - this does several nice things.

The pan is a single turn load, with a resistance of something like k*thickness/r^2 .

k is the resistivity of the material, and the thickness depends on whichever is smaller - the pan thickness, or a skin depth.

The skin depth varies with frequency - but you really want to be at the highest frequency you can. This is as many losses in the circuit - the ESR of the resonant caps and the plate inductor, are dependant on the circulating current in the resonant circuit. (well, its square).

Your ideal cooker would have a very good coupling between the pan and the coil, enabling it to operate at high frequency, minimising skin depth (and coincidentally enabling use of copper pans).

The ferrite helps with this by vastly improving the coupling to the pan in the face of the required ~15mm space that's taken up by the actual top of the cooker (glass or whatever), and some space or insulator over that to stop the coil overheating when the stovetop is at 250C.

If you made the coils multi-regional (or indeed much smaller) and maintained that 15mm gap, then you've effectively lifted the pan off the surface a bit more, worsening the coupling, and meaning that it doesn't heat nearly as well, or efficiently.

Hmm. I need to think some more about this. It is improving my knowledge of transformers :)