Please read my note a bit more carefully.
I did NOT suggest that inductance is a function of hysteresis loss.
The disappearance of hysteresis loss above the Curie point reduces the heat input to the workpiece. Because the total losses are lower, the Q of the work coil at resonance is higher.
At the same time the permeablity drops to one. It is THIS change that results in the immediate and measurable drop in work coil inductance. For optimum operation this requires a corresponding increase in tank capacitance.
I didn't comment on the typical permeabilty values of steels, because, taken in isolation, permeability figures can be very misleading. When modified by the frequency dependent skin effect and the poor coupling between coil and workpiece, the apparent permeability may drop to two or less - almost independent of the nominal DC value.
Measured results on a 1.1" ID work coil with and without
0.75" dia workpiece (all cold) :-workpiece inductance effective series loss at 1600Hz Air 0.94 uH 1.5 mOhm Steel 1.81 uH 9.7 mOhm Aluminium 0.81 uH 2.5 mOhm
The difference between the air series loss and the loaded series loss is a good indication of the fraction of the power which reaches the workpiece. The aluminium figures are roughly what could be expected from steel when above its Curie point.
The series loss component is a true measure of the power input to the workpiece. Eddy current loss and hysteresis loss are the basic loss mechanisms. Below Curie point both eddy current loss and hysteresis loss rise with increasing flux density
As the steel passes through its Curie point the reduced permeability results in a smaller fraction of the work coil field passing through the workpiece. This reduction in flux density results in a drop in eddy current loss which is in addition to the disappearance of hysteresis loss.
At higher frequencies (because of the smaller skin depth of the heating current) and with poorly coupled workpieces (only occupying a small fraction of the useful work coil field),the work coil inductance change is small, and as you point out, the flux density change can then be the dominant effect.
Jim