Steven,
It sounds like the circular disk will be mounted within an open frame, i.e. it will not have any heatsinking plates on either side of the disk, just open air. If that is the case, it would be expected that this device will burn up when run at 3 watt per square centimeter. With the conductor carrying over 3 amps, it would require a cross-sectional area of maybe 90-100 square mils to heat less than 45 dC as a single layer part. Since you have two layers contributing to heating, you might need a cross-sectional area of 180-200 square mils. You were proposing a conductor cross-sectional area of 68 square mils.
The self-heating can be reduced if the disk is able to be clamped between thermally conductive plates that do not interfere with the magnetic inductance that you require.
Vitreous Humor
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