I recommend the sizes (approximately, very difficult and not linear dependence)
For small furnaces height of liquid metal / diameter of liquid metal = 0,5
For the big furnaces from 0,5 to 1
The coil
Internal diameter / height = 1 - 1,2 (approximately, depends on thermal losses)
Coil height / height of liquid metal 0,9-1.3 (depends on thermal losses)
In small furnaces - small EFFICIENCY, the basic problem thermal losses.
I have specified factor of transformation 1/10 - 1/20 for connected one after another (not parallel) the coil and the condenser, a resonance on a secondary coil (low voltage)
For an input in the inverter of 220 volt of 50 Hz
The thermal protection for your furnace the coil/ crucible, is enough 2-2.5 sm
Thickness of a crucible not less than 5 mm (I am not assured, there is no operational experience with stainless steel
For an ordinary steel of 10 mm 17 000 Hz), desirable frequency of 66 000 Hz. It will allow to apply and a crucible from graphite
If you do not have electric leaks, it is possible to manage and without coil isolation.
I do isolation by special fiber glass fabric by the impregnated pitch
Two layers a thickness of a layer of 0,2 mm. I wind a copper tube on all length, a photo I will show after. Water in the coil cools isolation.
For industrial big coils, isolation multilayered, difficult
"Should I protect the inner wall of the crucible with some "stuff"?"
It is desirable, aluminium reacts with iron, but it is very difficult. I the reference to manufacturers of crucibles.
For a house, fusion admit also a steel crucible, OK
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Photo of furnaces for jewellers
http://www.mexel.narod.ru/Foto.html
The sizes of graphite crucibles for fusion of gold, silver, copper, FOR independent manufacturing
http://www.mexel.narod.ru/Tigel.html
Designs of furnaces
http://www.mexel.narod.ru/Draiv2.html
Thermal protection of crucibles, the sizes
http://www.mexel.narod.ru/Draiv1.html
http://www.mexel.ru/
Site in Russian
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