Agree with the above, answers. In particular if you look at the ratio between the thickness (or radius) and the electromagnetic penetration depth you have a dramatic change (decrease in efficiency) at a critical point. I point you to some publications that can give you all of the mathematics you need. See Figure 2.5 in the first reference.

Your heating rate is proportional to the square of the magnetic field. The magnetic field is impacted by the shape of the coil and the shape of the work piece (the graphite susceptor). At high frequency the 'work piece' excludes the magnetic field of the coil and concentrates the field into the airgap.

http://www.diva-portal.org/smash/get/diva2:630122/FULLTEXT01.pdf

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=true&tp=&arnumber=6626655&url=http://ieeexplore.ieee.org/iel7/41/6637065/06626655.pdf?arnumber=6626655

You can find more papers here:

http://www.metallurgy.no/Publications.htm

Most likely this relates to the conductivity of the graphite, which can vary over orders of magnitude.

Graphite can have different electrical conductivity and therefore different equivalent impedance form the point of view of the power stage.

I agree with Catherine that the conductivity at a given geometry determines the injected energy. The conductivity depends mainly on the ash content and porosity.

Porosity of graphite and also grain boundaries in sintered graphite crucibles, are two effective factors in response of crucible to the eddy current, and may change its behavior during induction heating.

I agree with Catherine, if she meant thermal conductivity. In addition, specific heat of graphite is also important. The highest processing temperature of graphite determines the degree of graphitization (perfection of graphitic structure), For example, graphitization at 3000 C will provide excellent thermal conductivity, while a lower temperature (1500 C) will lead to poorer thermal conduction of even to thermal insulation properties (depending on the nature of carbn precurosor)..

Agree with the above, answers. In particular if you look at the ratio between the thickness (or radius) and the electromagnetic penetration depth you have a dramatic change (decrease in efficiency) at a critical point. I point you to some publications that can give you all of the mathematics you need. See Figure 2.5 in the first reference.

Your heating rate is proportional to the square of the magnetic field. The magnetic field is impacted by the shape of the coil and the shape of the work piece (the graphite susceptor). At high frequency the 'work piece' excludes the magnetic field of the coil and concentrates the field into the airgap.

http://www.diva-portal.org/smash/get/diva2:630122/FULLTEXT01.pdf

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=true&tp=&arnumber=6626655&url=http://ieeexplore.ieee.org/iel7/41/6637065/06626655.pdf?arnumber=6626655

You can find more papers here:

http://www.metallurgy.no/Publications.htm

Thank you all for your answers - I have a lot to take in now!

Different grades of graphite have different electrical conductivity (amount of ash after burning would give you some indication about the graphite quality) and therefore they would heat in different ways. Beside of this some influence may have the amount and kind of binder added to graphite during crucibles production.

I have personally also observed that a given graphite crucible, whereas quite efficient during a first heating at 2800°C, was no more able to reach even 1500°C at the 3rd or 4th use, and even after increasing the power of the inductor. The reason was found to be related to the erosion of the crucible, which become thinner and thinner with time. Part of the crucible indeed turnt to carbon dust at such high temperatures. So this could be an additional reason for a loss of efficiency.

Alain

Degree of graphitization and R or H phases are other important factors.

Provided you have about 3 electromagnetic penetration depths in the wall thickness you will probably get good heating (5 would give even better results).

The results for heating of graphite will normally be good in the 5kHz and up.

Very high frequency will of course give very good results (~100 kHz), due to the low electromagnetic penetration depth.

For fixed coil current, you will get an increase in work piece heating by the square root of the frequency (f^0.5) at 'high frequency', due to the change of the electromagnetic penetration depth.

If you want to do some calculations, you of course need the electrical conductivity or resistivity of graphite vs. temperature. Graphite is a little bit special and first goes down and then back up in resistivity with temperature, which is very unusual.

If you don't have the data from the graphite producer, here are some good values to look at:

http://www.nist.gov/srm/upload/SP260-89.PDF

https://www-s.nist.gov/srmors/reports/8424.pdf?CFID=3035661&CFTOKEN=6edafc9ce82a2cac-4B9DC5E2-CC7F-F71B-D731FA33B4A3E950&jsessionid=f03033d68e4af4774bb0524c205336217d50

The above data also includes the thermal conductivity and other data useful for modelling purposes.

You will probably be happy doing model work using axial symmetry and I recommend considering using COMSOL.

There are three types of graphite, natural, artificial and synthetic.

Natural graphite is mined on natural deposits; artificial one is produced from coal, coke, carbides of boron, silicon, metals, during cooling of large masses of molten cast iron supersaturated with carbon, and so on.

Natural and artificial graphite comes from producers usually in particulate form as powders or flakes of several commodity groups. These row materials have colors from silvery (best quality material) to greasy black. The quality is determined mainly by the purity (carbon content) and graphite crystallite dimensions (the biggest crystallites have sizes of the order of hundreds of microns).

Particulate graphite is used to fabricate products of a necessary shape. For this purpose it is mixed with binding agents (as a rule coal-tar pitch, furan or phenolic synthetic resins). The initial pasty composition is pressed, baked, graphitized. Products have configuration of rods, plates, blocks, etc.

Synthetic graphite (pyrolytic graphite) is prepared by CVD methods typically by deposition onto a heated substrate (not necessarily graphitic) of thermal decomposition products of flowing gas mixtures containing hydrocarbons.

Answer to the question can be the following. Final graphite products (including of cause crucibles), depending on the quality of starting materials (including carbon content), fabrication methods and parameters, additional processing, are characterized by different density, porosity, degree of anisotropy, thermal, electrical and other properties.

For example, pyrographite have a minimal porosity (2–3 %), in other types porosity may be much higher. To reduce the porosity of a product, the latter is further impregnated with binding agents, baked, and graphitized. Such procedures can be done repeatedly.

Another example. The anisotropy of properties of graphite products obtained by extrusion is expressed quite clearly. On the contrary, it expressed less obviously when ordinal pressing of initial viscous masses is used.