Induction melting of steel - melting time calculation

Hi,
We're trying to size a small induction melting furnace (similar to those used in the jewelry making industry) for our application and I was wondering
if anyone with some experience in this subject can help answer the following question:
How long would it take to melt 3.5 lbs of 4140 Steel (2"Dia. x 4"L bar at 1600 deg. C, 7.8 g/cc) with a 10 KW medium frequency (10-30Khz) water-cooled induction melting machine using the proper crucible (350 cc capacity)? Are there any other factors missed here that would influence this calculation?
Here's a typical small melting furnace (this one is 9.5 KW):
http://tinyurl.com/8dujn
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I've no experience in melting steel in crucibles (I've melted lead and i had no worries about time). But there are equations for heating processes.
One dimensional heat equation
Diffusion Equation
Laplace's equation in two dimensions
d'Alambert, Dirichlet and Laplace made studies in the area.
The math is quite tricky.
--
With a blob of grease here and a bit of weld under there.
If you don't do it right it'll fall apart next year.