Thank you for the very fast / nightly and clear answer. Reading your answer I feel ashamed of myself that I could not answer it myself.
Only issue is, that the values are typical ones for induction heating, so I did not try to push temperature in too fast. 150mm steel bar to be heated up 300 K in about 3 minute (plus homogenization time) is industrial standard. I checked with the induction system supplier and they confirmed that the 400 W/cm2 heat flux is doable. So I sticked to the 400W/cm2 but did not introduce it as "heat flux" value but via the "heat transfer coefficient". I ended up with the same situation (much too low temperature, negative temperatures under the outer shell). Any numeric tricks to enforce the equations ?
So if you are correct, then still there is the question, why - with the high heat flux - does the material not heat up accordingly in AVERAGE? So we do have a body, we see a certain heat flux (18kW) but the mean temperature does not show up with corresponding values ?
By the way, is there any specific book on CFD that you would recommend before starting - in my case - compressible laminar CFD studies with Elmer ?
For my first trial (air filled pipe) I could not even set-up a mesh with two bodies. What is the recommended (if possible OS) preprocessor for CFD studies ?
Thank you again for your support on this excellent OS program,