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Thermal problems

Is it possible to use QuickField to calculate a 2D radiative transfer between two peace?
Not possible. Radiative heat transfer between two pieces should take into account surface positions, optical characteristics etc.

What is the definition of "surface Joule heat"?
Say, there are some heat losses in the body. It can be described by heat density. If you calculate integral of heat density in the whole body you will get Joule heat in the volume. If you calculate integral of heat density along the surface area of the body you will get Surface Joule heat.

It seems an HT problem only accepts heat generation from one problem. If the HT problem is linked to more than one problem, it picks the last problem listed. Is this how it is supposed to be? I want to model the heating by two RF generators.
Heat transfer problem can refer to only one source problem. So if you want to have more than 1 heat source you have to use "manual" coupling. I mean you solve 2 thermal problems each linked to specific magnetic problem. Then you summarize the temperatures.

As boundary condition of the bottom face we would like to use heat flux instead of setting fixed a temperature. Other boundary conditions are set to no-flux (i.e. "none") so neglecting convection. The problem is, that the program requests more boundary conditions.
To avoid indeterminacy when solving heat transfer problem you have to specify known temperature in any point or convection at any boundary.

Which is a rotation axis in axisymmetric problem?
The axis of rotation is a horizontal one. Z = X, R = Y.

is it possible to simulate liquid metal in the crucible inside inductor, for example aluminum in QuickField software?
You can specify conductivity of liquid. But you cannot simulate motion of the liquid.

What is the volume power of a heat source? (you can find it on the block label properties in a transient thermodynamic problem)
Volume power [W/m3] = Power [W] / Volume [m3]. The other name is power volume density.

How can I simply model heat transfer between a substance and a pipe that passes inside of it (and the liquid inside of the pipe)?
With QuickField you simulate solid(motionless) media only. You should remove liquid/gas and set convection condition on the boundary.

I am using radiation losses at the edge between conductor and air. After solving, the integrated heat flux depends on the direction of my contour. Not just the opposite sign, a different absolute value.
When you set a radiation condition at any edge that does not mean that the heat flux go through the edge. The flux runs away from the edge. Switch on the vectors of heat flux and you will see that there are two different fluxes: one from real conductor to the edge with radiation and another from air toward the edge with radiation. It is not correct to set radiation on inner surfaces.