Discussion Forum

I am trying to build a simple, 2D model of a resistively-heated tube furnace. The furnace is simply a hollow ceramic cylinder with wires passing down the length to act as resistive heating elements. In the end I'd like the model to incorporate (i) resistive heating in the wire heating elements, (ii) heat transfer from the wire to the air inside the furnace and the interior wall of the ceramic tube by radiation and convection, along with convective flow of the air in the furnace, (iii) thermal conduction through the ceramic cylinder wall, and (iv) heat transfer from the outside wall of the cylinder to the outside air, primarily by convection because it should not be hot enough for radiation to be important.

I am new to FEM in general and Comsol in particular, and while I have been through several of the relevant tutorials I am still stumped by several points in attempting to create my own model.

Here are some points of confusion:

1. The first attached file (tube_furnace_1.mph) is a very simple model with a circular heating element at the center and a surrounding region of air. For simplicity, I modeled the heating element as a boundary heat source where the power density (W/m^2) is calculated from a specified voltage drop along the wire and the wire geometry. What I don't understand is why Comsol wants to make this same boundary also thermally insulating, since there should (obviously) be a thermal flux across it. I can avoid this by specifying the temperature of the boundary, but this seems at odds with the idea of specifying a power density even though Comsol will happily let me have both. I guess I am confused about what the proper boundary condition here should be.

Also on the same model, Comsol cannot find a steady-state solution, even though the time-dependent solution seems to become constant at long times.

2. The second attached file (tube_furnace_2.mph) is the same model as above, but now with the ceramic cylinder included. Here I am confused about the right physics to use to incorporate thermal transport from the interior air to the cylinder and thermal conduction through the cylinder wall. If, as in the attached file, I use a "Heat transfer in solids" domain under the "Heat transfer in fluids" node, then Comsol complains that I have not specified the dynamic viscosity in the ceramic ... but I have told Comsol that the ceramic is a solid, so why does it need a viscosity? If I add a separate "Heat transfer in solids" node then I can avoid this error, but in this case there appears to be no coupling between the air in the cylinder and the cylinder walls.

I am sure that there are other errors I am making, but these two seem to be my primary stumbling blocks at present. Any suggestions would be greatly appreciated.

Todd Hufnagel