Thermal PDE in cylindrical coordinates at the origin

Question

Tobias 2019-1-11

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https://ww2.mathworks.cn/matlabcentral/answers/439350-thermal-pde-in-cylindrical-coordinates-at-the-origin

回答： Tobias 2019-7-29

Hi,

I have a problem with a thermal PDE in cylindrical coordinates. I followed the example in Heat Distribution in Circular Cylindrical Rod .

The script runs without errors, however the solution has peculiar spot at z = 0, r = 0 where the Temperature is constantly zero. The heat source at that spot is well larger than zero and all around the spot a temperature which is as expected is reached.

I tried changing several of the pde SolverOptions or choose the mesh differently, however nothing of what I tried was successful.

Does anybody have an idea what I can do to fix this issue?

Thanks in advance

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Answer 1

Tobias 2019-7-29

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My error was in not transforming the boundary condition correctly. I had assumed that the BC in the example just had a curios form, but the *region.y originated from the transfer to cylindrical coordinates.

With the correct BC the solution makes sense on the whole domain.

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Answer 2

Svetlana Pease 2019-1-11

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Hi Tobias,

Are you talking about the steady-state or transient solution? The only zero temperature I get is for the transient solution at t = 0 (time step is 1 for t = 0).

Regards,

Svetlana Pease

MathWorks Documentation Group

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Tobias 2019-1-18

Is there a possibility to create the mesh with two different Hmax? I naively tried to assembly the mesh in two steps but I was not allowed to change the read-only FEMesh.

If I calculate my problem in full 3d the problem does not appear (however I cannot choose my grid fine enough to get rid of other oscillations)