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Conjugate heat transfer pipe flow

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Hello,

I am trying to simulate a very simple laminar flow inside a pipe problem with a constant temperature at the walls. I have a cylinder made of water(liquid), and where one part is kept at a constant temperature at the wall, and rest of the wall changes from 293 to 393 for the remaining of the length.
My biggest issue is not so much the heat transfer part of the problem, but the velocity profile at various points of the pipe. I know I should get the same velocity profile everywhere and it should be a parabolic profile and since I am using a mean velocity of 0.02 m/s I know that my Vmax will be 0.04. However I only get this velocity profile at the inlet and not in the rest of the pipe. When I keep the walls temperature constant ( at 293 throughout) I get the correct velocity profile, it is only when I inflict the temperature gradient when the velocity profile changes, even though I am keeping my properties constant.
Any help will be appreciated. I am attaching my model

Thank you very much!

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