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Conjugate Heat Transfer in rectangular pipe with cylindrical pins

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Old   November 20, 2019, 09:46
Default Conjugate Heat Transfer in rectangular pipe with cylindrical pins
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I am trying to build a 1D model of CHT in a rectangular pipe with cylindrical pins. The idea is to compare it with a baseline case with no pins. The next step would be to construct the 3D CFD model.

The geometry consists of a rectangular metal pipe of thickness "t" and length "L", which has a rectangular cross section of sides "a" and "b". The interior of the pipe contains a grid of staggered cylinders of diameter "d", which cross the full height of the pipe. The geometry is shown in the two following images for clarity:

The fluid will evacuate a heat source modeled as constant along the length of the tube. There are namely 2 parameters of interest: the temperature of the metal at the exit section (so maximum metal temperature), and the pressure drop along the pipe from entrance to exit.

I have several questions concerning the heat transfer.

1. Considering the baseline case (no pins in the interior), the heat transfer coefficient between the solid and fluid is modeled with experimental correlations widely available in the literature. These correlations are normally functions of the Reynolds number. For this specific problem the characteristic length is normally taken as the hydraulic diameter. What determines the characteristic length of the problem?

2. Considering the case with the interior pins. Are there any available experimental correlations for the HTC/Nusselt Number that deal with flow inside of a pipe with cylindrical pins (or other types of obstacles)?

3. If a correlation does exist, what value should be chosen as the characteristic length this time? Should it still be the hydraulic diameter? Or is a small correction needed for the presence of the cylindrical pins?

4. If no experimental correlation exists, is it correct to consider the heat transfer as the superposition of two independent cases for which correlations exist? In this case I would consider the baseline case (flow inside a rectangular pipe) and cross-flow in a staggered bank of pins. In what way could I combine them to produce a feasible end result?

5. As far as the prediction of the results go, I expect the addition of the pins to increase the pressure drop along the pipe in relation to the baseline case, but to increase the heat transfer. This would be a consequence of the increase in surface area introduced by the pins. However, how would the HTC be affected?

Thanks in advance
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characteristic length, conjugate heat transfer, heat transfer coefficient, reynolds number

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