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Fourier number in fluid mechanics

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Old   April 18, 2017, 09:24
Default Fourier number in fluid mechanics
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Agustín Villa
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Hello everyone,

recently I noticed about the use of the Fourier number for heat transfer, which is
Fo=\alpha\frac{\Delta t}{\Delta x ^2}
and it should be taken into account to set the proper time step when heat transfer is present. Have you ever used it? I have been told that it should be taken into account in natural convection, specially at low Prandtl number, it is, when your thermal diffusivity alpha increases.
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Old   April 18, 2017, 12:50
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Filippo Maria Denaro
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This number appears only after a space-time discretization (in your example 1D) is performed. It makes sense for the analysis of the numerical stability constraint when explicit schemes are used. For example, a first order in time and second order in space (FTCS) scheme leads to fix a typical stability value <=1/2.
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Old   April 25, 2017, 01:15
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Yes it should be considered & it's super important for heat diffusion dominated problems.

In transient conjugate heat transfer problems for example, the Fourier number can limit your time-step much more than your convective Courant number (because alpha in solids is large).
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Old   April 25, 2017, 05:09
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Thanks for your answers. Most of the times, when I see this number, there is conjugate heat transfer. This number, should it be taken into account for single-phase heat transfer as well?
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Old   April 25, 2017, 05:52
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Quote:
Originally Posted by agustinvo View Post
Thanks for your answers. Most of the times, when I see this number, there is conjugate heat transfer. This number, should it be taken into account for single-phase heat transfer as well?

Yes! Again, this number appears only after a numerical discretization of the parabolic heat transfer is introduced. The physics dictates the value of alpha but dt and dx are of numerical character.
See Chap.2 http://mathcenter.hust.edu.cn/Upload...98740d59f8.pdf
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Old   April 25, 2017, 21:37
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Quote:
Originally Posted by agustinvo View Post
Thanks for your answers. Most of the times, when I see this number, there is conjugate heat transfer. This number, should it be taken into account for single-phase heat transfer as well?
Yes, it should be! However, usually the diffusion time-scale is small compared to convective time-scale in a fluid. For example, your cell Peclet number is usually more than 1 (and that is why you use upwind schemes). So usually your Courant number is usually limiting and not the Fourier number. However, I don't really have a feel for Fo vs Pe vs Co in natural convection. You should check to make sure. You are also right, for low Prandtl numbers the Fourier number becomes more important.
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