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Old   July 16, 1998, 09:48
Default BC for constant heat flux
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I am doing heat transfer calculations for duct flows with an in house code. The constant temperature BC was already written but I want to use constant heat flux BC in periodic flow case and I am using a finite volume code, any suggestions?

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Old   July 16, 1998, 10:36
Default Re: BC for constant heat flux
Jonas Larsson
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It's impossible to give an answer to that without further details.

The simple answer is that you just set

dT/dn = 1/k * q

on the wall-face of the control-volume when you derive your equations. q is given by you as a boundary condition.

How this should be implemented in your code depends entirely on what kind of code it is, how it is structured, which solution variables you are using, if you are resolving the boundary layer or if you are using wall function etc.
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Old   July 17, 1998, 15:02
Default Re: BC for constant heat flux
Philip Zwart
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If your code is a finite volume code this should be dead easy. Then the boundary conditions simply represent the flux integral through the boundary faces, which in your case is just the specified heat flux times the face area; ie, just dump q*A into the right-hand side of your equation. Then, after the equations are solved, you can back out the boundary temperature using the relationship

q = -k dT/dn

(or analogous expression if wall functions are used, as Jonas pointed out).

I'd also like to mention that some people have a far more convoluted approach to implementing boundary conditions in FV methods. The text by Hoffman & Chiang, for instance, wants to move the storage location for cells adjacent to the boundary onto the boundary face itself, so that the conservation equation for cells adjacent to the boundary is discarded for T-specified walls. This can lead to conceptual inconsistencies, including the need to apply flux-specified boundary conditions iteratively (rather than directly as above). Also, ambiguity issues similar to those mentioned in another thread from a few days ago can arise.

Hope this helps.
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