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CEL expression for calculating heat flux to be applied as surface boundary condition

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Old   January 5, 2016, 15:37
Default CEL expression for calculating heat flux to be applied as surface boundary condition
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Hi everyone,
I am modeling the heat transfer thorough the concrete wall placed outside by using CFX.
I need to write a CEL expression to calculate heat flux based on following formula to be applied as a surface boundary condition. The ultimate goal of modeling is to get the temperature at both sides of the concrete wall. On the other hand the input data is the total heat flux calculated by following formula and the output is the temperature at both sides of concrete wall.

[Geometry attached]

Total heat flux = qsun - qconv - qrad

where qsun = (1-γ)I =
If t (time) is between 21600 (s) to 64800 (s):
qsun = 0.6 (2.0616 e-15 t4 – 3.8000 e-10 t3+2.3570 e-5 t2-2.5992 e-1 t+4.3738 e+3)
else, qsun = 0.

so qsun is a known parameter as a function of time.


and qconv = h∞ (Tsurface - T∞)

and qrad = σε ((Tsurface)4 - (Tsky)4)


so qconv and qrad are functions of time and surface temperature.

Please note that finally the total heat flux will be as a function of time and surface temperature. On the other hand the surface temperature has to be calculated by modeling step by step and then has to be plugged in the formula mentioned above to get the next total heat flux..

Any help or clue to write mentioned CEL expression will be greatly appreciated.

Happy new year

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Old   January 5, 2016, 16:28
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It should be straightforward with a set of expression as below

Quote:
LIBRARY:
CEL:
EXPRESSIONS:
MyHeatFlux = HeatSun + HeatConv + HeatTrad
HeatSun = ...
HeatConv = MyHTC * (Temperature - Tinf)
HeatTrad = MyEmiss * sigma * (Temperature^4 - Tsky^4)
Tinf = ... [K]
Tsky = ... [K]
MyHTC = ... [ W m^-2 K^-1]
MyEmiss = ...
END
END
END
Recall to use MyHeatFlux at the boundary condition, and you should be set.

NOTE: The approach above may not always converge since the discretization code assumes there is no dependency of the heat flux on the surface temperature; therefore, some type of linearization must be introduced. You can do that by adding a Energy Boundary Source with 0 strength but with a non-zero Flux Coefficient (recall the coefficient must be negative). How to determine the Flux Coefficient ? You may need to work it out by linearizing MyHeatFlux respect to the Temperature, i.e. dMyHeatFlux/dTemperature = ....

Hope the above helps,
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Old   January 5, 2016, 20:57
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Opaque, thanks a lot for your kindly respond. It will be so helpful, so I will work on it and let you know the results.
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Old   April 17, 2018, 07:57
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Thanks a lot Opaque, it solved my problem.

Quote:
Originally Posted by Opaque View Post
It should be straightforward with a set of expression as below



Recall to use MyHeatFlux at the boundary condition, and you should be set.

NOTE: The approach above may not always converge since the discretization code assumes there is no dependency of the heat flux on the surface temperature; therefore, some type of linearization must be introduced. You can do that by adding a Energy Boundary Source with 0 strength but with a non-zero Flux Coefficient (recall the coefficient must be negative). How to determine the Flux Coefficient ? You may need to work it out by linearizing MyHeatFlux respect to the Temperature, i.e. dMyHeatFlux/dTemperature = ....

Hope the above helps,
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Old   August 18, 2018, 15:19
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Hi every body
I am facing same problem in CFX. I have a variable heat flux on a surface. Would you please let me know how you define source coefficient? Should it be a number, if yes then why its negative here. Thanks a lot
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Old   August 19, 2018, 06:27
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If you are applying a heat flux on a boundary then this is a simple boundary condition, not a source term (and therefore should not require a source term coefficient).

To apply a variable heat flux over a boundary simply express the heat flux on the boundary as a function which varies over the boundary. This could be a CEL expression, an interpolation function or a user fortran function.
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Old   August 19, 2018, 12:27
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Please accept my thanks for your prompt reply. My B.C is variable heat flux and I can add to CFX as a CEL expression. It's almost similar to this one just mentioned in above comment:


Quote:
LIBRARY:
CEL:
EXPRESSIONS:
MyHeatFlux = HeatSun + HeatConv + HeatTrad
HeatSun = ...
HeatConv = MyHTC * (Temperature - Tinf)
HeatTrad = MyEmiss * sigma * (Temperature^4 - Tsky^4)
Tinf = ... [K]
Tsky = ... [K]
MyHTC = ... [ W m^-2 K^-1]
MyEmiss = ...
END
END
END
However I don't know how to consider source coefficient. Would you please let me know what I should put as a source coefficient for "MyHeatFlux" in the software? In other words I would like to know how to linearzie dMyHeatFlux/dTemperature, and how to put this linearized term into flux coefficient.
Thanks
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Old   August 19, 2018, 19:53
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Did you read my post? I will say it again:

Quote:
this is a simple boundary condition, not a source term (and therefore should not require a source term coefficient).
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Old   August 19, 2018, 20:38
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Hello again. Many thanks for taking the time for replying. Step by step I could figure out to solve my problem. However according to CFX manual, I should use 2D sources which are associated with boundary condition. Once you activate energy equation source, there is flux coefficient. I supposed similar to 3D source definition, I should use coefficient for 2D as well. Please enlighten me if I am wrong. Based on what had been written above I should assign "a non-zero Flux Coefficient (recall the coefficient must be negative)." So I am confused whether I should go for flux coefficient or not. Please let me know when we use source coefficient or Flux coefficient.
Thanks a lot for your help Glenn.
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Old   August 19, 2018, 20:41
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Just make the wall a heat flux boundary and apply your heat flux that way. No source term required, no source term coefficient.
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Old   August 19, 2018, 20:45
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Thanks a lot again. If you don't mind, May I ask when we use source coefficient AKA flux coefficient? Just want to learn more about it.
Many thanks
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Old   August 19, 2018, 20:56
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You usually use source terms to apply to a volume rather than a boundary face. The only time you would use source terms on boundaries is to apply a boundary condition too complex to apply with the built in boundary functions.

If you want to apply a source term you really need to read the documentation on it as there are a few issues you need to consider. The source term coefficient is one of them. In some cases you can ignore the source term coefficient as the solver calculates it for you (I suspect your case will not require calculation), but in some cases you need to define it. You work out the source term coefficient as the derivative of the source term with respect to the key variable in the equation. So in your case it would be the derivative of your function WRT temperature.
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Old   August 19, 2018, 21:05
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Thanks Glenn, really appreciated. So I will consider my variable heat flux on the wall in CEL expression rather defining it as a heat flux source.
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Old   August 20, 2018, 16:20
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Hello again,


I came to know that my heat source also varies with temperature and coordination (its a radiation simulation in 1D direction). Would you please let me know what should I do for energy source, and source coefficient?


What I have realized is I can again use CEL expression, but I don't know what I have to consider for source coefficient. I am simulation 1D radiation in a channel.


Thanks a lot
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Old   August 20, 2018, 19:32
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Post #12 answers all those questions.
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