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

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January 5, 2016, 14:37
CEL expression for calculating heat flux to be applied as surface boundary condition
#1
New Member

R-Sh
Join Date: Oct 2014
Location: USA
Posts: 23
Rep Power: 11
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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January 5, 2016, 15:28
#2
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Join Date: Jun 2009
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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,

 January 5, 2016, 19:57 #3 New Member   R-Sh Join Date: Oct 2014 Location: USA Posts: 23 Rep Power: 11 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.

April 17, 2018, 06:57
#4
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Rohit Tiwari
Join Date: Nov 2016
Posts: 10
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Thanks a lot Opaque, it solved my problem.

Quote:
 Originally Posted by Opaque 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,

 August 18, 2018, 14:19 Same problem #5 New Member   Join Date: Aug 2018 Posts: 6 Rep Power: 7 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

 August 19, 2018, 05:27 #6 Super Moderator   Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 17,746 Rep Power: 143 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. CFD USER infinity likes this. __________________ Note: I do not answer CFD questions by PM. CFD questions should be posted on the forum.

 August 19, 2018, 11:27 #7 New Member   Join Date: Aug 2018 Posts: 6 Rep Power: 7 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

August 19, 2018, 18:53
#8
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Glenn Horrocks
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Location: Sydney, Australia
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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).
__________________
Note: I do not answer CFD questions by PM. CFD questions should be posted on the forum.

 August 19, 2018, 19:38 #9 New Member   Join Date: Aug 2018 Posts: 6 Rep Power: 7 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.

 August 19, 2018, 19:41 #10 Super Moderator   Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 17,746 Rep Power: 143 Just make the wall a heat flux boundary and apply your heat flux that way. No source term required, no source term coefficient. CFD USER infinity likes this. __________________ Note: I do not answer CFD questions by PM. CFD questions should be posted on the forum.

 August 19, 2018, 19:45 #11 New Member   Join Date: Aug 2018 Posts: 6 Rep Power: 7 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

 August 19, 2018, 19:56 #12 Super Moderator   Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 17,746 Rep Power: 143 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. CFD USER infinity likes this. __________________ Note: I do not answer CFD questions by PM. CFD questions should be posted on the forum.

 August 19, 2018, 20:05 #13 New Member   Join Date: Aug 2018 Posts: 6 Rep Power: 7 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.

 August 20, 2018, 15:20 #14 New Member   Join Date: Aug 2018 Posts: 6 Rep Power: 7 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

 August 20, 2018, 18:32 #15 Super Moderator   Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 17,746 Rep Power: 143 Post #12 answers all those questions. __________________ Note: I do not answer CFD questions by PM. CFD questions should be posted on the forum.