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1D integration in 3D domain, need help

Posted Dec 20, 2010, 10:53 a.m. EST Version 3.5a 1 Reply

Jiangjun Zheng
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Hi, All,

It is a static thermal conduction problem. The geometry is a cubic. The heat source is:
Q=[1-f(T)]*exp(-Int(g(x,y,z,T), 0, z))
T is the temperature.
f(T) is a 2D function of the surface temperature at z=0.
Int(g(T), 0, z)): means integration of g(T) from z=0 to z. g(T) is a function of the temperature in 3D.

So, I need help on two things:
1, f(T) is defined on the surface, but used in the 3D heat source. How to do that?
2, How to do the integration?

For 2, I tried to use an additional function: h(x,y,z,T), and make dh/dz=-g(T)h. For example, if g(T)=1, the function is dh/dz=h, and the boundary condition is h=const.. This method works well in 2D, not in 3D. see post:
www.comsol.eu/community/forums/general/thread/439/

Thanks a lot for your helps (in advance for this problem).

Best,
Jiang
1 Reply Last Post Jan 22, 2011, 4:08 p.m. EST
COMSOL Moderator

Hello Jiangjun Zheng

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Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Jan 22, 2011, 4:08 p.m. EST
Hi

Try the following:

First in 2D (x,y) load the heat Convection_2D.mph of the model library

Try with a "Boundary Projection Variable" of "General Transformation" type, orientation "y", call it Tx0 on Boundary of "1" x=0 and use T as variable. Then select destination domain and select all your "domains" and orientation y.

Then Tx0(y) = T(x=0,y) in the full domain

Then you can extrapolate to 3D, no ?

I would try an integration coupling variable on the domain for your integration

Check the doc and try these coupling variables on simple cases

--
Good luck
Ivar
Hi Try the following: First in 2D (x,y) load the heat Convection_2D.mph of the model library Try with a "Boundary Projection Variable" of "General Transformation" type, orientation "y", call it Tx0 on Boundary of "1" x=0 and use T as variable. Then select destination domain and select all your "domains" and orientation y. Then Tx0(y) = T(x=0,y) in the full domain Then you can extrapolate to 3D, no ? I would try an integration coupling variable on the domain for your integration Check the doc and try these coupling variables on simple cases -- Good luck Ivar

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