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Surface Integration of Heat/Energy Flux through all surfaces is not equal to the net heat source

Posted Dec 5, 2011, 11:54 a.m. EST Heat Transfer & Phase Change Version 4.2 8 Replies

Kapil Dev
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Hi,

I tried to simulate the temperature distribution and heat flux through different surfaces of a simple cubicle block. The geometry in the test model is a cubicle block with dimensions 20mmX20mmX20mm. I applied a boundary heat source of 45 W to one of the faces and used convective cooling coefficient of 5W/(m^2.K) for the remaining five faces.

The temperature distribution seems correct to me; the steady-state value of temperature matches with my analytical calculations. However, when I am computing the heat flux through different faces of cubicle block and computing the total power by multiplying the heat flux with area of each face, it is not summing to 45 W. I also used the inbuilt surface-integration function and I see the same issue. The total power for five surfaces is equal to 128.36W.

I am not sure what is going wrong here. Is there is problem with the model or do I have wrong understanding of heat transfer for this problem?

I will be very thankful if you could provide some insight on this. I am attaching the COMSOL model herewith. I used 4.2.0.228 version of COMSOL.

Thanks and Regards,
Kapil
8 Replies Last Post Dec 9, 2011, 1:53 p.m. EST
Nagi Elabbasi Facebook Reality Labs
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Posted: 1 decade ago Dec 6, 2011, 9:54 a.m. EST
You are integrating the heat flux magnitude. You should instead integrate the normal heat flux. That gives zero over all 6 sides, and 45W over 5 sides as expected.

Nagi Elabbasi
Veryst Engineering
You are integrating the heat flux magnitude. You should instead integrate the normal heat flux. That gives zero over all 6 sides, and 45W over 5 sides as expected. Nagi Elabbasi Veryst Engineering
Kapil Dev
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Posted: 1 decade ago Dec 7, 2011, 12:35 p.m. EST
Thanks Nagi Elabbasi!

That explains it for this simple geometry.

Would you tell me the significance of total heat-flux then? I mean, what exactly does it denote?

Actually, I tried to perform this kind of calculation for my real heat-transfer problem (would explain in the next post, if I am really stuck with the issue; I want to try to solve it myself first) and I am not able to confirm the conservation of energy/heat.

I believe that heat-flux happening outward (in the direction of normal vector) are considered +ve and inward flux is considered -ve.

Thanks again for the response!

Regards,
Kapil
Thanks Nagi Elabbasi! That explains it for this simple geometry. Would you tell me the significance of total heat-flux then? I mean, what exactly does it denote? Actually, I tried to perform this kind of calculation for my real heat-transfer problem (would explain in the next post, if I am really stuck with the issue; I want to try to solve it myself first) and I am not able to confirm the conservation of energy/heat. I believe that heat-flux happening outward (in the direction of normal vector) are considered +ve and inward flux is considered -ve. Thanks again for the response! Regards, Kapil
Kapil Dev
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Posted: 1 decade ago Dec 7, 2011, 4:31 p.m. EST
Hi again,

Just to explain the problem:

I changed the dimension of Si-block and added another solid block on the top of Si-block. I tried to simulate the heat flux and temperature distribution again. I see that now, the total normal heat flux through all surfaces does not sum to zero.

I am attaching the updated model herewith. Thanks for your help.

Regards,
kapil
Hi again, Just to explain the problem: I changed the dimension of Si-block and added another solid block on the top of Si-block. I tried to simulate the heat flux and temperature distribution again. I see that now, the total normal heat flux through all surfaces does not sum to zero. I am attaching the updated model herewith. Thanks for your help. Regards, kapil
Kapil Dev
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Posted: 1 decade ago Dec 7, 2011, 10:57 p.m. EST
I am not sure if I am posting too much. But, I found something fishy in the model simulations.

I tried to use thermally-insulating condition on face numbered 9, 10, 13, 16. But, after simulating it, when I calculate the normal heat flux through these surfaces, it is not zero.

Perhaps, this is causing the problem here??

Regards,
Kapil
I am not sure if I am posting too much. But, I found something fishy in the model simulations. I tried to use thermally-insulating condition on face numbered 9, 10, 13, 16. But, after simulating it, when I calculate the normal heat flux through these surfaces, it is not zero. Perhaps, this is causing the problem here?? Regards, Kapil
George Rosala
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Posted: 1 decade ago Dec 8, 2011, 4:28 a.m. EST
Hi Kapil,

See attached your first model solved, where the total convective flux equals the boundary heat source.

George
Hi Kapil, See attached your first model solved, where the total convective flux equals the boundary heat source. George
Kapil Dev
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Posted: 1 decade ago Dec 8, 2011, 7:00 p.m. EST
Dear George Rosala,

Thanks for the solving the issue. Nagi Elabbasi also suggested to calculate "total normal heat flux" instead of "total heat flux" and that verifies the conservation of heat/energy/power.

I am now adding more complexities to the model. As expected, I am facing issues at every step:-)

Thanks and Regards,
Kapil
Dear George Rosala, Thanks for the solving the issue. Nagi Elabbasi also suggested to calculate "total normal heat flux" instead of "total heat flux" and that verifies the conservation of heat/energy/power. I am now adding more complexities to the model. As expected, I am facing issues at every step:-) Thanks and Regards, Kapil
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Dec 9, 2011, 12:53 a.m. EST
Hi

do not forget to take a look at the KB there are some very pertinent discussion on flux calculation and FEM.

my way to improve things is often to use "boundary mesh" on both sides of critical discussion boundaries (applies to HT and to concentration diffusion same math equations) as the flux is linked to the local derivative that needs to be well resolved

FEM and mesh size is also a sampling issue, you need to resolve the gradients, as you use a Nyquist criteria for digital sampling of a signal

--
Good luck
Ivar
Hi do not forget to take a look at the KB there are some very pertinent discussion on flux calculation and FEM. my way to improve things is often to use "boundary mesh" on both sides of critical discussion boundaries (applies to HT and to concentration diffusion same math equations) as the flux is linked to the local derivative that needs to be well resolved FEM and mesh size is also a sampling issue, you need to resolve the gradients, as you use a Nyquist criteria for digital sampling of a signal -- Good luck Ivar
Kapil Dev
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Posted: 1 decade ago Dec 9, 2011, 1:53 p.m. EST
Thanks Ivar!

Actually, I also thought of the same and tried to create a controlled mesh instead of simple tetrahedral-mesh. I am trying to find the suitable mesh-size (based on temperature gradients), as you said. I am attaching the model with updated mesh herewith.

The knowledge-base was helpful; I am going through them more seriously now. Thanks.

Regards,
Kapil
Thanks Ivar! Actually, I also thought of the same and tried to create a controlled mesh instead of simple tetrahedral-mesh. I am trying to find the suitable mesh-size (based on temperature gradients), as you said. I am attaching the model with updated mesh herewith. The knowledge-base was helpful; I am going through them more seriously now. Thanks. Regards, Kapil

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