Heat Equation with Convection

[maguirre]

Hi everyone!
I've been using Elmer with the Heat and StatCurrent Solvers, the second one to calculate Joule Heating and the first for heat distribution and transfer from a solid to ambient by convection. As far as I understood, to tell Elmer to do the convection part I have to add the Heat Transfer Coeff. and External Temperature as a Boundary Condition and assign it to the faces I want, but here is the problem I encountered.

Heat Transfer Coeff. depends, between others, on the orientation of the surface dissipating, it's not the same the dissipation of a surface pointing upwards ("looking to the sky") than one pointing downwards ("looking to the floor"); the second one dissipates less because when the surrounding fluid heats, it tends to go up (by buoyancy) so first bumps with the surface (keeping it warmed a bit longer) and then escapes. How does Elmer deal with this? Does changing the unity vector for Gravity in Model->Setup (0 -1 0 to 0 0 -1 so it's pointing to minus-z) change something?

[kevinarden]

Buoyancy exist because of gravity, and is a function of gravity. It is caused by the weight of a buoyant object being pulled toward the source of gravity creating a pressure differential across the object displacing the fluid. Therefore, changing the unit vector for the gravitational force changes the direction of gravity and the direction of the buoyant force that always acts in the opposite direction of gravity. Also in zero gravity there are no buoyant forces, and changing the magnitude of gravity as well as it's direction changes the buoyant force.

[Rich_B]

Hello,

Feel free to post a few pictures, and/or your sif and geometry files.

If you are using Heat Transfer Coeff (HTC) and External Temperature, then this boundary condition replaces the surrounding air. The choice of the HTC is up to you, usually chosen based on experimental data. So if you chose two different coefficients, one for the top and one for the bottom, then you have accounted for the difference. Your model will be smaller and faster.

If you remove the HTC as a boundary condition, and instead model the air/fluid surrounding your device, then you can solve for the heat lost from the device to the surrounding air. Your model will be larger and slower.

Rich.

[maguirre]

Thank you both!

Therefore, changing the unit vector for the gravitational force changes the direction of gravity and the direction of the buoyant force that always acts in the opposite direction of gravity.

Yes, I assumed the same as you @kevinarden, but the results for two similar problems (I will attach the files here, I rename the case.sif for you to recognize them) gave me the same results, one with g=[0 -1 0 9.81] and the other with g=[0 0 -1 9.81].

This is the case with g=[0 -1 0 9.81]:
https://drive.google.com/file/d/148paoH ... share_link
https://drive.google.com/file/d/1E8PX5b ... share_link

and this with g=[0 0 -1 9.81]
https://drive.google.com/file/d/1UVZseF ... share_link
https://drive.google.com/file/d/107Ii0w ... share_link

As you can see, both temperature distributions gave the same with different g's.

If you are using Heat Transfer Coeff (HTC) and External Temperature, then this boundary condition replaces the surrounding air. The choice of the HTC is up to you, usually chosen based on experimental data. So if you chose two different coefficients, one for the top and one for the bottom, then you have accounted for the difference. Your model will be smaller and faster.

That's something that could solve the problem, but in the future, I will have to simulate complicated structures so it won't be feasible. At that point, I think I'll have to simulate the surrounding air as you propose.

[kevinarden]

There is no difference because there are no buoyancy forces defined in the solution. To get buoyancy forces you have to add the stokes equation and turn on the buoyancy forces and compute the convection.

[maguirre]

There is no difference because there are no buoyancy forces defined in the solution. To get buoyancy forces you have to add the stokes equation and turn on the buoyancy forces and compute the convection.

Could you explain it in more detail? Because I try to do it with no success. If I add the N-S equation (besides the StatCurr+Heat) I cannot apply it to any body (the StatCurr+Heat is applied to the sheet already), or if I turn on the equation inside StatCurr+Heat it cannot compute anything because it needs the viscosity data (the body is a solid, copper to be precise, so no viscosity)

[kevinarden]

With no viscosity, most people would not include buoyancy forces in something like a metal such as copper. But if you want to include buoyancy forces in a metal the you have to assign it a viscosity, even it it is a big number like 100.0. It can be done, but buoyancy in metals is usually ignored for this reason. Without buoyancy than heat conduction in metal is unaffected by gravity, and therefore the direction of the gravity unit has no impact. In this example buoyancy is included with a very high viscosity to represent a metal. Not sure what it represents in the physical world but it is simulated. Not sure what buoyancy means in heat convection in a metal. But if you want to include it then you have to assume that the metal is flowing and has a viscosity.

difference.png

(174.35 KiB) Not downloaded yet

Left side is gravity vector Z, right side is gravity vector Y.

box.zip

(16.76 KiB) Downloaded 37 times

More fundamentally, if there is no flow there is no buoyancy, if there is flow than there is viscosity, even if a very high number,

[Rich_B]

Hello,

There is an ElmerGUI tutorial that may be helpful for you, if you want to simulate the air and heat convection due to bouyancy surrounding your model. Search for 'Rayleigh-Benard' in ElmerTutorials.pdf located here:

https://www.nic.funet.fi/pub/sci/physics/elmer/doc/

Rich.

[maguirre]

Oh! I know what you mean. No, you are right, It doesn't make sense to add viscosity to a solid and that's why I could not understand your proposal.

What I want to know is if I set the boundary condition (BC) with the same Heat Transf. Coeff. (HTC) and Ext. Temp. in every face (but not the ones with the potentials), Elmer takes into account that the "surrounding air" (in quotation marks because there is not a literal body assigned as air) has buoyancy and will affect the position of the sheet when computing.

As far as I understood from @Rich_B answer that doesn't happen so if I want to use HTC and Ext. Temp. as BC, I have to manually assign different coeff. for each face based on experimental data, with this sheet is totally feasible, but with more complex multi-body simulations I'll have to add a body as Air and do what you are proposing. Anyway, thank you!!

[maguirre]

Hello,

There is an ElmerGUI tutorial that may be helpful for you, if you want to simulate the air and heat convection due to bouyancy surrounding your model. Search for 'Rayleigh-Benard' in ElmerTutorials.pdf located here:

https://www.nic.funet.fi/pub/sci/physics/elmer/doc/

Rich.

Thank you very much! That's exactly what I'm looking at now.