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Heat transfer between 2 plates (2D)
Posted Jul 10, 2009, 9:47 a.m. EDT 3 Replies
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Hello,
we have the following easy 2D problem:
We have two similar plates beeing in contact on one side, on the other sides both plates are isolated.
The first plate has an inital temperature of 40 degC and the other plate has an inital temperature of 20 degC.
We use an assembly with identity pairs.
It's obvious that both plates should have a steady-state temperature of 30 degC.
The problem is that COMSOL gives different solutions for different mesh refinements. It never really converges to the value of 30 degC, it's kind
of oscillating and the error is much too big (second position after decimal point). We don't expect it to be a numerical error here.
Another thing is the following:
Why does the Postprocessor sometimes show a rainbow gradient of the temperature even though the value of min/max is the same?
What do we make wrong? Any solutions to this problem?
Thank you very much!
we have the following easy 2D problem:
We have two similar plates beeing in contact on one side, on the other sides both plates are isolated.
The first plate has an inital temperature of 40 degC and the other plate has an inital temperature of 20 degC.
We use an assembly with identity pairs.
It's obvious that both plates should have a steady-state temperature of 30 degC.
The problem is that COMSOL gives different solutions for different mesh refinements. It never really converges to the value of 30 degC, it's kind
of oscillating and the error is much too big (second position after decimal point). We don't expect it to be a numerical error here.
Another thing is the following:
Why does the Postprocessor sometimes show a rainbow gradient of the temperature even though the value of min/max is the same?
What do we make wrong? Any solutions to this problem?
Thank you very much!
3 Replies Last Post Jul 10, 2009, 1:37 p.m. EDT
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Posted:
2 decades ago
Your problem is an interesting one and certainly understand your logic. However, you must think about the type of equation system you are solving which at steady-state is a Laplacian-type equation system if the material properties are constant. You must impose either a Dirichlet constraint somewhere on the boundary (fix a temperature) or you must impose a Neumann constraint on the boundary and add a heat source. COMSOL is doing exactly what it should do. You have imposed a mathematically ill-posed constraint on this system !
Try the following:
1) fix a single point somewhere on the model equal to 30 C (or any other temperature for that matter)
2) after that works, unset this temperature and impose a non-zero heat flux on the boundary and a non-zero heat source somewhere internal to the system.
In either case (without even looking at your model), I bet it will converge to a steady state.
Please let us know how it goes.
Try the following:
1) fix a single point somewhere on the model equal to 30 C (or any other temperature for that matter)
2) after that works, unset this temperature and impose a non-zero heat flux on the boundary and a non-zero heat source somewhere internal to the system.
In either case (without even looking at your model), I bet it will converge to a steady state.
Please let us know how it goes.
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Posted:
2 decades ago
I have looked at your file.
I found out that there were two boundaries at the interface between the plates, and that stationary solver was chosen.
Here is what I did.
In the draw mode, I combined the two plates "keeping the interior boundaries".
In Physics>Subdomain, I made sure that the initial temperatures were 40[degC] and 20[degC]
In Physics>Properties, I changed the "analysis type" from 'stationary' to 'transient'
In Solve>Solver parameters.., I chose 'time dependent' for "Solver" and gave 0 for the first value and 10*3600 for the last value and 3600 for the step size in the time stepping.
I did not touch the relative and the absolute tolerances and solved it.
It seems working. You may change the absolute tolerance for better accuracy.
I found out that there were two boundaries at the interface between the plates, and that stationary solver was chosen.
Here is what I did.
In the draw mode, I combined the two plates "keeping the interior boundaries".
In Physics>Subdomain, I made sure that the initial temperatures were 40[degC] and 20[degC]
In Physics>Properties, I changed the "analysis type" from 'stationary' to 'transient'
In Solve>Solver parameters.., I chose 'time dependent' for "Solver" and gave 0 for the first value and 10*3600 for the last value and 3600 for the step size in the time stepping.
I did not touch the relative and the absolute tolerances and solved it.
It seems working. You may change the absolute tolerance for better accuracy.
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Posted:
2 decades ago
Hyoung Kim has sparked my interest. I too have now looked at your problem. I have attached an updated model file. I also realized that you need to combine both regions into a single region, and make the common boundary an interior boundary with "continuity" as the boundary type. You had an insulated boundary on all 4 sides of both subdomains so there was no communication between the two.
I also realized that this becomes a linear problem since all the properties are constant, and you are left with solving a Laplacian which is the classical diagonally-dominate, symmetric, etc. So, you can solve very fast steady state. It now gives you 30 C everywhere from you initial conditions.
An interesting variation is to use some of the other solvers and see what you get. Try the nonlinear solver and you have to force it to iterate. You also have to refine the mesh to get near 30 C. It is an interesting problem.
I also realized that this becomes a linear problem since all the properties are constant, and you are left with solving a Laplacian which is the classical diagonally-dominate, symmetric, etc. So, you can solve very fast steady state. It now gives you 30 C everywhere from you initial conditions.
An interesting variation is to use some of the other solvers and see what you get. Try the nonlinear solver and you have to force it to iterate. You also have to refine the mesh to get near 30 C. It is an interesting problem.
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