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Weak form of heat conduction :)
Posted Apr 21, 2010, 8:06 a.m. EDT 3 Replies
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Dear All
I try to study the heat conduction model by using the PDE mode.
dT/dt = -k {d^2 T/d x^2}
BC :
k dT/dx = 0 at x = 0
and
k dT/dx = h(Tin - T)
I am sucess both General PDE and Coeff modes but for the Weak form it does not work for me.
I thougth that I did some input mistake but i can put my figer on it.
Could u give me a advices for this problem please?
Thanks in advance. :)
Krit
I try to study the heat conduction model by using the PDE mode.
dT/dt = -k {d^2 T/d x^2}
BC :
k dT/dx = 0 at x = 0
and
k dT/dx = h(Tin - T)
I am sucess both General PDE and Coeff modes but for the Weak form it does not work for me.
I thougth that I did some input mistake but i can put my figer on it.
Could u give me a advices for this problem please?
Thanks in advance. :)
Krit
3 Replies Last Post Apr 22, 2010, 8:23 a.m. EDT
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Posted:
1 decade ago
Hi
Are you sure you should leave your boundary condition "2" with constr = -T and not just "0" ?
But then is it "0" and not 293.15[K] for boundary "1", Comsol is working in absolute Kelvin
by the way H is missing in your pdf (just to be complet ;)
nice example,
do you mind if I keep it and use it perhaps in a future course ?
Have fun Comsoling
Complement:
having had a little more time to read it in details, I have some further doubts:
in your model you have a Dirichlet condition on the left side x=0, but you state a Neumann in the pdf, and you impose two Neumann conditons on a simple second order PDE, for me this is an ill conditionned, non unique soluton case, and Comsol will have some trouble solving it like that, but as I said before thats NOT what I read in the model, you need a fixed point dor an unique solution.
Any comments?
Ivar
Are you sure you should leave your boundary condition "2" with constr = -T and not just "0" ?
But then is it "0" and not 293.15[K] for boundary "1", Comsol is working in absolute Kelvin
by the way H is missing in your pdf (just to be complet ;)
nice example,
do you mind if I keep it and use it perhaps in a future course ?
Have fun Comsoling
Complement:
having had a little more time to read it in details, I have some further doubts:
in your model you have a Dirichlet condition on the left side x=0, but you state a Neumann in the pdf, and you impose two Neumann conditons on a simple second order PDE, for me this is an ill conditionned, non unique soluton case, and Comsol will have some trouble solving it like that, but as I said before thats NOT what I read in the model, you need a fixed point dor an unique solution.
Any comments?
Ivar
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Posted:
1 decade ago
Dear Ivar
Thanks for your kindness reply. My problem is similar as plain wall with the symmetrically cooled by heat convection so that the BC at the left side is Neumann with ( dT/dx = 0) and the other side BC is also Neumann (k dT/dx = h(Tin-T)). basically i need to get the solution like in the attachment files by using weak mode. :)
I try to work out by using comsol's user's guide and modelling guide anyway I still doubts in some points. I would be appreciate that if u could give more an explanation please?
-------------------------------------------------------------------------------------------------
1. what is constr options?
if i state the constr = "-T" or "0", what is going on with the nuemann BC in both case?
-------------------------------------------------------------------------------------------------
2. As u mention in the complement
2.1 in your model you have a Dirichlet condition on the left side x=0,
but you state a Neumann in the pdf,
- I need to use the Neumann BC at the left side k dT/dx = 0.. Could u tell me please how to programme it in the weak form?
--------------------------------------------------------------------------------------------------
2.2 you impose two Neumann conditons on a simple second order PDE, for me this is an ill conditionned, non unique soluton case, and Comsol will have some trouble solving it like that, but as I said before thats NOT what I read in the model, you need a fixed point for an unique solution.
--------------------------------------------------------------------------------------------------
- What does it mean " I need to fixed point"?
Thank you so muchhhhhhhhh xD
Krit
Thanks for your kindness reply. My problem is similar as plain wall with the symmetrically cooled by heat convection so that the BC at the left side is Neumann with ( dT/dx = 0) and the other side BC is also Neumann (k dT/dx = h(Tin-T)). basically i need to get the solution like in the attachment files by using weak mode. :)
I try to work out by using comsol's user's guide and modelling guide anyway I still doubts in some points. I would be appreciate that if u could give more an explanation please?
-------------------------------------------------------------------------------------------------
1. what is constr options?
if i state the constr = "-T" or "0", what is going on with the nuemann BC in both case?
-------------------------------------------------------------------------------------------------
2. As u mention in the complement
2.1 in your model you have a Dirichlet condition on the left side x=0,
but you state a Neumann in the pdf,
- I need to use the Neumann BC at the left side k dT/dx = 0.. Could u tell me please how to programme it in the weak form?
--------------------------------------------------------------------------------------------------
2.2 you impose two Neumann conditons on a simple second order PDE, for me this is an ill conditionned, non unique soluton case, and Comsol will have some trouble solving it like that, but as I said before thats NOT what I read in the model, you need a fixed point for an unique solution.
--------------------------------------------------------------------------------------------------
- What does it mean " I need to fixed point"?
Thank you so muchhhhhhhhh xD
Krit
Attachments:
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Posted:
1 decade ago
Hi
I cannot reply fully here, no free time just now, I will try to come back later or over the week-end,
but my first reaction is that a second order PDE with two Neumann BC's is not going to give you an unique solution (to be checked) and therefore cannot be solved with COMSOL.
furthermore in my understanding the "constr" is a "non-weak" point constraint (à la Dirichlet) so you should certainly not use it as "-T" which means T=0 in your case (it's OK for a hybrid BC).
Check the modelling.pdf doc for more theory, but I agree they are missing some simple example. Take a look on the forum too, I beleive this has been discussed there is a "search" function by the [Go] just above.
In your case, the way I understand it, is that the k*dT/dx(0)=0 means derivative/slope of T=0 or "horizontal" (as k<>0), and then if you define the slope at the other end your solution à la "a+b*x^2" has still one unknown. You need to fix the "height" (a Dirichlet BC) or the absolute value of a point in there, do you follow me ? Consider just the spatial equation, the time is independent, (no?)
Or is it that I have missed a point, that is quickly done anyhow, when one is in a hurry ?
What I suspect is that you have not used the correct temperatures (mixing absolute T[K] in Kelvin, and gauge values in [degC], that is why I suspect that you want a constr = (293.15-T) in addition to your dT/dx(x=0)=0. But note that anyhow at x=0 then d(a+b*"x=0"^2)/dx = 0 in all cases, no ?
check your equations, the results should anyhow give T>0[K] to stay within the usual physical range ;)
Finally if you check your physics, on BC "2" you bring in heat or energy, on BC "1" you have no energy exchange, so your bar will heat up to the max temperature at t=infinity, no? you should get a almost straigth line
Have fun Comsoling
Ivar
I cannot reply fully here, no free time just now, I will try to come back later or over the week-end,
but my first reaction is that a second order PDE with two Neumann BC's is not going to give you an unique solution (to be checked) and therefore cannot be solved with COMSOL.
furthermore in my understanding the "constr" is a "non-weak" point constraint (à la Dirichlet) so you should certainly not use it as "-T" which means T=0 in your case (it's OK for a hybrid BC).
Check the modelling.pdf doc for more theory, but I agree they are missing some simple example. Take a look on the forum too, I beleive this has been discussed there is a "search" function by the [Go] just above.
In your case, the way I understand it, is that the k*dT/dx(0)=0 means derivative/slope of T=0 or "horizontal" (as k<>0), and then if you define the slope at the other end your solution à la "a+b*x^2" has still one unknown. You need to fix the "height" (a Dirichlet BC) or the absolute value of a point in there, do you follow me ? Consider just the spatial equation, the time is independent, (no?)
Or is it that I have missed a point, that is quickly done anyhow, when one is in a hurry ?
What I suspect is that you have not used the correct temperatures (mixing absolute T[K] in Kelvin, and gauge values in [degC], that is why I suspect that you want a constr = (293.15-T) in addition to your dT/dx(x=0)=0. But note that anyhow at x=0 then d(a+b*"x=0"^2)/dx = 0 in all cases, no ?
check your equations, the results should anyhow give T>0[K] to stay within the usual physical range ;)
Finally if you check your physics, on BC "2" you bring in heat or energy, on BC "1" you have no energy exchange, so your bar will heat up to the max temperature at t=infinity, no? you should get a almost straigth line
Have fun Comsoling
Ivar