2D Heat Conduction

[John Assael]

Hi,
Are there any 2D Heat conduction examples or anything similar that could be helpful?
Thank you in advance!

[Praveen C]

Look at the "Session 7" here

http://numerik.uni-hd.de/~lehre/SS10/dealcompact/

It deals with heat conduction problem.

praveen

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[John Assael]

Thank you very much for your answer but I dont really get it I use the fourier's equation to calculate the conduction is there anything similar?
Kind regards,
J.

[John Assael]

Anybody with 2D heat conduction examples?

[Wolfgang Bangerth]

On 01/08/2013 05:02 PM, John Assael wrote:
> Anybody with 2D heat conduction examples?

I don't understand your previous comment:

> Thank you very much for your answer but I dont really get it I use
> the fourier's equation to calculate the conduction is there anything
> similar?

We may think of different things for the term "heat conduction". To me,
the heat equation is

d/dt u - \Delta u = f

What is it for you?

Best
W.


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------------------------------------------------------------------------
Wolfgang Bangerth email: bang...@math.tamu.edu
www: http://www.math.tamu.edu/~bangerth/

[Andrew]

Hi

I think the misunderstanding here is that Wolfgang's "version" assumes
that the conductivity tensor is the identity tensor and that the heat
capacity is unity,

define the heat flux vector as q = - k grad u
then rewrite the governing equation as
c d / dt u + div q = 0
(give or take a source term)

have a look at the following for extensive details of the implementation
in deal.II
https://dl.dropbox.com/u/65506484/Masterarbeit_final.pdf

Regards
Andrew

[John Assael]

I agree fully, whete u is ofcourse the
temperature.
This the equation I need to solve.
Thank you

[Wolfgang Bangerth]

OK. So do you want to solve it in mixed form (with q and u both
variables you want to solve for) or are you willing to insert one
equation into the other and get
c d/dt u - div k grad u = f
?

In the first case, you should look at step-20 and step-21. In the latter
case, the difference to the link previously posted is simply the
existence of coefficients c, k. If you convert the equation to the weak
form, they are just factors when computing the mass matrix and the
stiffness matrix, everything else is exactly the same.

Best
W.

PS - thanks, Andrew, for bridging the terminology gap :-)

On 01/09/2013 03:37 AM, John Assael wrote:
> I agree fully, whete u is ofcourse the
> temperature.
> This the equation I need to solve.
> Thank you
>
> On Jan 9, 2013 9:20 AM, "Andrew" <mcbride...@gmail.com

> <mailto:mcbride...@gmail.com>> wrote:
>
> Hi
>
> I think the misunderstanding here is that Wolfgang's "version"
> assumes that the conductivity tensor is the identity tensor and that
> the heat capacity is unity,
>
> define the heat flux vector as q = - k grad u
> then rewrite the governing equation as
> c d / dt u + div q = 0
> (give or take a source term)
>
> have a look at the following for extensive details of the
> implementation in deal.II

> https://dl.dropbox.com/u/__65506484/Masterarbeit_final.__pdf

> <https://dl.dropbox.com/u/65506484/Masterarbeit_final.pdf>
>
> Regards
> Andrew
>
>
>
> On 09/01/2013 01:59, Wolfgang Bangerth wrote:
>
> On 01/08/2013 05:02 PM, John Assael wrote:
>
> Anybody with 2D heat conduction examples?
>
>
> I don't understand your previous comment:
>
> Thank you very much for your answer but I dont really
> get it I use
> the fourier's equation to calculate the conduction is
> there anything
> similar?
>
>
> We may think of different things for the term "heat conduction".
> To me, the heat equation is
>
> d/dt u - \Delta u = f
>
> What is it for you?
>
> Best
> W.
>
>
>