## anisotropic thermal conductivity

### anisotropic thermal conductivity

HI

I have been unsuccessfully trying to input orthotropic 2D thermal conductivities into the heat equation model.

I thought this was supported in Elmer based on the discussion of Model 1 - Heat Equation where it says that "For solids, conduction may be anisotropic and the conductivity a tensor"

I followed the Tutorial 10 approach for an anisotropic Youngs modulus on page 50 to no avail. A result from one of my many attempts is given below:

Excerpt from the SIF file:

Material 1
Name = "solid"

Density = 1550
Heat Capacity = 1450
Heat Conductivity
size 2 2
real 0.1 0.6
0.6 0.1
end
End

Elmer tells me:

Error:: Model Input:
Error:: Model Input: Unknown specifier: [end]
Error:: Model Input: In Section: [material 1]
Error:: Model Input: For propert name: [0.6 0.1]

Is it possible to have solve a solids heat conduction problem with anisotropic thermal conductivity using Elmer?
If so, can you please explain how to do it?

thanks

gsw
gsw_001

Posts: 3
Joined: 17 Mar 2010, 07:25

### Re: anisotropic thermal conductivity

I would also be very interested in the answer.
eraikkon

Posts: 2
Joined: 03 May 2010, 12:34

### Re: anisotropic thermal conductivity

Hi

I think that the expression for heat conductivity is missing a line feed between the two rows. In fact you can have all the entries on the same row, the size decleration alone decleares the size, not the layout of the numbers. I would try with the following:
Code: Select all
`Heat Conductivity(2,2) = Real 0.1 0.6 \                              0.6 0.1`

or as the variabletype is known a priori simply
Code: Select all
`Heat Conductivity(2,2) = 0.1 0.6 0.6 0.1`

-Peter
raback

Posts: 3216
Joined: 22 Aug 2009, 11:57
Location: Espoo, Finland

### Re: anisotropic thermal conductivity

Hi,
According to the above view, I think

(a) If I have a 2D model, kx = 1.0 & ky = 0.0, so
Heat conductivity(2,2) = Real 1.0 0.0 0.0 0.0

(b) Same as (a), kx = 0.0 & ky = 1.0, so
Heat conductivity(2,2) = Real 0.0 0.0 0.0 1.0

(c) If I have a 3D model, kx = 0, ky = 0 & kz=1.0, so
Heat conductitvity(3,3) = Real 0.0 0.0 0.0 0.0 0.0 1.0

Is that correct?

BR,
Taco.
tacojoi

Posts: 20
Joined: 16 Mar 2011, 14:22

### Re: anisotropic thermal conductivity

Yep, except in 3D you need 9 components, not six. -Peter
raback

Posts: 3216
Joined: 22 Aug 2009, 11:57
Location: Espoo, Finland

### Re: anisotropic thermal conductivity

Hi, Peter,

Thanks a lot.

Taco
tacojoi

Posts: 20
Joined: 16 Mar 2011, 14:22

### Re: anisotropic thermal conductivity

Hi,
Seeing the much relevance of anisotropic heat conduction in solids, I am trying to refresh this discussion started 7 years ago.
2D Model
kx = 0, ky = 1.0, so
Code: Select all
`Heat conductitvity(2,2) = Real 0.0 0.0  0.0 1.0`

3D Model
kx =1. 0, ky = 5.0 & kz=1.50, so
Code: Select all
`Heat conductitvity(3,3) = Real 1.0 0.0 0.0 0.0 5.0 0.0 0.0 0.0 1.50`

Yours Sincerely,
Anil Kunwar
annier

Posts: 1080
Joined: 27 Aug 2013, 13:51

### Re: anisotropic thermal conductivity

Hi All,
Is it possible to vary the anisotropic material property with coordinates in Elmer?
1. viewtopic.php?f=3&t=3139&start=0&hilit=tensor+variable
2. viewtopic.php?f=7&t=2267&start=0&hilit=user+subroutine

Variation of a tensor with Coordinate
1.viewtopic.php?f=3&t=3802&start=0&hilit=tensor+matc
2. viewtopic.php?f=3&t=110 (length limit of matc)

Yours Sincerely,
Anil Kunwar
annier

Posts: 1080
Joined: 27 Aug 2013, 13:51