Orthotropic Conductivity on Face

Hi. My domain is as shown in the images attached.

I am trying to place orthotropic conductivity on face 3 and uniform conductivity on faces 1&2. The code/solution fails with the following syntax:

kappa = 1;
orthoK = [0.75*kappa,0 ; 0, 0.85*kappa];
model.MaterialProperties([1 2]) = materialProperties(ThermalConductivity=kappa, ...
                           MassDensity=1,SpecificHeat=1);
model.MaterialProperties(3) = materialProperties(ThermalConductivity=orthoK, ...
                           MassDensity=1,SpecificHeat=1);

The code also fails with this test:

orthoK = [kappa,0 ; 0, kappa];

but would run fine with this (not what I need though):

orthoK = [kappa];

It also fails with this syntax that I have seen in the documentation online:

ortho = [0.75*kappa 0.85*kappa];

Can anyone tell me the proper syntax?

Thanks!

Answer 1

[Torsten]

I found

orthoK = [0.75*kappa; 0.85*kappa];

in the documentation - thus a column instead of a row vector.

[Paul Safier]

Something is off with that, perhaps.

I feel like I should get the same result with this:

model.MaterialProperties([1 2]) = materialProperties(ThermalConductivity=kappa, ...
                           MassDensity=1,SpecificHeat=1);
orthoK = kappa*ones(2,2);
%orthoK = [kappa;kappa]; % Other option also doesn't match below
model.MaterialProperties(3) = materialProperties(ThermalConductivity=orthoK, ...
                           MassDensity=1,SpecificHeat=1);

as I do with this:

model.MaterialProperties([1 2]) = materialProperties(ThermalConductivity=kappa, ...
                           MassDensity=1,SpecificHeat=1);

model.MaterialProperties(3) = materialProperties(ThermalConductivity=kappa, ...
                           MassDensity=1,SpecificHeat=1);

But they are NOT the same. The first code snippet (with the orthotropic conductivity format but set to kappa) does not solve correctly...

[Torsten]

I think you mean

orthoK = kappa*eye(2);

or

orthoK = [kappa;kappa];

instead of

orthoK = kappa*ones(2,2);

[Paul Safier]

The test would be to mimic setting a uniform conductivity (kappa = 1). Shouldn't that have the cross-directional terms also set to 1?

conductivityMatrix = [kx, kxy; kyx, ky];

Thus:

conductivityMatrix = ones(2,2);

Right?

Regardless, in neither of the options you list can you get the same results as using the single scalar value of 1.

[Torsten]

The "usual" energy equation has no cross-derivative terms, thus kxy = kyx = 0.

If I have the time, I'll look up the documentation and see if I can find something useful.

[Torsten]

Which model type are you using ? model = femodel ? model = thermalModel ? model = createpde ?

[Paul Safier]

I'm using:

model = femodel(AnalysisType="thermalSteady",Geometry=gm);

[Paul Safier]

I made a small test problem and was able to get results using this format that I gleaned from the full pdf documentation.

orthoK = [0.75*kappa ; 0 ; 0 ; 0.8*kappa];

However, my problem has a nonlinear boundary condition and is more involved so there is something peculiar about my problem that does not permit a proper solution (at the nonlinear BC) when using an orthotropic conductivity. For the small test problem, I also tried a nonlinear BC and it worked as well, so the issue is specific to my problem. Oh well, more troubleshooting to be had. Thanks for the help, @Torsten.