Thermal conductivity function

[Bernhard]

Hi all,

i managed to get the Java tool for results extraction running, thanks again for your Support!

Now i would like to trace back the thermal conductivity / lambda value from the temperature and water content in each cell.

The material of interest is spruce radial ("Fichte radial").

In the material description, correction factors for temperature and water mass load are given - i could reproduce the table values and diagrams in the material description so far. Unfortunately, no table values for combined temperature and moisture correction are given.

My question:

The Lambda correction factor for water mass load is given in a relative manner (% per % mass load). Do I have to apply it to the standard Lambda value (0.09 W/mK in this case), or AFTER temperature correction? (i guess the latter ..)

Or can the Lambda value for each cell and Point of time be extracted from the result files by the Java tool?

Thanks for your help!

Cheers, Bernhard

[Thomas]

The Lambda correction factor for water mass load is given in a relative manner (% per % mass load). Do I have to apply it to the standard Lambda value (0.09 W/mK in this case), or AFTER temperature correction?

Hi Bernhard,
the two corrections are multiplicative corrections, so it does not matter in which order they are applied.

The Lambda corrected for the moisture-dependence is

L(w) = L0 * (1 + b*w/r), let us write this L(w) = L0*(1+B) for simplicity.

The Lambda corrected for the temperature-dependence is [*]

L(temp) = L0 + L0*a*(temp-10°C) = L0 * (1 + a*(temp-10°C)) , let us write this L(temp) = L0*(1+A)


Now if you first correct for moisture and then for temperature, you have

L(w, temp) = [L0*(1+B)]*(1+A) = L0*(1+B)*(1+A)

If you first correct for temperature and then for moisture, you have

L(w, temp) = [L0*(1+A)]*(1+B) = L0*(1+A)*(1+B)

which is the same.

Kind regards,
Thomas


[*] I noticed there is a typo in the formula as given in the WUFI online help.

[Bernhard]

Hi Thomas,

thanks for your quick answer!

Both corrections are multiplicative? I'm a bit confused now..

For "Fichte radial" the Approximation Parameters are given as

Humidity factor: 1,3 %/mass% - "unitless" multiplicator, so far so good.
Temperature factor: 2*10^-4 W/mK^2 - "additive" multiplicator with unit!

(means: the absolute Lambda difference only depends on temperature, not on moisture..).

That's why I was asking for the right order... With the given units of the factors, it does make a difference what comes first.. Or did I get something wrong?

Cheers

Bernhard

[Thomas]

Both corrections are multiplicative? I'm a bit confused now..

For "Fichte radial" the Approximation Parameters are given as

Humidity factor: 1,3 %/mass% - "unitless" multiplicator, so far so good.
Temperature factor: 2*10^-4 W/mK^2 - "additive" multiplicator with unit!

Hi Bernhard,
with "multiplicative corrections" I meant to refer to the fact that in both cases the corrections can be described as multiplications of the original Lambdas with multiplicative factors (1+A) and (1+B), respectively.

The approximation parameters you refer to are used to compute A and B:

(1+A) = (1 + a*(temp-10°C)), where a is the "temperature-dependent thermal conductivity supplement [W/mK^2]" given in the material database.

(1+B) = (1 + b*w/rho), where b is the "moisture-dependent thermal conductivity supplement [% / M-%]" given in the material database.

(Please note that the approximation parameter "a" cannot simply be an additive correction to Lambda0 because it has units W/mK^2, whereas Lambda has units W/mK).

Kind regards,
Thomas