What is your geometry? (1, 2 or 3-D?) If it is a simple 1D geometry, analytical results are probably available, see e.g. Carslaw/Jaeger: Conduction of heat in solids. If it is a more complex 2D/3D geometry, you may use standard discretization techniques (see. e.g. Incropera/deWitt: Principles of heat and mass transfer) and use the free software accompanyng the book to solve the conduction equation.

Dear Erling,

Thank you for quick reply. I did not mention, that this is for 2 and 3-D examples. Can you recommend other software for someone who does not have this book?

Best regards,

Piotr

Check the internet. Use search key 'Numerical heat conduction' or similar terms. I tried, and it took me 10 seconds to find this one:

http://energy.concord.org/energy2d/

E.g. Therm 7, free 2D software for that. https://windows.lbl.gov/software/therm/therm.html

I can also recommend Therm as a user friendly free 2D software. Also german WUFI software has a free version for non-commercial use (registration needed). When needed, you can look on the software list on the polish IBPSA organization website (in Polish only). They have made a nice classification depending on the software application.

https://wufi.de/en/software/licenses/

http://ibpsa-poland.org/?page_id=37

I recommend Openfoam

Dear Erling, Balázs, Łukasz and Omar,

Thank you for answers. Although I am still looking for a software which will calculate the linear thermal transmittance factor - ψ, the software you presented may be helpful in other issues.

Maybe I missed the functionality of listed software, but I did not find ψ calculations.

The total transmittance is the compounded individuals. It's also total heat flow over total temperature difference. It is the inverse of the resistances.

Transmittance or resistances will be calculated internally, they may not necessarily be reported as such, but it's easy to derive from its numerous forms.

Dear Piotr, I suggest 'Therm' developed by LBNL. Nevertheless to calculate the psi-value you should make your own calculation following the procedure reported in EN ISO 10211:2008.

Dear Arnaud, Dear Stefano, Dear all,

Thank you a lot. 

I was asked to find a software which enable psi calculations and as a result gives the linear thermal transmittance factor - ψ.

How about commercial solutions? Which would you recommend?

Best regards,

Piotr

Most FEA software can calculate conductivity.