For a case, I have calculated theoretically and experimentally the overall thermal resistance through a composite solid. However, I am wondering whether there is any other way to calculate the overall thermal resistance without employing the Fourier law.
Best Regards
Hello,
Ohm's law is often used as an analogy when doing calculations involving thermal resistance.
Here is an example:
https://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node118.html
Calculations for steady state conditions are simple. Thermal resistance of each layer equals its thickness divided by its thermal conductivity. Total thermal resistance equals total sum of all the layers' thermal resistances.
Heat flux is similar to the electric current (Ohm's law) - it equals temperature difference (like voltage difference) divided by the total thermal resistance.
In case of non-steady conditions it will be much more complicated.
This book (translated from French) probably can help:
Thermal Quadrupoles: Solving the Heat Equation through Integral Transforms 1st Edition
by Denis Maillet (Author), Stéphane André (Author), Jean Christophe Batsale (Author), Alain Degiovanni (Author), Christian Moyne (Author)
I assume that, in order to calculate the thermal resistance, you depend on using the material's thermal conductivities. As such, the thermal conductivity is defined from Fourier's law, and no matter how you twist your calculations (e.g. using electrical resistance analogy), you end up using some form of Fourier's law. Of course you can skip the thermal conductivity concept alltogether and use the fundamental approach, calculating the phonon transport (electron movements and lattice vibrations). However that will be a heap of work, and probably won't get you anywhere (unless your geometry consist of very thin layers).
Technically, there is the graphical method of preparing the 'flux plot'. Though this gives a lot of physical insight, it is prone to human error and requires some degree of expertise.
A better option is the shape factor approach - this is available for standard geometries.
Details can be found in textbooks by Incropera, Cengel etc.
Dear Hanan Hamid , Akhan Tleoubaev , Erling Næss , Saleel Ismail
Thank you for your worthy answers.
If you can use ANSYS, it is best way to find you solution but still it will use Fourier law.
Thanks
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