Thermo-Electric toolbox

1. Notations

In the thermo-electric model, we have 4 parameters

  • \(\sigma\) the electrical conductivity

  • \(k\) the thermal conductivity

  • \(T_c\) the water cooling temperature

  • \(h\) the heat transfer coefficient

These parameters can be scalars of fields.

We gather in the following table parameter ranges, nominal values as well as units for \(\sigma, k, T_c, h\).

Table 1. Table of parameters for the simulation



Nominal value




\(53\cdot 10^{6}\)

\(S \cdot m^{-1}\)




\(W\cdot m^{-1} \cdot K^{-1}$\)








\(W \cdot m^{-2} \cdot K^{-1}\)

In the linear case, we first solve for \(V\) and then for \(T\) using \(V\) to compute the Joule effect that generates heat inside \(\Omega\).

2. Running the Thermo-electric application

Using Docker, you can run Feel++ model application and in particular the thermo-electric model using the following command

Docker command
$ docker run -it -v $HOME/feel:/feel feelpp/feelpp-toolboxes:latest

Then type the following command in docker environment to run the model

Running Thermo-Electric model
$ cd Testcases/models/thermoelectric/test
$ mpirun -np 4 /usr/local/bin/feelpp_toolbox_thermoelectric_3d --config-file model.cfg