Effective Thermal Conductivity

To compute the effective thermal conductivity, we average the flux over a given contact. For example, assuming a rectangular domain with size \(L_x \times L_y\), the effective thermal conductivity for a perturbation applied along x (\(\kappa_{xx}\)) is given by

\[\kappa_{xx} = \alpha\int_{-L_y/2}^{L_y/2}\mathbf{J}(L/2,y)\cdot \mathbf{\hat{n}}dy\]

where \(\alpha =-L_x/L_y/\Delta T_{\mathrm{ext}}\). To this end, we define the boundary region name and the normalization factor \(alpha\)

from openbte.objects import EffectiveThermalConductivity

effective_kappa = EffectiveThermalConductivity(normalization=-1,contact='Periodic_x')