Thermal conductivity heat flow may not be exactly the same as the direction of the thermal gradient. In metals, thermal conductivity approximately tracks electrical conductivity according to the Wiedemann–Franz law, as freely moving valence electrons transfer not only electric current but also heat energy. However, the general correlation between electrical and thermal conductance does not hold for other materials, due to the increased importance of phonon carriers for heat in non-metals. Highly electrically conductive silver is less thermally conductive than diamond, which is an electrical insulator, but due to its orderly array of atoms it is conductive of heat via phonons. The
Thermal conductivity Time variation due to phonon decay is described with a relaxation time ("τ") approximation which states that the more the phonon number deviates from its equilibrium value, the more its time variation increases. At steady state conditions and local thermal equilibrium are assumed we get the following equation Using the relaxation time approximation for the Boltzmann equation and assuming steady-state conditions, the phonon thermal conductivity "λ" can be determined. The temperature dependence for "λ" originates from the variety of processes, whose significance for "λ" depends on the temperature range of interest. Mean free path is one factor that determines the