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 containing "I" terms have to be zero. Now if we assume that where "δ" is the Dirac delta function, "I" terms get the following expressions By substituting these expressions to the equation for "λ", we see that it goes to zero. Therefore, "P"("x") has to be delta function. In an isotropic medium the thermal conductivity is the parameter "k" in the Fourier expression for the heat flux where formula_2 is the heat flux (amount of heat flowing per second and per unit area) and formula_66 the temperature gradient. The sign in the expression is chosen so that always "k" >