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
Electrical resistivity and conductivity equations can be worked out by hand, but for very accurate answers in complex cases, computer methods like finite element analysis may be required. In some applications where the weight of an item is very important, resistivity density products are more important than absolute low resistivity – it is often possible to make the conductor thicker to make up for a higher resistivity; and then a low resistivity density product material (or equivalently a high conductivity to density ratio) is desirable. For example, for long distance overhead power lines, aluminium is frequently used rather than copper (Cu) because it is