Conduction in solids, Study notes of Heat and Mass Transfer

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Behavior of solids , liquids & gases

due to thermal conductivity

BATCH A

- SE BIOTECH

Thermal Conductivity:

 Thermal Conductivity is defined as ‘the quantity of

heat transmitted through unit thickness of a material

in a direction normal to the surface of unit area due to

unit temperature gradient under steady state

condition’.

 S/I Unit: W/(m K)

The effect of temperature on thermal conductivity is different for metals and nonmetals. In metals conductivity is primarily due to free electrons. Following the Wiedemann–Franz law, thermal conductivity of metals is approximately proportional to the absolute temperature (in kelvin) times electrical conductivity. In pure metals the electrical conductivity decreases with increasing temperature and thus the product of the two, the thermal conductivity, stays approximately constant. In alloys the change in electrical conductivity is usually smaller and thus thermal conductivity increases with temperature, often proportionally to temperature. On the other hand, heat conductivity in nonmetals is mainly due to lattice vibrations (phonons). Except for high quality crystals at low temperatures, the phonon mean free path is not reduced significantly at higher temperatures. Thus, the thermal conductivity of nonmetals is approximately constant at low temperatures. At low temperatures well below the Debye temperature, thermal conductivity decreases, as does the heat capacity.

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. Eg: Thermal Conductance of:

1. Silver 429 W/(m K)
2. Diamond 900 W/(m K) .