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2.3.7 Thermal conductivities

Definition and units

The thermal conductivity, λ, of a substance may be defined as the quantity of heat transmitted, Q, due to unit temperature gradient, in unit time under steady conditions in a direction normal to a surface of unit area, when the heat transfer is dependent only on the temperature gradient.

λ  =  − Q		∂T
		∂n

In this section thermal conductivity values are assembled for metallic, semi-conducting and insulating elements, representative groups of alloys, refractories and miscellaneous constructional and insulating materials, some liquids and some gases. The values are expressed in the SI unit W m⁻¹ K⁻¹ throughout. Factors for converting to other units are as follows:

1 W m⁻¹ K⁻¹      =  0.01 J cm cm⁻² s⁻¹ K⁻¹

                       =  0.002 388 cal cm cm⁻² s⁻¹ K⁻¹

                       =  0.859 8 kcal m m⁻² h⁻¹ K⁻¹

                       =  0.001 926 Btu in ft⁻² s⁻¹ °F⁻¹

                       =  6.933 Btu in ft⁻² h⁻¹ °F⁻¹

                       =  0.577 8 Btu ft ft⁻² h⁻¹ °F⁻¹

                       =  0.000 160 5 Btu ft ft⁻²s⁻¹ °F⁻¹

More extensive collections of thermal conductivity data will be found in Touloukian et al. (1970a, b and c).

Thermal conductivities of metallic elements

The thermal conductivity values in the table below are for metallic elements in the purest polycrystalline condition for which reliable measurements have been reported. Entries in italics relate to the liquid phase.

The thermal conductivities of less pure samples of these elements will be lower than the values given below. Thermal conductivity invariably decreases with decreasing purity; such dependence being weak at ambient and higher temperatures but very strong at cryogenic temperatures.

    ^† Values for the a-axis which approximate to the polycrystal; those for the b-axis are 91 and 88 and for the c-axis are 16.5 and 16 at 173.2 and 273.2 K.

Thermal conductivities of single crystals of some non-cubic metals at normal temperature

Thermal conductivities of alloys

At low temperatures the thermal conductivity of a given metal tends to increase in proportion to the reciprocal of its residual resistivity ρ₀. Many metals, especially good electrical conductors, have thermal conductivities that follow the simple relation

at very low temperatures and at temperatures higher than their Debye temperature; L₀ being the Lorentz coefficient 2.45 × 10⁻⁸ W s⁻¹ K⁻², σ the electrical conductivity in S m⁻¹ and T the absolute temperature. This behaviour enables the thermal conductivities of metallic samples to be estimated fairly reliably from simple electrical resistivity measurements.

As the thermal conductivities of alloys depend strongly on their mechanical and thermal history (heat treatment) as well as on their chemical composition, the values tabulated below should be regarded as typical for the compositions listed. For many groups of alloys the thermal conductivity of a particular sample, near room temperature and above, can be estimated within about 6% from its more easily measured electrical conductivity using the relation λ = LσT + C. The optimum values for L and C for different alloy types are as follows:

For more detailed information on the relationship between the thermal and electrical conductivities of alloys see: Powell (1965), Hust and Clark (1971).

Thermal conductivities of alloys at ambient and elevated temperatures