Providing that the measured substance is homogeneous and ΔT is sufficiently small, a thermal conductivity value λ at a specific mean temperature can be defined. And although λ is considered to be an intrinsic property, and thus independent of thickness, there are many practical cases where the body is inhomogeneous, or a composite, and the measured property contains other modes of heat transfer, such as radiation and convection. This is why there is dependence on specimen thickness, emissivity of bounding surfaces and gas and moisture flow. In such circumstances the result is usually presented as an apparent or effective thermal conductivity.
The expression for λ is developed assuming the material as being 100 % pure, 100 % theoretically dense, homogeneous, free of defects and having dimensions greater than the mean free path of its parts. Any deviation from the ideal reduces the thermal conductivity value. Also, thermal conductivity can be highly dependent on temperature.
Solids are available in many purities and forms, from near theoretical density to low density solid, particulate and fibrous structures where the influences of impurity, density, particle size and form, contribution of a gas or other fluid are significant and in many cases radiation can often be a dominant mode of heat transfer within the material. If the thickness is below the mean free path as in very thin (sub-micrometre) films and microporous solids, boundary effects also occur that lower thermal conductivity value. Anisotropy due to crystal structure, material type and form and method of fabrication can cause large variations in property depending on the heat flow direction within the material.
For fluids thermal conductivity is highly dependent on purity, density and gas pressure. Many fluids are transparent to thermal radiation and also highly subject to convection, depending on the temperature and heat flow conditions.
In the most common practical temperature range of 100 < T < 3000 K, thermal conductivity ranges from values of 103 W/(mĚK) for pure single crystals such as natural diamond to below 10-4 W/(mĚK) for the best polished gold foil multi-layered types of thermal insulation operating in a vacuum environment at cryogenic temperatures.This behaviour is illustrated by alumina (see figure), an oxide ceramic that can exist in many forms, ranging from a dense pure single crystal (sapphire) through to solids of different purities and decreasing porosity and density, to low density powder and fibre products.
Thermal conductivity of alumina with different porosities.
Thermal conduction in a material has two dominant components: one due to electrons λe (for example, metals and alloys) and one due to lattice waves or phonons λg in insulators. There are additional contributions due to scattering processes (e.g. defects, dislocations, boundaries etc.) and interactions between electrons and phonons λi. Radiation λr becomes an increasingly important factor if the medium transmits, especially as the temperature increases.For a material that is highly porous and therefore has a low density, e.g. fibrous or cellular thermal insulation, the effect due to solid conduction λS becomes comparatively minor and the overall heat transmission becomes dominated by the gaseous environment (or lack of it, as in a vacuum) λgas and by radiation λr. Depending on the conditions and the density, a convective component λcon, can also occur.
Heat transmission v. density at 300 K: illustrating how heat transfer within thermal insulation divides into individual components.
For thermal diffusivity the relationship with thermal conductivity (a = λ ρ C) is valid only for homogeneous materials in which diffusive heat transfer occurs, i.e. the dominant mode of heat transmission is by solid conduction processes only.
Thermal diffusivity values cover a broad range although not as large as that for thermal conductivity, as shown in the diagram of thermal diffusivity values of different types of materials.
Thermal diffusivity of different types of material.