Thermal conduction is defined as the transport of energy due to random molecular motion across a temperature gradient.

It is distinguished from energy transport by convection and molecular work in that it does not involve macroscopic flows or work-performing internal stresses.

This assumption could be violated in systems that are unable to attain local equilibrium, as might happen in the presence of strong nonequilibrium driving or long-ranged interactions.

In engineering practice, it is common to work in terms of quantities which are derivative to thermal conductivity and implicitly take into account design-specific features such as component dimensions.

For instance, thermal conductance is defined as the quantity of heat that passes in unit time through a plate of particular area and thickness when its opposite faces differ in temperature by one kelvin.

The disadvantage is that a well-engineered experimental setup is usually needed, and the time required to reach steady state precludes rapid measurement.

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.

Therefore, many insulating materials function simply by having a large number of gas-filled pockets which obstruct heat conduction pathways.

Examples of these include expanded and extruded polystyrene (popularly referred to as "styrofoam") and silica aerogel, as well as warm clothes.

Natural, biological insulators such as fur and feathers achieve similar effects by trapping air in pores, pockets, or voids.

The thermal conductivity through bulk materials in porous or granular form is governed by the type of gas in the gaseous phase, and its pressure.

[28] At low pressures, the thermal conductivity of a gaseous phase is reduced, with this behaviour governed by the Knudsen number, defined as

Any expressions for thermal conductivity which are exact and general, e.g. the Green-Kubo relations, are difficult to apply in practice, typically consisting of averages over multiparticle correlation functions.

[31] A notable exception is a monatomic dilute gas, for which a well-developed theory exists expressing thermal conductivity accurately and explicitly in terms of molecular parameters.

In a simplified picture of a solid, thermal conduction occurs by two mechanisms: 1) the migration of free electrons and 2) lattice vibrations (phonons).

This modification has been carried out, yielding revised Enskog theory, which predicts a density dependence of the thermal conductivity in dense gases.

varies significantly depending on the particular form of the interparticle interactions: this is a result of the energy exchanges between the internal and translational degrees of freedom of the molecules.

An example of a simple but very rough theory is that of Bridgman, in which a liquid is ascribed a local molecular structure similar to that of a solid, i.e. with molecules located approximately on a lattice.

[51][failed verification] This was done by assuming that the relaxation time τ decreases with increasing number of atoms in the unit cell and then scaling the parameters of the expression for thermal conductivity in high temperatures accordingly.

[52] At low temperatures (< 10 K) the anharmonic interaction does not influence the mean free path and therefore, the thermal resistivity is determined only from processes for which q-conservation does not hold.

To U-process to occur the decaying phonon to have a wave vector q1 that is roughly half of the diameter of the Brillouin zone, because otherwise quasimomentum would not be conserved.

[50][52] Thermal conductivity is usually described by the Boltzmann equation with the relaxation time approximation in which phonon scattering is a limiting factor.

Another approach is to use analytic models or molecular dynamics or Monte Carlo based methods to describe thermal conductivity in solids.

This is achieved by introducing interface scattering mechanism, which requires structures whose characteristic length is longer than that of impurity atom.

Because thermal conductivity depends continuously on quantities like temperature and material composition, it cannot be fully characterized by a finite number of experimental measurements.

This capability is important in thermophysical simulations, where quantities like temperature and pressure vary continuously with space and time, and may encompass extreme conditions inaccessible to direct measurement.

[53] For the simplest fluids, such as monatomic gases and their mixtures at low to moderate densities, ab initio quantum mechanical computations can accurately predict thermal conductivity in terms of fundamental atomic properties—that is, without reference to existing measurements of thermal conductivity or other transport properties.

If such an expression is fit to high-fidelity data over a large range of temperatures and pressures, then it is called a "reference correlation" for that material.

Thermophysical modeling software often relies on reference correlations for predicting thermal conductivity at user-specified temperature and pressure.

Thermal conductivity can also be computed using the Green-Kubo relations, which express transport coefficients in terms of the statistics of molecular trajectories.