## Thermal conductivity |

The **thermal conductivity** of a material is a measure of its ability to

Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal conductivity. For instance, metals typically have high thermal conductivity and are very efficient at conducting heat, while the opposite is true for insulating materials like

The defining equation for thermal conductivity is , where is the

- definition
- units
- measurement
- experimental values
- influencing factors
- theoretical prediction
- conversion from specific to absolute units, and vice versa
- equations
- see also
- references
- further reading
- external links

Consider a solid material placed between two environments of different temperatures. Let be the temperature at and be the temperature at , and suppose . A possible realization of this scenario is a building on a cold winter day: the solid material in this case would be the building wall, separating the cold outdoor environment from the warm indoor environment.

According to the ^{[1]}

The constant of proportionality is the thermal conductivity; it is a physical property of the material. In the present scenario, since heat flows in the minus x-direction and is negative, which in turn means that . In general, is always defined to be positive. The same definition of can also be extended to gases and liquids, provided other modes of energy transport, such as

For simplicity, we have assumed here that the does not vary significantly as temperature is varied from to . Cases in which the temperature variation of is non-negligible must be addressed using the more general definition of discussed below.

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.

Energy flow due to thermal conduction is classified as heat and is quantified by the vector , which gives the heat flux at position and time . According to the second law of thermodynamics, heat flows from high to low temperature. Hence, it is reasonable to postulate that is proportional to the gradient of the temperature field , i.e.

where the constant of proportionality, , is the thermal conductivity. This is called Fourier's law of heat conduction. In actuality, it is not a law but a *definition* of thermal conductivity in terms of the independent physical quantities and .^{[2]}^{[3]} As such, its usefulness depends on the ability to determine for a given material under given conditions. The constant itself usually depends on and thereby implicitly on space and time. An explicit space and time dependence could also occur if the material is inhomogeneous or changing with time.^{[4]}

In some solids, thermal conduction is

where is symmetric, second-rank ^{[5]}

An implicit assumption in the above description is the presence of

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. For a plate of thermal conductivity , area and thickness , the conductance is , measured in W⋅K^{−1}.^{[6]} The relationship between thermal conductivity and conductance is analogous to the relationship between

**Thermal resistance** is the inverse of thermal conductance.^{[6]} It is a convenient measure to use in multicomponent design since thermal resistances are additive when occurring in ^{[7]}

There is also a measure known as the *unit area* of a plate of particular thickness when its opposite faces differ in temperature by one kelvin.^{[8]} In ^{[9]} The reciprocal of the heat transfer coefficient is **thermal insulance**. In summary, for a plate of thermal conductivity , area and thickness , we have

- thermal conductance = , measured in W⋅K
^{−1}.- thermal resistance = , measured in K⋅W
^{−1}.

- thermal resistance = , measured in K⋅W
- heat transfer coefficient = , measured in W⋅K
^{−1}⋅m^{−2}.- thermal insulance = , measured in K⋅m
^{2}⋅W^{−1}.

- thermal insulance = , measured in K⋅m

The heat transfer coefficient is also known as **thermal admittance** in the sense that the material may be seen as admitting heat to flow.^{[citation needed]}

An additional term, ^{[citation needed]} It is measured in the same units as thermal conductance and is sometimes known as the *composite thermal conductance*. The term * U-value* is also used.

Finally, ^{[10]}

- .

As such, it quantifies the *thermal inertia* of a material, i.e. the relative difficulty in heating a material to a given temperature using heat sources applied at the boundary.^{[11]}