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
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
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 . 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.
In some solids, thermal conduction is
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. The relationship between thermal conductivity and conductance is analogous to the relationship between
There is also a measure known as the
The heat transfer coefficient is also known as thermal admittance in the sense that the material may be seen as admitting heat to flow.[
An additional term,
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.