# Heat current

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{{More citations needed|date=December 2009}}
{{Infobox physical quantity|othernames=Thermal current|unit=[Watt](/source/Watt)|dimension=wikidata|derivations=<math>H = {\Delta Q \over \Delta t} = {\Delta T \over R} </math>|symbols=''H''}}
A '''heat current''' or '''thermal current''' is a kinetic exchange rate between [molecule](/source/molecule)s, relative to the material in which the [kinesis](/source/Kinematics) occurs. It is defined as the net rate of flow of [heat](/source/heat). The [SI unit](/source/SI_Unit) of heat current is the [watt](/source/watt), which is the flow of heat across a surface at the rate of one [Joule](/source/Joule) per second.

For [conduction](/source/Conduction_(heat)), heat current is defined by [Fourier's law](/source/Fourier's_law)<ref>{{Cite book |last1=B. Arfken |first1=George |last2=F. Griffing |first2=David |last3=C. Kelly |first3=Donald |last4=Priest |first4=Joseph |date=1984 |title=International Edition University Physics |chapter=Chapter 23 - HEAT TRANSFER |chapter-url=https://www.sciencedirect.com/science/article/abs/pii/B9780120598588500285 |pages=430–443 |publisher=Academic Press |doi=10.1016/B978-0-12-059858-8.50028-5 |isbn=978-0-12-059858-8 }}</ref> as
: <math> \frac{\partial Q}{\partial t} = -k \oint_S{\overrightarrow{\nabla} T \cdot \,\overrightarrow{dS}} </math>
where
:<math>\big. \frac{\partial Q}{\partial t}\big.</math> is the amount of heat transferred per unit time [W] and
:
:<math>\overrightarrow{dS}</math> is an oriented surface area element [m<sup>2</sup>]
The above [differential equation](/source/differential_equation), when [integrated](/source/Integral) for a homogeneous material of 1-D geometry between two endpoints at constant temperature, gives the heat flow rate as:
: <math> \big. \frac{\Delta Q}{\Delta t} = -k A \frac{\Delta T}{\Delta x} </math>
where
: ''A'' is the cross-sectional surface area,
: <math>\Delta T</math> is the temperature difference between the ends,
: <math>\Delta x</math> is the distance between the ends.

For [thermal radiation](/source/thermal_radiation), heat current is defined as
:<math>W = \sigma \cdot A \cdot T^4</math>
where the [constant of proportionality](/source/constant_of_proportionality) <math>\sigma</math> is the [Stefan–Boltzmann constant](/source/Stefan%E2%80%93Boltzmann_constant), <math>A</math> is the radiating surface area, and <math>T</math> is temperature.

Heat current can also be thought of as the total [phonon](/source/phonon) distribution multiplied by the energy of one phonon, times the [group velocity](/source/group_velocity) of the [phonon](/source/phonon)s. The phonon distribution of a particular phonon mode is given by the [Bose-Einstein](/source/Bose%E2%80%93Einstein_statistics) factor, which is dependent on temperature and [phonon](/source/phonon) energy.

==See also==
* [Thermal conduction](/source/Thermal_conduction)
* [Thermal conductivity](/source/Thermal_conductivity)

==References==
{{Reflist}}

{{DEFAULTSORT:Heat Current}}
Category:Heat transfer

{{Thermodynamics-stub}}

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Adapted from the Wikipedia article [Heat current](https://en.wikipedia.org/wiki/Heat_current) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Heat_current?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.