Heat current

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{{Infobox physical quantity|othernames=Thermal current|unit=Watt|dimension=wikidata|derivations=$H\; =\; \{\backslash Delta\; Q\; \backslash over\; \backslash Delta\; t\}\; =\; \{\backslash Delta\; T\; \backslash over\; R\}$|symbols=H}}

A heat current or thermal current is a kinetic exchange rate between molecules, relative to the material in which the kinesis occurs. It is defined as the net rate of flow of heat. The SI unit of heat current is the watt, which is the flow of heat across a surface at the rate of one Joule per second.

For conduction, heat current is defined by Fourier's law{{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 }} as

: $\backslash frac\{\backslash partial\; Q\}\{\backslash partial\; t\}\; =\; -k\; \backslash oint\_S\{\backslash overrightarrow\{\backslash nabla\}\; T\; \backslash cdot\; \backslash ,\backslash overrightarrow\{dS\}\}$

where

:$\backslash big.\; \backslash frac\{\backslash partial\; Q\}\{\backslash partial\; t\}\backslash big.$ is the amount of heat transferred per unit time [W] and

:

:$\backslash overrightarrow\{dS\}$ is an oriented surface area element [m²]

The above differential equation, when integrated for a homogeneous material of 1-D geometry between two endpoints at constant temperature, gives the heat flow rate as:

: $\backslash big.\; \backslash frac\{\backslash Delta\; Q\}\{\backslash Delta\; t\}\; =\; -k\; A\; \backslash frac\{\backslash Delta\; T\}\{\backslash Delta\; x\}$

where

: A is the cross-sectional surface area,

: $\backslash Delta\; T$ is the temperature difference between the ends,

: $\backslash Delta\; x$ is the distance between the ends.

For thermal radiation, heat current is defined as

:$W\; =\; \backslash sigma\; \backslash cdot\; A\; \backslash cdot\; T^4$

where the constant of proportionality $\backslash sigma$ is the Stefan–Boltzmann constant, $A$ is the radiating surface area, and $T$ is temperature.

Heat current can also be thought of as the total phonon distribution multiplied by the energy of one phonon, times the group velocity of the phonons. The phonon distribution of a particular phonon mode is given by the Bose-Einstein factor, which is dependent on temperature and phonon energy.