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A heat current is a kinetic exchange rate between molecules, relative to the material in which the kinesis occurs. It is defined as 
, where Q is heat and t is time.
For conduction, heat current is defined by Fourier's law as
where
is the amount of heat transferred per unit time [W] and
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:
where
- A is the cross-sectional surface area,
- ΔT is the temperature difference between the ends,
- Δx is the distance between the ends.
For thermal radiation, heat current is defined as
where the constant of proportionality σ 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.
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