Heat Current

A heat current is a kinetic exchange rate between molecules, relative to the material in which the kinesis occurs. It is defined as, where is heat and is time.

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

where

is the amount of heat transferred per unit time and
is an oriented surface area element

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,
is the temperature difference between the ends,
is the distance between the ends.

For thermal radiation, heat current is defined as

where the constant of proportionality is the Stefan–Boltzmann constant, is the radiating surface area, and 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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