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 d Q d t , where Q is heat and t is time.

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

∂ Q ∂ t = − k ∮ S ∇ → T ⋅ d S →

where

∂ Q ∂ t is the amount of heat transferred per unit time [W] and d S → 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:

Δ Q Δ t = − k A Δ T Δ x

where

A is the cross-sectional surface area, Δ T is the temperature difference between the ends, Δ x is the distance between the ends.

For thermal radiation, heat current is defined as

W = σ ⋅ A ⋅ T 4

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.HEAT CAPACITY HAS DIMENSIONAL FORMULA [ML^2T^-3]