Heat current

A heat current is a kinetic exchange rate between molecule

Molecule

A molecule is defined as an electrically neutral group of at least two atoms in a definite arrangement held together by very strong chemical bonds. Molecules are distinguished from polyatomic ions in this strict sense...

s, relative to the material in which the kinesis

Kinematics

Kinematics is the branch of classical mechanics that describes the motion of objects without consideration of the causes leading to the motion....

 occurs. It is defined as , where is heat

Heat

In physics and thermodynamics, heat is the process of energy transfer from one body or system due to thermal contact, which in turn is defined as an energy transfer to a body in any other way than due to work performed on the body....

 and is time

Time

Time is a component of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify the motions of objects...

.

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

Differential equation

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...

, when integrated

Integral

Integration is an important concept in mathematics which, together with differentiation, forms one of the main operations in calculus. Given a function ƒ of a real variable x and an interval [a, b] of the real line, the definite integralis defined informally...

 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

Thermal radiation

Thermal radiation is electromagnetic radiation emitted from the surface of an object which is due to the object's temperature. An example of thermal radiation is the infrared radiation emitted by a common household radiator or electric heater. A person near a raging bonfire will feel the radiated...

, 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

Phonon

In physics, a phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the atomic lattice of a solid. The study of phonons is an important part of solid state physics, because phonons play a major role in many of the physical properties of solids, including a material's...

 distribution multiplied by the energy of one phonon, times the group velocity

Group velocity

The group velocity of a wave is the velocity with which the overall shape of the wave's amplitudes — known as the modulation or envelope of the wave — propagates through space....

 of the phonon

Phonon

In physics, a phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the atomic lattice of a solid. The study of phonons is an important part of solid state physics, because phonons play a major role in many of the physical properties of solids, including a material's...

s.

A heat current is a kinetic exchange rate between molecule

Molecule

A molecule is defined as an electrically neutral group of at least two atoms in a definite arrangement held together by very strong chemical bonds. Molecules are distinguished from polyatomic ions in this strict sense...

s, relative to the material in which the kinesis

Kinematics

Kinematics is the branch of classical mechanics that describes the motion of objects without consideration of the causes leading to the motion....

 occurs. It is defined as , where is heat

Heat

In physics and thermodynamics, heat is the process of energy transfer from one body or system due to thermal contact, which in turn is defined as an energy transfer to a body in any other way than due to work performed on the body....

 and is time

Time

Time is a component of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify the motions of objects...

.

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

Differential equation

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...

, when integrated

Integral

Integration is an important concept in mathematics which, together with differentiation, forms one of the main operations in calculus. Given a function ƒ of a real variable x and an interval [a, b] of the real line, the definite integralis defined informally...

 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

Thermal radiation

Thermal radiation is electromagnetic radiation emitted from the surface of an object which is due to the object's temperature. An example of thermal radiation is the infrared radiation emitted by a common household radiator or electric heater. A person near a raging bonfire will feel the radiated...

, 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

Phonon

In physics, a phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the atomic lattice of a solid. The study of phonons is an important part of solid state physics, because phonons play a major role in many of the physical properties of solids, including a material's...

 distribution multiplied by the energy of one phonon, times the group velocity

Group velocity

The group velocity of a wave is the velocity with which the overall shape of the wave's amplitudes — known as the modulation or envelope of the wave — propagates through space....

 of the phonon

Phonon

In physics, a phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the atomic lattice of a solid. The study of phonons is an important part of solid state physics, because phonons play a major role in many of the physical properties of solids, including a material's...

s. The phonon distribution of a particular phonon mode is given by the Bose-Einstein factor, which is dependent on temperature and phonon

Phonon

In physics, a phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the atomic lattice of a solid. The study of phonons is an important part of solid state physics, because phonons play a major role in many of the physical properties of solids, including a material's...

energy.