Editing Flux (section)

=== Transport fluxes ===
Eight of the most common forms of flux from the transport phenomena literature are defined as follows: {{Citation needed|date=May 2025}}
# [[Transport phenomena#Momentum transfer|Momentum flux]], the rate of transfer of [[momentum]] across a unit area (N·s·m<sup>−2</sup>·s<sup>−1</sup>). ([[Newton's law of viscosity]])<ref name="Physics P.M">{{cite book|title=Essential Principles of Physics |author1=P.M. Whelan |author2=M.J. Hodgeson |edition=2nd|year=1978|publisher=John Murray|isbn=0-7195-3382-1}}</ref>
# [[Heat flux]], the rate of [[heat]] flow across a unit area (J·m<sup>−2</sup>·s<sup>−1</sup>). ([[Fourier's law|Fourier's law of conduction]])<ref>{{cite book | last=Carslaw | first=H.S. |author2=Jaeger, J.C. | title=Conduction of Heat in Solids  | edition=Second | year=1959 | publisher=Oxford University Press | isbn=0-19-853303-9 }}</ref> (This definition of heat flux fits Maxwell's original definition.)<ref name="Maxwell" />
# [[Diffusion flux]], the rate of movement of molecules across a unit area (mol·m<sup>−2</sup>·s<sup>−1</sup>). ([[Fick's law of diffusion]])<ref name="Physics P.M" />
# [[Volumetric flux]], the rate of [[volume]] flow across a unit area (m<sup>3</sup>·m<sup>−2</sup>·s<sup>−1</sup>). ([[Darcy's law|Darcy's law of groundwater flow]])
# [[Mass flux]], the rate of [[mass]] flow across a unit area (kg·m<sup>−2</sup>·s<sup>−1</sup>). (Either an alternate form of Fick's law that includes the molecular mass, or an alternate form of Darcy's law that includes the density.)
# [[Radiative flux]], the amount of energy transferred in the form of [[photons]] at a certain distance from the source per unit area per second (J·m<sup>−2</sup>·s<sup>−1</sup>). Used in astronomy to determine the [[Magnitude (astronomy)|magnitude]] and [[spectral class]] of a star.  Also acts as a generalization of heat flux, which is equal to the radiative flux when restricted to the electromagnetic spectrum.
# [[Energy flux]], the rate of transfer of [[energy]] through a unit area (J·m<sup>−2</sup>·s<sup>−1</sup>). The radiative flux and heat flux are specific cases of energy flux.
# [[Particle flux]], the rate of transfer of particles through a unit area ([number of particles] m<sup>−2</sup>·s<sup>−1</sup>)

These fluxes are vectors at each point in space, and have a definite magnitude and direction. Also, one can take the [[divergence]] of any of these fluxes to determine the accumulation rate of the quantity in a control volume around a given point in space.  For [[incompressible flow]], the divergence of the volume flux is zero.

==== Chemical diffusion ====
As mentioned above, chemical [[mass flux#Molar fluxes|molar flux]] of a component A in an [[isothermal]], [[Isobaric process|isobaric system]] is defined in [[Fick's law of diffusion]] as:
<math display="block">\mathbf{J}_A = -D_{AB} \nabla c_A</math>
where the [[nabla symbol]] ∇ denotes the [[gradient]] operator, ''D<sub>AB</sub>'' is the diffusion coefficient (m<sup>2</sup>·s<sup>−1</sup>) of component A diffusing through component B, ''c<sub>A</sub>'' is the [[concentration]] ([[mole (unit)|mol]]/m<sup>3</sup>) of component A.<ref>{{cite book | last=Welty |author2=Wicks, Wilson and Rorrer | year=2001 | title=Fundamentals of Momentum, Heat, and Mass Transfer | edition=4th | publisher=Wiley | isbn=0-471-38149-7 }}</ref>

This flux has units of mol·m<sup>−2</sup>·s<sup>−1</sup>, and fits Maxwell's original definition of flux.<ref name="Maxwell">{{cite book | last=Maxwell | first=James Clerk| author-link=James Clerk Maxwell | year=1892 | title=Treatise on Electricity and Magnetism | publisher=Courier Corporation| isbn=0-486-60636-8}}</ref>

For dilute gases, kinetic molecular theory relates the diffusion coefficient ''D'' to the particle density ''n'' = ''N''/''V'', the molecular mass ''m'', the collision [[Cross section (physics)|cross section]] <math>\sigma</math>, and the [[Thermodynamic temperature|absolute temperature]] ''T'' by
<math display="block">D = \frac{2}{3 n\sigma}\sqrt{\frac{kT}{\pi m}}</math>
where the second factor is the [[mean free path]] and the square root (with the [[Boltzmann constant]] ''k'') is the [[Maxwell–Boltzmann distribution#Typical speeds|mean velocity]] of the particles.

In turbulent flows, the transport by eddy motion can be expressed as a grossly increased diffusion coefficient.