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Flux




In the various subfields of Physics , there exist two common usages of the term flux, both with rigorous mathematical frameworks.
  • In the study of Transport Phenomena ( Heat Transfer , Mass Transfer and Fluid Dynamics ), flux is defined as the amount that flows through a unit area per unit time, the Volumetric Flow Rate .1 Flux in this definition is a Vector .

  • In the field of Electromagnetism , flux is usually the Integral of a Vector quantity over a finite surface. The result of this integration is a Scalar quantity.2 The Magnetic Flux is thus the integral of the magnetic vector field B over a surface, and the electric flux is defined similarly. Using this definition, the flux of the Poynting Vector over a specified surface is the rate at which electromagnetic energy flows through that surface. Confusingly, the Poynting vector is sometimes called the ''power flux'', which is an example of the first usage of flux, above.3 p.357 It has units of Watt s per Square Metre (W/m2)


One could argue, based on the work of James Clerk Maxwell 4, that the transport definition precedes the more recent way the term is used in electromagnetism. The specific quote from Maxwell is "''In the case of fluxes, we have to take the integral, over a surface, of the flux through every element of the surface. The result of this operation is called the Surface Integral of the flux. It represents the quantity which passes through the surface''".

In addition to these common mathematical definitions, there are many more loose usages found in fields such as biology.


TRANSPORT PHENOMENA


Flux definition and theorems

Flux is surface bombardment rate. There are many fluxes used in the study of transport phenomena. Each type of flux has its own distinct unit of measurement along with distinct physical constants. Six of the most common forms of flux from the transport literature are defined as:
#''Momentum flux'', the rate of transfer of Momentum across a unit area (N·s·m-2·s-1). (Newtonian fluid, Viscous Flow )
#''Heat flux'', the rate of Heat flow across a unit area (J·m-2·s-1). ( Fourier's Law )5 (This definition of heat flux fits Maxwell's original definition.6)
#''Chemical flux'', the rate of movement of molecules across a unit area (mol·m-2·s-1). ( Fick's Law Of Diffusion )
#''Volumetric flux'', the rate of Volume flow across a unit area (m3·m-2·s-1). ( Darcy's Law )
#''Mass flux'', the rate of Mass flow across a unit area (kg·m-2·s-1). (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 moving in the form of Photons at a certain distance from the source per Steradian per second (J·m-2·s-1). Used in astronomy to determine the 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 infrared spectrum.

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.

The fundamental laws that govern this process include:
  • Newton's law of viscosity

  • Fourier's law of convection

  • Fick's law of diffusion.

  • Darcy's law of groundwater flow



Chemical diffusion

Flux, or diffusion, for gaseous molecules can be related to the Function :

:\Phi = 2\pi\sigma_{ab}^2\sqrt{ rac{8kT}{\pi N}}

where
N

k

T

:\sigma_{ab} is the mean free path between the molecules ''a'' and ''b''.

Chemical molar flux of a component A in an Isothermal , Isobaric System is also defined in Ficks's First Law as:

:\overrightarrow{J_A} = -D_{AB}
abla c_A

where
:D_{AB} is the molecular diffusion coefficient (m2/s) of component A diffusing through component B,
:c_A is the concentration ( Mol /m3) of species A.7

This flux has units of mol·m−2·s−1, and fits Maxwell's original definition of flux.8

Note:
abla (" Nabla ") denotes the Del operator.


Quantum mechanics

See Also: Probability current


In Quantum Mechanics , particles of mass m in the state \psi(r,t) have a probability density defined as