Flux Totally Explained

Everything about Flux totally explained

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. 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. 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. It has units of watts per square metre (Wm^-2)

One could argue, based on the work of James Clerk Maxwell, 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've 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). (Newton's law of viscosity,)

Heat flux, the rate of heat flow across a unit area (J·m^-2·s^-1). (Fourier's law of convection) (This definition of heat flux fits Maxwell's original definition.)

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 of groundwater flow)

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.

Energy flux, the rate of transfer of energy through a unit area (J·m^-2·s^-1). The radiative flux and heat flux are specific cases of energy flux. 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

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

Phi = 2pisigma_

. Its flux is called the magnetic flux. The time-rate of change of the magnetic flux through a loop of wire is minus the electromotive force created in that wire. The direction is such that if current is allowed to pass through the wire, the electromotive force will cause a current which "opposes" the change in magnetic field by itself producing a magnetic field opposite to the change. This is the basis for inductors and many electric generators.

Poynting vector

The flux of the Poynting vector through a surface is the electromagnetic power, or energy per unit time, passing through that surface. This is commonly used in analysis of electromagnetic radiation, but has application to other electromagnetic systems as well.

Biology

In general, 'flux' in biology relates to movement of a substance between compartments. There are several cases where the concept of 'flux' is important.

The movement of molecules across a membrane: in this case, flux is defined by the rate of diffusion or transport of a substance across a permeable membrane. Except in the case of active transport, net flux is directly proportional to the concentration difference across the membrane, the surface area of the membrane, and the membrane permeability constant.

In ecology, flux is often considered at the ecosystem level - for instance, accurate determination of carbon fluxes using techniques like eddy covariance (at a regional and global level) is essential for modeling the causes and consequences of global warming.

Metabolic flux refers to the rate of flow of metabolites along a metabolic pathway, or even through a single enzyme. A calculation may also be made of carbon (or other elements, for example nitrogen) flux. It is dependent on a number of factors, including: enzyme concentration; the concentration of precursor, product, and intermediate metabolites; post-translational modification of enzymes; and the presence of metabolic activators or repressors. Metabolic control analysis and flux balance analysis provide frameworks for understanding metabolic fluxes and their constraints.Further Information

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