Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. A flux is either a concept based in physics or used with applied mathematics. Both concepts have mathematical rigor, enabling comparison of the underlying mathematics when the terminology is unclear. For transport phenomena, flux is a vector quantity, describing the magnitude and direction of the flow of a substance or property. In electromagnetism, flux is a scalar quantity, defined as the surface integral of the component of a vector field perpendicular to the surface at each point.
The concept of heat flux was a key contribution of Joseph Fourier, in the analysis of heat transfer phenomena. His seminal treatise Théorie analytique de la chaleur (The Analytical Theory of Heat), defines fluxion as a central quantity and proceeds to derive the now well-known expressions of flux in terms of temperature differences across a slab, and then more generally in terms of temperature gradients or differentials of temperature, across other geometries. One could argue, based on the work of James Clerk Maxwell, that the transport definition precedes the 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.— James Clerk Maxwell
According to the first definition, flux may be a single vector, or flux may be a vector field / function of position. In the latter case flux can readily be integrated over a surface. By contrast, according to the second definition, flux is the integral over a surface; it makes no sense to integrate a second-definition flux for one would be integrating over a surface twice. Thus, Maxwell's quote only makes sense if "flux" is being used according to the first definition (and furthermore is a vector field rather than single vector). This is ironic because Maxwell was one of the major developers of what we now call "electric flux" and "magnetic flux" according to the second definition. Their names in accordance with the quote (and first definition) would be "surface integral of electric flux" and "surface integral of magnetic flux", in which case "electric flux" would instead be defined as "electric field" and "magnetic flux" defined as "magnetic field". This implies that Maxwell conceived of these fields as flows/fluxes of some sort.
Given a flux according to the second definition, the corresponding flux density, if that term is used, refers to its derivative along the surface that was integrated. By the Fundamental theorem of calculus, the corresponding flux density is a flux according to the first definition. Given a current such as electric current—charge per time, current density would also be a flux according to the first definition—charge per time per area. Due to the conflicting definitions of flux, and the interchangeability of flux, flow, and current in nontechnical English, all of the terms used in this paragraph are sometimes used interchangeably and ambiguously. Concrete fluxes in the rest of this article will be used in accordance to their broad acceptance in the literature, regardless of which definition of flux the term corresponds to.
In transport phenomena (heat transfer, mass transfer and fluid dynamics), flux is defined as the rate of flow of a property per unit area, which has the dimensions [quantity]·[time]−1·[area]−1. The area is of the surface the property is flowing "through" or "across". For example, the magnitude of a river's current, i.e. the amount of water that flows through a cross-section of the river each second, or the amount of sunlight energy that lands on a patch of ground each second, are kinds of flux.
Here are 3 definitions in increasing order of complexity. Each is a special case of the following. In all cases the frequent symbol j, (or J) is used for flux, q for the physical quantity that flows, t for time, and A for area. These identifiers will be written in bold when and only when they are vectors.
First, flux as a (single) scalar:
In this case the surface in which flux is being measured is fixed, and has area A. The surface is assumed to be flat, and the flow is assumed to be everywhere constant with respect to position, and perpendicular to the surface.
Second, flux as a scalar field defined along a surface, i.e. a function of points on the surface:
As before, the surface is assumed to be flat, and the flow is assumed to be everywhere perpendicular to it. However the flow need not be constant. q is now a function of p, a point on the surface, and A, an area. Rather than measure the total flow through the surface, q measures the flow through the disk with area A centered at p along the surface.
Finally, flux as a vector field:
In this case, there is no fixed surface we are measuring over. q is a function of a point, an area, and a direction (given by a unit vector, ), and measures the flow through the disk of area A perpendicular to that unit vector. I is defined picking the unit vector that maximizes the flow around the point, because the true flow is maximized across the disk that is perpendicular to it. The unit vector thus uniquely maximizes the function when it points in the "true direction" of the flow. [Strictly speaking, this is an abuse of notation because the "arg max" cannot directly compare vectors; we take the vector with the biggest norm instead.]
These direct definitions, especially the last, are rather unwieldy. For example, the argmax construction is artificial from the perspective of empirical measurements, when with a Weathervane or similar one can easily deduce the direction of flux at a point. Rather than defining the vector flux directly, it is often more intuitive to state some properties about it. Furthermore, from these properties the flux can uniquely be determined anyway.
If the flux j passes through the area at an angle θ to the area normal , then
where · is the dot product of the unit vectors. This is, the component of flux passing through the surface (i.e. normal to it) is j cos θ, while the component of flux passing tangential to the area is j sin θ, but there is no flux actually passing through the area in the tangential direction. The only component of flux passing normal to the area is the cosine component.
A (and its infinitesimal) is the vector area, combination of the magnitude of the area through which the property passes, A, and a unit vector normal to the area, . The relation is . Unlike in the second set of equations, the surface here need not be flat.
Finally, we can integrate again over the time duration t1 to t2, getting the total amount of the property flowing through the surface in that time (t2 − t1):
Eight of the most common forms of flux from the transport phenomena literature are defined as follows:
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.
This flux has units of mol·m−2·s−1, and fits Maxwell's original definition of flux.
In turbulent flows, the transport by eddy motion can be expressed as a grossly increased diffusion coefficient.
So the probability of finding a particle in a differential volume element d3r is
Then the number of particles passing perpendicularly through unit area of a cross-section per unit time is the probability flux;
The surface has to be orientable, i.e. two sides can be distinguished: the surface does not fold back onto itself. Also, the surface has to be actually oriented, i.e. we use a convention as to flowing which way is counted positive; flowing backward is then counted negative.
The surface normal is usually directed by the right-hand rule.
Conversely, one can consider the flux the more fundamental quantity and call the vector field the flux density.
Often a vector field is drawn by curves (field lines) following the "flow"; the magnitude of the vector field is then the line density, and the flux through a surface is the number of lines. Lines originate from areas of positive divergence (sources) and end at areas of negative divergence (sinks).
See also the image at right: the number of red arrows passing through a unit area is the flux density, the curve encircling the red arrows denotes the boundary of the surface, and the orientation of the arrows with respect to the surface denotes the sign of the inner product of the vector field with the surface normals.
If the surface encloses a 3D region, usually the surface is oriented such that the influx is counted positive; the opposite is the outflux.
The divergence theorem states that the net outflux through a closed surface, in other words the net outflux from a 3D region, is found by adding the local net outflow from each point in the region (which is expressed by the divergence).
If the surface is not closed, it has an oriented curve as boundary. Stokes' theorem states that the flux of the curl of a vector field is the line integral of the vector field over this boundary. This path integral is also called circulation, especially in fluid dynamics. Thus the curl is the circulation density.
We can apply the flux and these theorems to many disciplines in which we see currents, forces, etc., applied through areas.
One way to better understand the concept of flux in electromagnetism is by comparing it to a butterfly net. The amount of air moving through the net at any given instant in time is the flux. If the wind speed is high, then the flux through the net is large. If the net is made bigger, then the flux is larger even though the wind speed is the same. For the most air to move through the net, the opening of the net must be facing the direction the wind is blowing. If the net is parallel to the wind, then no wind will be moving through the net. The simplest way to think of flux is "how much air goes through the net", where the air is a velocity field and the net is the boundary of an imaginary surface.
An electric "charge," such as a single electron in space, has a magnitude defined in coulombs. Such a charge has an electric field surrounding it. In pictorial form, an electric field is shown as a dot radiating "lines of flux" called Gauss lines. Electric Flux Density is the amount of electric flux, the number of "lines," passing through a given area. Units are Gauss/square meter.
and one for the D-field (called the electric displacement):
This quantity arises in Gauss's law – which states that the flux of the electric field E out of a closed surface is proportional to the electric charge QA enclosed in the surface (independent of how that charge is distributed), the integral form is:
where ε0 is the permittivity of free space.
If one considers the flux of the electric field vector, E, for a tube near a point charge in the field the charge but not containing it with sides formed by lines tangent to the field, the flux for the sides is zero and there is an equal and opposite flux at both ends of the tube. This is a consequence of Gauss's Law applied to an inverse square field. The flux for any cross-sectional surface of the tube will be the same. The total flux for any surface surrounding a charge q is q/ε0.
In free space the electric displacement is given by the constitutive relation D = ε0 E, so for any bounding surface the D-field flux equals the charge QA within it. Here the expression "flux of" indicates a mathematical operation and, as can be seen, the result is not necessarily a "flow", since nothing actually flows along electric field lines.
with the same notation above. The quantity arises in Faraday's law of induction, in integral form:
where dℓ is an infinitesimal vector line element of the closed curve C, with magnitude equal to the length of the infinitesimal line element, and direction given by the tangent to the curve C, with the sign determined by the integration direction.
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.
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.
The DeLorean time machine is a fictional automobile-based time travel vehicle device featured in the Back to the Future franchise. In the feature film series, Dr. Emmett L. Brown builds a time machine based on a DeLorean car, to gain insights into history and the future. Instead, he ends up using it to travel over 130 years of Hill Valley history (from 1885 to 2015) with Marty McFly to change the past for the better and to undo the negative effects of time travel. One of the cars used in filming is on display in Paarl South Africa and the official Back to the Future DeLorean can be viewed at the Petersen Automotive Museum.Dysentery
Dysentery is an inflammatory disease of the intestine, especially of the colon, which always results in severe diarrhea and abdominal pains. Other symptoms may include fever and a feeling of incomplete defecation. The disease is caused by several types of infectious pathogens such as bacteria, viruses and parasites.Electric flux
In electromagnetism, electric flux is the measure of the distribution of the electric field through a given surface, although an electric field in itself cannot flow. It is a way of describing the electric field strength at any distance from the charge causing the field.
The electric field E can exert a force at any point in space. The electric field is proportional to the gradient of the voltage. The electric field is capable of moving point charged particles. The ratio of the force over the flow is an impedance.Electromagnetic induction
Electromagnetic or magnetic induction is the production of an electromotive force (i.e., voltage) across an electrical conductor in a changing magnetic field.
Michael Faraday is generally credited with the discovery of induction in 1831, and James Clerk Maxwell mathematically described it as Faraday's law of induction. Lenz's law describes the direction of the induced field. Faraday's law was later generalized to become the Maxwell–Faraday equation, one of the four Maxwell equations in his theory of electromagnetism.
Electromagnetic induction has found many applications, including electrical components such as inductors and transformers, and devices such as electric motors and generators.Faraday's law of induction
Faraday's law of induction (shortly called Faraday's law throughout this document) is a basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF)—a phenomenon called electromagnetic induction. It is the fundamental operating principle of transformers, inductors, and many types of electrical motors, generators and solenoids.The Maxwell–Faraday equation (listed as one of Maxwell's equations) describes the fact that a spatially varying (and also possibly time-varying, depending on how a magnetic field varies in time) electric field always accompanies a time-varying magnetic field, while Faraday's law states that there is EMF (electromotive force, defined as electromagnetic work done on a unit charge when it has traveled one round of a conductive loop) on the conductive loop when the magnetic flux through the surface enclosed by the loop varies in time.
Historically, Faraday's law had been discovered and one aspect of it (transformer EMF) was formulated as the Maxwell–Faraday equation later. Interestingly, the equation of Faraday's law can be derived by the Maxwell–Faraday equation (describing transformer EMF) and the Lorentz force (describing motional EMF). The integral form of the Maxwell–Faraday equation describes only the transformer EMF, while the equation of Faraday's law describes both the transformer EMF and the motional EMF.Flux (metallurgy)
In metallurgy, a flux (derived from Latin fluxus meaning “flow”) is a chemical cleaning agent, flowing agent, or purifying agent. Fluxes may have more than one function at a time. They are used in both extractive metallurgy and metal joining.
Some of the earliest known fluxes were carbonate of soda, potash, charcoal, coke, borax, lime, lead sulfide and certain minerals containing phosphorus. Iron ore was also used as a flux in the smelting of copper. These agents served various functions, the simplest being a reducing agent, which prevented oxides from forming on the surface of the molten metal, while others absorbed impurities into the slag, which could be scraped off the molten metal.
As cleaning agents, fluxes facilitate soldering, brazing, and welding by removing oxidation from the metals to be joined. Common fluxes are: ammonium chloride or rosin for soldering tin; hydrochloric acid and zinc chloride for soldering galvanized iron (and other zinc surfaces); and borax for brazing, braze-welding ferrous metals, and forge welding.
In the process of smelting, inorganic chlorides, fluorides (see fluorite), limestone and other materials are designated as "fluxes" when added to the contents of a smelting furnace or a cupola for the purpose of purging the metal of chemical impurities such as phosphorus, and of rendering slag more liquid at the smelting temperature. The slag is a liquid mixture of ash, flux, and other impurities. This reduction of slag viscosity with temperature, increasing the flow of slag in smelting, is the original origin of the word flux in metallurgy. Fluxes are also used in foundries for removing impurities from molten nonferrous metals such as aluminium, or for adding desirable trace elements such as titanium.
In high-temperature metal joining processes (welding, brazing and soldering), flux is a substance which is nearly inert at room temperature, but which becomes strongly reducing at elevated temperatures, preventing oxidation of the base and filler materials. The role of a flux is typically dual: dissolving the oxides already present on the metal surface, which facilitates wetting by molten metal, and acting as an oxygen barrier by coating the hot surface, preventing its oxidation.
For example, tin-lead solder attaches very well to copper, but poorly to the various oxides of copper, which form quickly at soldering temperatures. By preventing the formation of metal oxides, flux enables the solder to adhere to the clean metal surface, rather than forming beads, as it would on an oxidized surface.
In some applications molten flux also serves as a heat-transfer medium, facilitating heating of the joint by the soldering tool or molten solder.
Fluxes for soft soldering are typically of organic nature, though inorganic fluxes, usually based on halogenides and/or acids, are also used in non-electronics applications. Fluxes for brazing operate at significantly higher temperatures and are therefore mostly inorganic; the organic compounds tend to be of supplementary nature, e.g. to make the flux sticky at low temperature so it can be easily applied.Flux (software)
Flux is a software suite released by Media Machines which consists of Flux Player and Flux Studio.
Flux Player is a VRML/X3D viewer that works both as plugin in Internet Explorer, and as standalone program in Windows. Flux Studio is a VRML/X3D editor that works in Windows. Both programs supports Windows Me/2000 and higher.
Flux Player and Flux Studio are freely downloadable for any usage under a proprietary Flux Player and Flux Studio license.
Flux software is developed by Tony Parisi, who coworked with Mark Pesce on the development of the experimental VRML prototype called Labyrinth. Flux Studio can successfully import and export *.WRL, *.X3DV and *.X3D files.
Initial distribution version of Flux Player 2.0 and Flux Studio 2.0 was released on February 21, 2007; while final distribution version of Flux Player 2.1 and Flux Studio 2.1 was released on May 28, 2007.Gauss's law
In physics, Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field.
The surface under consideration may be a closed one enclosing a volume such as a spherical surface.
The law was first formulated by Joseph-Louis Lagrange in 1773, followed by Carl Friedrich Gauss in 1813, both in the context of the attraction of ellipsoids. It is one of Maxwell's four equations, which form the basis of classical electrodynamics. Gauss's law can be used to derive Coulomb's law, and vice versa.Hemodialysis
Hemodialysis, also spelled haemodialysis, or simply dialysis, is a process of purifying the blood of a person whose kidneys are not working normally. This type of dialysis achieves the extracorporeal removal of waste products such as creatinine and urea and free water from the blood when the kidneys are in a state of kidney failure. Hemodialysis is one of three renal replacement therapies (the other two being kidney transplant and peritoneal dialysis). An alternative method for extracorporeal separation of blood components such as plasma or cells is apheresis.
Hemodialysis can be an outpatient or inpatient therapy. Routine hemodialysis is conducted in a dialysis outpatient facility, either a purpose built room in a hospital or a dedicated, stand-alone clinic. Less frequently hemodialysis is done at home. Dialysis treatments in a clinic are initiated and managed by specialized staff made up of nurses and technicians; dialysis treatments at home can be self-initiated and managed or done jointly with the assistance of a trained helper who is usually a family member.Irradiance
In radiometry, irradiance is the radiant flux (power) received by a surface per unit area. The SI unit of irradiance is the watt per square metre (W/m2). The CGS unit erg per square centimetre per second (erg·cm−2·s−1) is often used in astronomy. Irradiance is often called intensity because it has the same physical dimensions, but this term is avoided in radiometry where such usage leads to confusion with radiant intensity.
Spectral irradiance is the irradiance of a surface per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. The two forms have different dimensions: spectral irradiance of a frequency spectrum is measured in watts per square metre per hertz (W·m−2·Hz−1), while spectral irradiance of a wavelength spectrum is measured in watts per square metre per metre (W·m−3), or more commonly watts per square metre per nanometre (W·m−2·nm−1).Latent heat
Latent heat is thermal energy released or absorbed, by a body or a thermodynamic system, during a constant-temperature process — usually a first-order phase transition.
Latent heat can be understood as heat energy in hidden form which is supplied or extracted to change the state of a substance without changing its temperature. Examples are latent heat of fusion and latent heat of vaporization involved in phase changes, i.e. a substance condensing or vaporizing at a specified temperature and pressure.The term was introduced around 1762 by British chemist Joseph Black. It is derived from the Latin latere (to lie hidden). Black used the term in the context of calorimetry where a heat transfer caused a volume change in a body while its temperature was constant.
In contrast to latent heat, sensible heat is a heat transfer that results in a temperature change in a body.Lumen (unit)
The lumen (symbol: lm) is the SI derived unit of luminous flux, a measure of the total quantity of visible light emitted by a source. Luminous flux differs from power (radiant flux) in that radiant flux includes all electromagnetic waves emitted, while luminous flux is weighted according to a model (a "luminosity function") of the human eye's sensitivity to various wavelengths. Lumens are related to lux in that one lux is one lumen per square meter.
The lumen is defined in relation to the candela as
1 lm = 1 cd ⋅ sr.A full sphere has a solid angle of 4π steradians, so a light source that uniformly radiates one candela in all directions has a total luminous flux of 1 cd × 4π sr = 4π cd⋅sr ≈ 12.57 lumens.Magnetic field
A magnetic field is a vector field that describes the magnetic influence of electrical currents and magnetized materials. In everyday life, the effects of magnetic fields are often seen in permanent magnets, which pull on magnetic materials (such as iron) and attract or repel other magnets. Magnetic fields surround and are created by magnetized material and by moving electric charges (electric currents) such as those used in electromagnets. Magnetic fields exert forces on nearby moving electrical charges and torques on nearby magnets. In addition, a magnetic field that varies with location exerts a force on magnetic materials. Both the strength and direction of a magnetic field varies with location. As such, it is an example of a vector field.
The term 'magnetic field' is used for two distinct but closely related fields denoted by the symbols B and H. In the International System of Units, H is measured in units of amperes per meter and B is measured in teslas, which are equivalent to newtons per meter per ampere. H and B differ in how they account for magnetization. In a vacuum, B and H are the same aside from units; but in a magnetized material, B/ and H differ by the magnetization M of the material at that point in the material.
Magnetic fields are produced by moving electric charges and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property, their spin. Magnetic fields and electric fields are interrelated, and are both components of the electromagnetic force, one of the four fundamental forces of nature.
Magnetic fields are widely used throughout modern technology, particularly in electrical engineering and electromechanics. Rotating magnetic fields are used in both electric motors and generators. The interaction of magnetic fields in electric devices such as transformers is studied in the discipline of magnetic circuits. Magnetic forces give information about the charge carriers in a material through the Hall effect. The Earth produces its own magnetic field, which shields the Earth's ozone layer from the solar wind and is important in navigation using a compass.Magnetic flux
In physics, specifically electromagnetism, the magnetic flux (often denoted Φ or ΦB) through a surface is the surface integral of the normal component of the magnetic field B passing through that surface. The SI unit of magnetic flux is the weber (Wb) (in derived units: volt seconds), and the CGS unit is the maxwell. Magnetic flux is usually measured with a fluxmeter, which contains measuring coils and electronics, that evaluates the change of voltage in the measuring coils to calculate the magnetic flux.Radiant flux
In radiometry, radiant flux or radiant power is the radiant energy emitted, reflected, transmitted or received, per unit time, and spectral flux or spectral power is the radiant flux per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. The SI unit of radiant flux is the watt (W), that is the joule per second (J/s) in SI base units, while that of spectral flux in frequency is the watt per hertz (W/Hz) and that of spectral flux in wavelength is the watt per metre (W/m)—commonly the watt per nanometre (W/nm).Soldering
Soldering (AmE: , BrE: ) is a process in which two or more items are joined together by melting and putting a filler metal (solder) into the joint, the filler metal having a lower melting point than the adjoining metal. Unlike welding, soldering does not involve melting the work pieces. In brazing, the filler metal melts at a higher temperature, but the work piece metal does not melt. In the past, nearly all solders contained lead, but environmental and health concerns have increasingly dictated use of lead-free alloys for electronics and plumbing purposes.Transformer
A transformer is a static electrical device that transfers electrical energy between two or more circuits. A varying current in one coil of the transformer produces a varying magnetic flux, which, in turn, induces a varying electromotive force across a second coil wound around the same core.
Electrical energy can be transferred between the two coils, without a metallic connection between the two circuits. Faraday's law of induction discovered in 1831 described the induced voltage effect in any coil due to changing magnetic flux encircled by the coil.
Transformers are used for increasing or decreasing the alternating voltages in electric power applications, and for coupling the stages of signal processing circuits.
Since the invention of the first constant-potential transformer in 1885, transformers have become essential for the transmission, distribution, and utilization of alternating current electric power. A wide range of transformer designs is encountered in electronic and electric power applications. Transformers range in size from RF transformers less than a cubic centimeter in volume, to units weighing hundreds of tons used to interconnect the power grid.Æon Flux
Æon Flux is an American avant-garde science fiction animated television series that aired on MTV November 30, 1991, until October 10, 1995, with film, comic book, and video game adaptations following thereafter. It premiered MTV's Liquid Television experimental animation show, as a six-part serial of short films, followed in 1992 by five individual short episodes. In 1995, a season of ten half-hour episodes aired as a stand-alone series. Æon Flux was created by Korean American animator Peter Chung.The live-action movie Æon Flux, loosely based upon the series and starring Charlize Theron, was released in theaters on December 2, 2005, preceded in November of that year by a tie-in video game of the same name based mostly on the movie but containing some elements of the original TV series.Æon Flux (film)
Æon Flux is a 2005 American science fiction spy action film based on the animated science fiction television series of the same name created by Peter Chung, which aired on MTV from 1991-1995. It was directed by Karyn Kusama, written by Phil Hay and Matt Manfredi, and produced by Gale Anne Hurd, David Gale, Gary Lucchesi and Greg Goodman. The film was produced by MTV Films, Lakeshore Entertainment, Babelsberg Film Studio and Valhalla Motion Pictures. It stars Charlize Theron as the title character, Marton Csokas, Jonny Lee Miller, Sophie Okonedo, Pete Postlethwaite, and Frances McDormand.
The film was released on December 2, 2005 by Paramount Pictures in the United States. The film was poorly reviewed by critics and grossed $52.3 million on a production budget of $65 million.