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in field theory. The flux of a vector field through the surface Σ is expressed by the surface integral
∫∫∑(a·n) ds = ∫∫∑ (ax dydz + ay dzdx + az dxdy)
where a = (ax, ay, az) and n is the unit vector normal to Σ. The variation of n is assumed here to be continuous over Σ. For the field of velocities of particles in a fluid, the flux of the vector field is equal to the quantity of the fluid flowing per unit time through Σ.
a substance used in metallurgical processes to form slag or control the composition of slag, to prevent molten metals from reacting with ambient gases, or to dissolve oxides when metals are soldered or welded. In the smelting and refining of metals, fluxes are introduced to produce slags with prescribed physical and chemical properties, to slag gangue and fuel ash, and to dissolve objectionable impurities. Fluxes are used, for example, to reduce the refractoriness or viscosity of metals or to alter their electrical conductivity.
Fluxes may be basic, acid, or neutral. Basic fluxes, which contain oxides of calcium, magnesium, iron, or other metals, include limestone, dolomite, pyrite cinder, lime, and sodium carbonate. Acid fluxes—such as quartz, sand, and flint—contain silica. Neutral fluxes contain alumina or calcium fluoride and include clay, bauxites, crushed firebrick, and fluorspar.
Melts of ferrous metals and alloys are protected against oxidation by covering or protective fluxes; chlorides and fluorides of alkali and alkaline-earth metals—for example, rock salt, sylvinite, carnallite, cryolite, borax, and rosin—are most often used for this purpose. The fluxes used in soldering and welding include rosin, borax, zinc chloride, ammonium chloride, and fluorspar. A number of fluxes that are melted and processed in advance have been developed for arc welding; when such fluxes are used, welding is performed directly under the flux.
I. D. REZNIK