Flux

Lore & Background

The word flux comes from Latin: fluxus means 'flow', and fluere is 'to flow'. As fluxion, this term was introduced into differential calculus by Isaac Newton. The concept of heat flux was a key contribution of Joseph Fourier in the analysis of heat transfer phenomena; his treatise Théorie analytique de la chaleur defines fluxion as a central quantity and derives expressions of flux in terms of temperature differences and gradients. According to the source, one could argue based on the work of James Clerk Maxwell that the transport definition precedes the definition of flux used in electromagnetism. Maxwell wrote: '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.' The source notes that Maxwell's quote only makes sense if 'flux' is used according to the transport definition, which is ironic because Maxwell was a major developer of what is now called electric flux and magnetic flux according to the electromagnetism definition. Due to conflicting definitions of flux and the interchangeability of flux, flow, and current in nontechnical English, all related terms are sometimes used interchangeably and ambiguously. In transport phenomena, flux is defined as the rate of flow of a property per unit area, with dimensions [quantity]·[time]⁻¹·[area]⁻¹.

Reader's Guide

Flux is a foundational concept bridging mathematics and physics, with two primary definitions that cause ongoing ambiguity. In transport phenomena, flux is a vector quantity describing the magnitude and direction of flow of a substance or property, defined as rate per unit area. In vector calculus, flux is a scalar quantity defined as the surface integral of the perpendicular component of a vector field over a surface. The source highlights that Maxwell's work on electromagnetism used the transport definition conceptually, even as he developed what are now called electric and magnetic flux under the electromagnetism definition. This duality means that terms like flux density and current density can refer to different quantities depending on context. The mathematical framework provides three levels of definition: scalar flux for uniform perpendicular flow through a flat surface, scalar field flux for non-uniform perpendicular flow, and vector field flux for flow in arbitrary directions. These definitions are nested, each a special case of the next. The concept's significance lies in its application across heat transfer, mass transfer, fluid dynamics, and electromagnetism, though the source notes that concrete fluxes in the rest of the article are used according to broad acceptance in the literature regardless of which definition they correspond to.

Did You Know?

• The word flux comes from Latin fluxus meaning 'flow' and fluere meaning 'to flow'.
• Isaac Newton introduced the term 'fluxion' into differential calculus.
• Joseph Fourier's treatise Théorie analytique de la chaleur defined fluxion as a central quantity in heat transfer.
• James Clerk Maxwell's quote on flux implies he conceived of electric and magnetic fields as flows or fluxes of some sort.