In the various subfields of physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, there exist two common usages of the term flux, both with rigorous mathematical frameworks.
  • In the study of transport phenomena
    Transport Phenomena
    Transport Phenomena is the first textbook that is about transport phenomena. It is specifically designed for chemical engineering students...

     (heat transfer
    Heat transfer
    Heat transfer is a discipline of thermal engineering that concerns the exchange of thermal energy from one physical system to another. Heat transfer is classified into various mechanisms, such as heat conduction, convection, thermal radiation, and phase-change transfer...

    , mass transfer
    Mass transfer
    Mass transfer is the net movement of mass from one location, usually meaning a stream, phase, fraction or component, to another. Mass transfer occurs in many processes, such as absorption, evaporation, adsorption, drying, precipitation, membrane filtration, and distillation. Mass transfer is used...

     and fluid dynamics
    Fluid dynamics
    In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...

    ), flux is defined as flow per unit area, where flow is the movement of some quantity per time. Flux, in this definition, is a vector.

  • In the fields of electromagnetism
    Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...

     and mathematics
    Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

    , flux is usually the integral
    Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus...

     of a vector quantity, flux density
    Flux density
    -Formal Statement:The flux density is simply defined as the amount of flux passing through a unit-area. -Mathematical Statement:The flux density would essentially be the number of field lines passing through a defined unit-area...

    , over a finite surface.