Flux definition
Flux is the rate of transfer of energy, particles or heat of fluid across a given surface. It is the presence of a force field in a specified physical medium or the flow of energy through a surface.
What is the flux density
The amount of magnetic or electric flux passing through a unit area is called flux density.
Flux density is described as an effect that is pass or travels through a surface or substance, whether it actually moves or not. Flux is a concept in vector calculus and applied mathematics which has many applications to physics.
Flux is a vector quantity, described by the magnitude and direction both when the object is flow. The different object shows a different property. In vector calculus, the flux is a scalar quantity. Flux is defined as the surface integral of only the perpendicular component of a vector field over a surface.
Flux as flow rate per unit area
In acceleration phenomena (heat transfer, mass transfer, and fluid dynamics), flux is defined as the rate of flow of a material per unit area, which has three dimensions quantity, time and area.
The area is of the surface is the property of flowing material through or across some surface. For example, the magnitude of a river current, so the amount of water that flows through a crosssection area of a river in each second, or the amount of sunlight radiation that lands on a patch of ground each second. These all are kinds of flux.
The general mathematical definition of flux
Here are 3 definitions or three cases in increasing order of complexity a flux. Each is a special case of the following. In all cases the symbol j is used for flux density, q is used for the physical quantity that can flow, t is for time, and A is for the area. These all identifiers will be written in bold form, only when they are vectors.
Case 1
Flux as a single scalar quantity:
In this case, the surface in which flux is being measured is a fixed area (A). Let the surface is assumed to be flat, and the flow of material is assumed to be everywhere constant with respect to position, and perpendicular to the surface.
Case 2
Flux as a scalar field and defined along a surface, so a function of points is on the surface:
When we assumed that the surface is to be flat, and the flow is assumed to be everywhere perpendicular to surface. However, the flow need not be constant speed. Now q is a function of p, a point on the surface and A is an area. Rather than measure the total flow of material through the surface, we only measure q that flow through the disk with area A centered at p along the surface.
Case 3
Flux as a vector field so:
There is no fixed surface in this case. We are measuring magnitude direction and vector field. The q is a function of a point, A is an area, and n is a direction (given by a unit vector), and j measures the flow through the disk having an area A that is perpendicular to that unit vector. It is defined as the unit vector that maximizes the flow of material around the point.
The true flow is at maximum across the disk that is perpendicular to it. Then the unit vector completely maximizes the function when its points flow in true.
Transport fluxes
There are eight of the most common forms of flux from the transport phenomena, which are defined as follows:

Momentum flux
The momentum flux is defined as the rate of transfer of momentum across a unit area. Its unit is (N·s/m^{2}·s^{1}).

Heat flux
Heat flux is defined as the rate of heat flow across a unit area. Its unit is (J/m^{2}·s^{1}).

Diffusion flux
Diffusion flux is defined as the rate of movement of molecules across a unit area. Its unit is (mol/m^{2}·s^{1}).

Volumetric flux
Volumetric flux is defined as the rate of volume flow across a unit area. Its unit is (m^{3}/m^{2}·s^{1}).

Mass flux
Mass flux is defined as the rate of mass flow across a unit area. Its unit is (kg/m^{2}·s^{1}).

Radiative flux
Radiative flux is defined as the amount of energy transferred in the form of photons at a certain distance from the source per unit area per second. Its unit is (J/m^{2}·s^{1}).
Radiative flux is used in the astronomy branch to determine the magnitude and different spectral class of a star. It also acts as a generalization of heat flux, which is equal to the Radiative flux when is only restricted to the electromagnetic spectrum.

Energy flux
Energy flux is defined as the rate of transfer of energy through a unit area. Its unit is (J/m^{2}·s^{1}). The Radiative flux and heat flux are special cases of energy flux.

Particle flux
Particle flux is defined as the rate of transfer of particles through a unit area. Its unit is (number of particles/m^{2}·s^{1})
These fluxes are vectors quantities at each point in space and have define and specific 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.