# Flux Terminology: Scalar Flux vs. Flux Density in Different Contexts

• etotheipi
In summary, there is a discrepancy in the usage of the term "flux" in different contexts. In surface integrals, the scalar result is usually referred to as flux while the vector field is called the flux density. However, in other contexts, flux is used to denote the vector field itself. It may be more consistent to use the first approach (fluxes for scalars and flux densities for vector fields), but it is unclear which usage is preferred. It is possible that the term "density" is sometimes omitted, leading to confusion. This is evident in the example of Fick's law of diffusion, where the diffusion flux vector is measured per unit area per unit time but is still referred to as "flux." It is possible that
etotheipi
Forgive me if a similar thread has been posted before... I was doing some questions and I just noticed an apparent discrepancy in how the term "flux" is thrown around.

In the context of surface integrals, the scalar result is usually termed the flux whilst the vector field is termed the flux density, i.e. in $$\phi = \iint_S \mathbf{F} \cdot d\mathbf{S}$$ the ##\phi## would be flux through ##S## and ##\mathbf{F}## the flux density. This is also the terminology used in electromagnetism.

However in other contexts we appear to use flux to denote the vector field; e.g. we let the volumetric flux ##\mathbf{v}## be the velocity, and call the flow rate $$\frac{dV}{dt} = \iint_S \mathbf{v} \cdot d\mathbf{A}$$ The same goes for mass flow rates, current densities, and so on. Is one of these old usage/preferred over the other? To me it seems it would be more consistent to use the first approach (fluxes for the scalars and flux densities for the vector fields), but I'm not sure which is preferred. I wondered whether anyone could clarify - thanks!

etotheipi said:
. I was doing some questions and I just noticed an apparent discrepancy in how the term "flux" is thrown around... To me it seems it would be more consistent to use the first approach (fluxes for the scalars and flux densities for the vector fields)
Could it be that "density" was simply omitted sometimes?

vanhees71 and etotheipi
A.T. said:
Could it be that "density" was simply omitted sometimes?

It could well be, I'm not too sure. The question itself was regarding Fick's law of diffusion where you have ##\mathbf{J} = - D\nabla \phi## and ##\mathbf{J}## is usually called the diffusion flux vector, even though it is measured per unit area per unit time. Maybe they're just being sloppy?

## 1. What is flux?

Flux is a term used in science to describe the flow of a physical quantity through a surface or boundary. It can refer to the movement of energy, particles, or matter.

## 2. What is the difference between flux and flow?

Flux and flow are often used interchangeably, but there is a subtle difference. Flux refers to the amount of a quantity that passes through a surface, while flow refers to the rate at which the quantity moves.

## 3. What are the units of flux?

The units of flux depend on the type of quantity being measured. For example, the units of energy flux are watts per square meter, while the units of mass flux are kilograms per square meter per second.

## 4. How is flux related to the laws of thermodynamics?

Flux is a fundamental concept in the study of thermodynamics. The first law of thermodynamics states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. Flux is used to quantify the transfer of heat and work in this equation.

## 5. Can flux be negative?

Yes, flux can be negative. This occurs when the quantity is moving in the opposite direction of the surface or boundary being measured. For example, if heat is flowing out of a system, the heat flux would be negative.

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