 Energy flux

An energy flux describes transport of energy across a surface. A flux density ${\mathbf{j}}_E$ has units of power per area; the total outward power through $S$ is ${\int }_S{\mathbf{j}}_E\cdot \mathbf{n}dS$, with outward unit normal $\mathbf{n}$. A local conservation law relates the divergence of ${\mathbf{j}}_E$ to the time derivative of the energy density and any sources.

For a one-dimensional inviscid gas with velocity $u$, pressure $p$, mass density $\rho$ and internal energy density $W$, the total mechanical-plus-internal energy flux isThe first two terms advect internal energy and kinetic energy. The term $pu$ is pressure work: a moving section of area $A$ transmits force $pA$ at velocity $u$, giving power $pAu$. This formula assumes negligible viscous stress and heat conduction; those processes contribute their own energy-transfer terms when retained.

Energy flux is a measure of the rate at which energy is transferred or radiated through a given surface area. It quantifies how much energy passes through a unit area in a specific direction per unit of time. The concept is commonly used in fields such as physics, engineering, and environmental science to describe the flow of energy.