A transport quantity is a property that is subject to transport by bulk fluid flow and/or by molecular interactions. The quantities may be conserved or nonconserved properties. Typical transport quantities include mass, momentum, and thermal energy.
Conserved quantity
In transport phenomena, the following quantities are conserved (as written for a control volume $CV$ of volume $V$)
$m=\iiint \limits _{CV}{\rho dV}$

(1)

$E=\iiint \limits _{CV}{\left(\rho {{\hat {u}}+{{1} \over {2}}v^{2}+gz}\right)dV}$

(2)

${\bf {P}}=\iiint \limits _{CV}{\rho {\bf {v}}dV}$

(3)

${\bf {L}}=\iiint \limits _{CV}{\rho \left({{\bf {r}}\times {\bf {v}}}\right)dV}$

(4)

The change in the amount of a conserved quantity in a control volume is exactly equal to the flow of the conserved quantity into the control volume minus the flow of the conserved quantity out of the control volume.
Nonconserved quantity
Mechanical and thermal energy
The total energy can be broken into two parts, the mechanical energy and the thermal (or internal) energy,
$ME=\iiint \limits _{CV}{\left({{{1} \over {2}}v^{2}+gz}\right)dV}$

(5)

$U=\iiint \limits _{CV}{\rho {\hat {u}}dV}$

(6)

Here, a macroscopic balance on either the mechanical or internal energy must include a nonconservative term that describes either the conversion (consumption) of mechanical energy due to friction or the generation of internal energy due to friction.
Mass in a multicomponent mixture
In systems that are made up of more than one component,
$m=\sum \limits _{\alpha =1,N}{m_{\alpha }}$

(7)

and,
$m_{\alpha }=\iiint \limits _{CV}{\rho _{\alpha }dV}$

(8)

While the total mass (the sum of the individual masses) is conserved, the mass of each component $\alpha$ is not conserved if there is either a homogenous or an inhomogeneous reaction. This can also be written on a molar basis
$n_{\alpha }=\iiint \limits _{CV}{c_{\alpha }dV}$

(9)
