Transport equation for the local residence time of a fluid

Abstract

The residence time of a fluid particle (or local residence time) is the time that the particle has spent inside a domain since its entry. A transport equation that provides the local residence time field is derived by the balance on a control volume of a variable denominated ”quantity of residence time”. A similar transport equation has been derived previously, but a more general expression is obtained through the present derivation. While the earlier equation is applicable to steady state, constant density flows, the equation proposed here can be applied to transient flows where density changes occur. The derivation also clarifies how to treat boundary conditions, a matter that has raised uncertainty in previous works. Furthermore, the concept of residence time of a chemical species is introduced, and the corresponding equation is formulated for specific cases.