Transient forced convection in an isothermal fluid-saturated porous medium layer: effective permeability and boundary layer thickness

Abstract

Transient forced convection in an isothermal saturated porous-medium layer is analyzed analytically on the basis of the Forchheimer-Brinkman-extended Darcy equation. An analytical solution describing the transient regime is obtained by considering the ensemble average velocity of the fluid flow as much larger than the fluctuations in the fluid velocity. This solution provides a better knowledge of the features of the flow within the porous layer. Among other results is presented an expression for the effective porous-medium permeability, as a function of the Darcy number, of the Reynolds number, and of a "relaxation time" characteristic of the transient regime. The solution found also indicates that an appropriate periodic forcing of the pressure gradient may increase the effective permeability of the porous layer to fluid flow.