Structure of the dependence of Darcy and Forchheimer coefficients on porosity

The coefficients of the Darcy and Forchheimer terms are presented and analysed as functions of the porosity. Before this, we briefly review the development of theories for flow in a saturated porous medium. Thermal convection problems in a porous medium are also revisited with a view to bringing out the structure of the dependence on the porosity as a physical effect determining when convective overturning will occur. Finally, it is proved that the solution to flow in a Forchheimer porous material depends continuously on changes in the porosity.