A REINVESTIGATION OF LAMINAR CHANNEL FLOW PASSING OVER POROUS BED

Abstract

ABSTRACT Laminar shear flows in channels with porous media bed are reinvestigated in the present study. The problem is similar to multiple-layered Poiseuille flow; the upper layer is homogeneous fluid, while the lower layer is rigid porous media flow. The conventional Navier-Stokes equation simplified by the fully developed channel flow condition is used to deal with the upper layer flow. The governing equation of laminar porous media flow derived in Song [7] is simplified and applied to the porous media bed. The analytical solution obtained in this study not only provides more reasonable fluid velocity inside the porous media bed than the one Darcy's law gives, but is also capable of clearly describing the partial-slip boundary condition given in Beavers and Joseph [1]. We further find that when the thinickness of the porous media bed divided by the square root of specific permeability approaches infinity, the nondimensional parameter α in the partial-slip boundary condition is only a function of porosity; i.e. .