Page 251 - Fundamentals of The Finite Element Method for Heat and Fluid Flow

CONVECTION IN POROUS MEDIA
Solid wall
Velocity profile 243

Figure 8.2 Viscous forces on a bounding wall of a porous medium

porosity approaches a value of unity. The discussion on convection in porous media in
this chapter will be brief and based on the generalized porous medium approach. Readers
should be aware of the CBS scheme and the notations used in the previous chapter before
reading this section.

8.2 Generalized Porous Medium Flow Approach

In this section, a generalized model for solving porous medium flows will be presented. Let
us consider the balance of mass, momentum, energy and species for two-dimensional flow
in a fluid-saturated porous medium of variable porosity. The derivations are very similar to
the one discussed in Chapter 7. We shall assume the medium to be isotropic with constant
physical properties, except for the medium porosity. Let a f be the fraction of area available
for flow per unit of cross-sectional area (Figure 8.3), at a location in a given direction. In
fact, a f is an averaged quantity, the average being taken over the length scale of the voids
(or the length scale of the particles, if the porous bed is made up of particles), in the flow
direction. For an isotropic porous bed, a f will be identical in all directions and can also
be equal to the local bed porosity, . In spite of averaging over the void length scale, the

∆ x 1

Fluid

∆ x 2

Solid

Figure 8.3 Fluid-saturated porous medium. Infinitesimal control volume