Page 187 - gas transport in porous media

181
Chapter 10: Natural Convection Gas Transport in Porous Media
law to account for a quadratic drag. A generalized model for the fluid flow through a
porous media was developed during the past couple of decades which accounts for the
inertial and boundary effects, and the quadratic drag. These effects are incorporated by
using this general flow model known as the Brinkman-Forchheimer-extended Darcy
model.
A comprehensive literature review on natural convection gas transport in porous
media is conducted targeting different categories of interest. These categories are
1. Natural Convection from a Horizontal Surface Embedded in a Porous Medium
2. Natural Convection from a Vertical Surface
3. Natural Convection from an Inclined Surface
4. Natural Convection in Vertical Channels
5. Natural Convection around Cylinders
6. Natural Convection around Spheres
7. Natural Convection in Enclosures
8. Double-Diffusive Natural Convection within a Porous Medium.

10.2 NATURAL CONVECTION FROM A HORIZONTAL SURFACE

Convection heat transfer from surfaces embedded in porous media has received sub-
stantial amount of attention because of applications in geophysical and energy-related
engineering problems. Comprehensive reviews were presented by Cheng (1985) and
Nield and Bejan (1992).
The problem of steady free convection in a porous medium adjacent to a horizontal
impermeable heated surface, with variable wall temperature was investigated by
Chang and Cheng (1983) using the method of matched asymptotic expansions. The
effects of fluid entrainment, streamwise heat conduction and upward-drift induced
friction were taken into consideration in the second and third-order theory for which
similarity solutions were obtained.
The free convective boundary layer above a near-horizontal heated flat surface
bounding a saturated porous medium was studied by Rees and Riley (1985). Two
configurations were considered: one where the component of the buoyancy force
along the surface assisted the flow, the other opposed the flow. Series solutions were
developed: one valid near the leading edge, where the flow was driven along by an
induced pressure gradient, and for the favorable case only, an asymptotic solution,
where the flow was driven along by the direct action of buoyancy forces.
Boundary-layer analysis was performed by Pop and Gorla (1991) for free convec-
tion flow over a hot horizontal surface embedded in a porous medium saturated with
a gas with variable properties. The variable gas properties were accounted for via
the assumption that thermal conductivity and dynamic viscosity were proportional to
temperature. A similarity solution was shown to exist for the case of constant surface
temperature. Numerical results for the stream function, horizontal velocity, and tem-
perature profiles within the boundary layer as well as for the mass of entrained gas,
surface slip velocity, and heat transfer rate at different values of the wall-temperature