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Chapter 10: Natural Convection Gas Transport in Porous Media
considered to be isothermal and adiabatic, respectively. The flow in the porous region
was modeled by a modified Darcy’s law where Brinkman’s extension was incorpo-
rated to allow the non-slip condition to be satisfied. A finite-difference scheme was
used to numerically solve the field equations in the two regions.
Beckermann et al. (1986) performed a numerical study of non-Darcian natural
convection in a vertical enclosure filled with a porous medium. The flow was mod-
eled using the Brinkman-Forchheimer-extended Darcy equations. The governing
equations were solved using the SIMPLER algorithm and good agreement with pre-
viously reported numerical and experimental results was found. They demonstrated
the importance of non-Darcian effects. For high Darcy numbers (Da > 10 −4 ), both
boundary and inertial effects were of the same order of magnitude and had to be
used simultaneously. In addition, Forchheimer’s extension had to be included for
Pr ≤ 1.0 for all Darcy numbers. Finally, Nusselt number correlations were presented
for three different ranges of the Darcy number covering a wide range of governing
parameters.
Vafai and Sarkar (1987) analyzed the condensation and phase change processes
in an enclosure partially filled with a porous insulation. The effect of variations in
the porous insulation thickness on the moisture, relative humidity, temperature, and
condensation rate fields was investigated. The problem was modeled as a transient,
multiphase flow in a composite slab consisting of a porous portion followed by an
air gap with impermeable, adiabatic horizontal boundaries and permeable vertical
boundaries. The thickness of the porous insulation was varied between 60 and 100%
of the overall thickness of the enclosure. For some typical conditions in a building
insulation, it was found that the condensation rate and the resultant liquid accumula-
tion did not increase significantly as the thickness of the insulation was decreased in
the aforementioned range. Condensation and phase change processes in an enclosure,
which was completely filled with a porous medium, was investigated earlier by Vafai
and Sarkar (1986).
The applicability of the Boussinesq approximation was investigated for natural
convection in a fluid-saturated porous cavity with vertical walls maintained at differ-
ent temperatures and insulated horizontal walls by Peirotti et al. (1987). Numerical
calculations were performed for water and air for a wide range of Rayleigh num-
bers and aspect ratios. Flow and temperature fields and heat-transfer rates, obtained
through the evaluation of a model that includes temperature-dependent properties,
were presented. The authors concluded that under certain circumstances the Nusselt
number evaluated through the Boussinesq approximation differs substantially from
the Nusselt number obtained with this model.
A numerical study of heat and mass transfer with phase change in porous materials
was performed by Vafai and Tien (1989). The problem was modeled by a system of
transient inter-coupled equations governing the two-dimensional multiphase transport
process in porous media. The solution algorithm allowed full simulation without
any significant simplifications. The variations and the interrelationships between the
temperature vapor density, condensation rate, liquid content and the fluid velocity
fields were demonstrated and discussed in detail. The aspect ratio of the porous matrix