Page 200 - gas transport in porous media

Khanafer and Vafai
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porous medium in the presence of a transverse magnetic field and fluid heat genera-
tion effects was studied numerically by Khanafer and Chamkha (1998). The walls of
the enclosure were maintained at constant temperature. The flow in the porous region
was modeled using the Brinkman-extended Darcy’s law to account for the no-slip
conditions at the walls. The control volume method was used to solve the governing
balance equations for different values of the Darcy number, Hartmann number, and
the inclination angle. The obtained numerical results were presented graphically in
terms of streamlines and isotherms as well as velocity and temperature profiles at
midsections of the cavity to illustrate interesting features of the solution.
A pressure-velocity solution for natural convection for fluid saturated heat gen-
erating porous medium in a square enclosure was analyzed using the finite element
method by Das and Sahoo (1999). The numerical solutions obtained for a wide range
of fluid Rayleigh number, Darcy number, and heat generating number for a Prandtl
number of unity. It was observed that the peak temperature occurs at the top central
part and weaker velocity prevails near the vertical walls of the enclosure due to the
heat generation. The modified Rayleigh number used by earlier investigators cannot
explain explicitly the effect of heat generation parameter on natural convection within
anenclosurehavingdifferentiallyheatedverticalwalls.Asexpected, increasingDarcy
number, results in a higher peak velocity. Experimental investigations are performed
for natural convective heat transfer in a composed rectangular-parallelogrammic
enclosure by Hwang and Kim (1999). The experiments covered a range of modi-
fied Grashof numbers utilizing various inclination angles. The air-filled enclosure
consists of vertical heat source and sink walls, and adiabatic top and bottom walls.
The effects of a guide vane installed within the composed enclosure and the dimen-
sionless channel depth were studied. Experimental results were given as plots of
Nusselt number vs. the inclined angles and dimensionless channel depth.
Thick layers of highly permeable loose-fill insulation are used to thermally insulate
attics in modern building technology. Since the use of highly permeable insulation
leads to an increase in air movement not only in the porous layer (insulation) but
also in the fluid layer (attics), it is interest to determine the influence of natural
and forced convection on thermal properties of the insulating porous medium. In
related to this type of application, a numerical investigation of natural convection
in horizontal porous media heated from below was analyzed both numerically and
experimentally by Shankar and Hagentoft (2000). The combined effect of air flow
within the open portion of the cavity as well as the porous layer was investigated. The
results obtained from the numerical computations were compared with experimental
findings.
As an application to the nuclear waste management, Webb (2001) provided
a method that allows one to compute an equivalent permeability using Darcy’s law
based on open space flow physics. It was done for a square enclosure with and without
a porous media fill. Webb and Hickox (2001) applied the equivalent permeability anal-
ysis to horizontal concentric cylinders and compared the results to a CFD calculation
for horizontal concentric cylinders.