Page 199 - gas transport in porous media

Chapter 10: Natural Convection Gas Transport in Porous Media
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the same author (1993) performed an analytical study to identify the range of influence
of each term of the general equation for flow within a fluid saturated porous medium.
Natural convection in a shallow laterally heated air-filled cavity was investigated
numerically by Wright et al. (1995) using a primitive variable formulation of the
governing equations. Solutions were obtained for the entire flow field using a coupled
solver combined with an FAS non-linear multigrid convergence accelerator. While
care was taken to use a high-order, bounded discretization scheme for convective
transport, the overall stability and efficiency of the approach was enhanced through
the use of a defect correction. This combination of features enabled solutions to be
found for very fine grids. Results for the flow in the end region of such cavities were
compared qualitatively with the predictions of asymptotic theory for large aspect
ratio, A (length: height), up to values of A higher than previously reported (A = 100);
the particular case of A = 20 was considered for Rayleigh numbers in the range of
8
3
10 to 10 . Finally it was demonstrated how such solutions can be further enhanced
by using locally refined grids in the end regions.
The theory of thermally driven convection of dry air in a porous medium was
reviewed by Stauffer and Auer (1997). Because of the differences in the physical
properties of air and water, initiation of convection required the product of thermal
gradient and permeability to be thousands of times greater for air than for water.
Finite amplitude analysis of the problem for Ra < 300 revealed that (1) at low
thermal gradient, Ra vs. Nu curves are nearly the same for air and water; (2) the slope
of the Ra vs. Nu curve matches well with experimental data reported by others for
water; (3) time to reach steady state decreases approximately as the square root of
Nusselt number.
Multiple steady-state solutions of natural convection in an inclined enclosure with
a fluid layer and a heat-generating porous bed were investigated numerically using
the finite volume method by Chen and Lin (1997). The conservation equations for
the porous layer were based on a general flow model, which includes boundary and
inertial effects. The flow in the fluid layer was modeled by Navier-Stokes equations.
The method of pseudo arc-length continuation was adapted in studying the effects of
tilt angle on flow pattern and heat transfer. It was found that, based on the title angle,
there exists two groups of solutions with quite different flow pattern and heat transfer
behavior. The effects of aspect ratio on flow pattern and heat transfer have also been
studied. Prandtl number of 0.7 is assumed in that study.
Natural convection heat transfer in a fluid saturated variable porosity medium was
investigated by Nithiarasu et al. (1997a). A generalized non-Darcian porous medium
for natural convection was developed taking into account linear and non-linear matrix
drag components as well as the inertial and viscous forces within the fluid. A Prandtl
number of unity was assumed in that study. The authors established that the thickness
of the porous layer and the nature of variation in porosity substantially affect the
natural convection flow pattern as well as the heat transfer features.
The problem of unsteady, laminar, two-dimensional hydromagnetic natural con-
vection heat transfer in an inclined square enclosure filled with a fluid-saturated