Page 193 - gas transport in porous media

Chapter 10: Natural Convection Gas Transport in Porous Media
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Nusselt and Sherwood numbers are deduced. For some particular cases, quantita-
tive comparisons with previous works reported in the literature were reported and
the agreement between theoretical results and experimental data was found to be
satisfactory.
A mathematical model governing free convection boundary-layer flow over an
isothermal inclined plate embedded in a thermally stratified porous medium in the
presence of a non-uniform transverse magnetic field was developed by Chamkha
(1997b). The resulting equations of that study account for non-Darcian boundary and
inertial effects of the porous medium and allow for variable ambient temperature. In
addition, the applied magnetic field was assumed to be an increasing function of the
distancealongtheplate. Prandtlnumberofunitywasassumedinthatstudy. Theresults
showed that as the Hartmann number increases, both the skin-friction coefficient and
the local Nusselt number are increased. The radiation effect of an optically dense
viscous incompressible fluid along a heated inclined flat surface maintained at a
uniform temperature and embedded in porous media was studied numerically by
Hossain and Pop (1997). The results of that study showed that as the buoyancy
parameter increases, the local Nusselt number increases.

10.5 NATURAL CONVECTION IN A VERTICAL CHANNEL
Analytical solutions for fully developed MHD natural convection flow in open-ended
vertical porous channels were presented by Al-Nimr and Hader (1999) using a Darcy
model. Four fundamental boundary conditions have been investigated and the cor-
responding fundamental solutions were obtained. Expressions for the flow and heat
transfer parameters were given in terms of the Darcy number, Prandtl number and
other parameters.
Transient natural convection between two vertical walls filled with a porous mate-
rial having variable porosity was analyzed numerically by Paul et al. (2001) in which
inertial and variable porosity effects were investigated. The Brinkman-Forchheimer-
extended Darcy model was used to simulate the momentum transfer in the porous
domain. A numerical scheme for the transient solution of the governing equations
was devised to investigate the channeling effect on the velocity field due to variable
porosity of the porous matrix. The finer grid points taken near the walls revealed that
the influence of variable porosity is significant only near the heated wall. It was found
that the Darcy model predicts an enhancement in the air velocity near the heated wall
compared to the general flow model. Formation of the boundary layer near the heated
wall was the result of the Brinkman term and its effect was strongly dependent on the
diameter of the spherical beads.

10.6 NATURAL CONVECTION ABOUT CYLINDERS

The local nonsimilarity solution method was applied by Minkowycz and Sparrow
(1974) to solve for natural convection on a vertical cylinder for conditions where there
were large deviations from the flat plate results. To assess and insure the accuracy