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Chapter 10: Natural Convection Gas Transport in Porous Media
The nonsimilar boundary layer equations were solved numerically employing a very
efficient finite difference scheme in combination with an iterative method for solving
the resulting ordinary differential equations. The temporal neutral stability theory for
wavelike disturbances of Tollmien-Schlichting type is then presented for the velocity
and temperature functions. The corresponding eigenvalue problem for the distur-
bance amplitude functions is also solved numerically using a very accurate method.
Results are presented graphically for both the basic and disturbance velocity and
temperature profiles for some values of the modified local Grashof number G and
suction or injection parameter X. The Prandtl number Pr is taken to be 0.73 (air)
throughout this paper. The results show clearly the important role that the suction
or injection parameter X may have on the base and disturbed flow characteristics.
Chamkha (1997a) analyzed free convection flow of an electrically conducting fluid
along a vertical plate embedded in a thermally stratified porous medium in the pres-
ence of a uniform normal magnetic field. In his study Chamkha (1997a) considered
non-Darcian effects, Hartmann and Hall effects of magnetohydrodynamics, as well
as thermal stratification effects.
The transient free convection boundary-layer flow of a viscous and incompressible
fluid adjacent to a semi-infinite vertical flat plate is investigated for Prandtl number
of unity by Harris et al. (1998). An analytical solution was presented which is valid
at small values of τ. The existence of two solutions was demonstrated which is
physically acceptable. Hossain et al. (1999) analyzed the effect of radiation on the
natural convective flow of an optically dense incompressible fluid along a uniformly
heated vertical plate with uniform suction. The governing nonsimilar boundary-layer
equations were analyzed using (i) series solution for small values of ξ (a scaled
streamwise coordinate); (ii) asymptotic solution for large ξ; and (iii) a full numerical
solution. The solutions were expressed in terms of the local shear stress and local rate
of heat transfer. The effects of varying the Prandtl number (1 ≤ Pr ≤ 5), the radiation
parameter, and the surface temperature parameter were determined.
Watanabe et al. (1999) conducted a theoretical study for the stability characteristics
ofthelaminarfreeconvectionboundarylayerflowalongaverticalporous(permeable)
flat plate subject to a constant heat flux. The disturbance equations were solved
numerically on the basis of the linear stability theory for a wide range of values of the
modified Grashof number, G, and some values of the suction or injection parameter
X using air as the fluid medium. These solutions indicate the important role of the
parameters G and X on the flow and heat transfer characteristics.
The effect of thermal radiation on the natural convection flow along a uniformly
heated vertical plate embedded in porous medium with variable viscosity and uniform
suction velocity was investigated numerically by Hossain et al. (2001). The fluid
consideredinthisstudywasconsideredtobeopticallydense. Thegoverningequations
were analyzed using a variety of methods: (i) a series solution for small values of
a scaled streamwise coordinate; (ii) an asymptotic solution for large values of the
scaled streamwise coordinate; and (iii) a full numerical solution using the Keller box
method. The solutions are expressed in terms of the local shear stress and the local
heat transfer rate. The working fluid was taken to have a Prandtl number of unity.