Page 195 - gas transport in porous media

Chapter 10: Natural Convection Gas Transport in Porous Media
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which characterizes the non-Darcy fluid, and the curvature parameter. The natural
convection from a heated circular cylinder into an unbounded porous medium was
investigated for the full range of Rayleigh numbers by Ingham and Pop (1987). At
small Rayleigh numbers a qualitative solution was obtained and at large Rayleigh
numbers the second-order boundary-layer solution was found that took into account
the first-order plume solution.
The effect of conduction-radiation on natural convection flow of an optically dense
viscous incompressible fluid along an isothermal cylinder of elliptic cross section
was investigated by Hossain et al. (1998). The boundary layer equations governing
the flow were shown to be nonsimilar. Full numerical solutions of the governing
equations were obtained using the implicit finite difference method. The solutions
were expressed in terms of the Nusselt number against the eccentric angle alpha in
the range (0, π). The working fluid was assumed to have a unit value for the Prandtl
number, Pr. It was found that the rate of heat transfer from the slender body is higher
than the corresponding one for the blunt body and that the radiation field further
enhances this increase.
Theflowandheattransferbytransientnaturalconvectioninaverticalcylinderfilled
with air saturated porous medium was studied by Slimi et al. (1998). The cylinder is
opened at both ends and heated with a constant wall heat flux density. That study was
carried out using the Forchheimer-extended Darcy flow model and a two-temperature
model. The results of that study provided the validity of the Darcy flow model and
the thermal boundary layer approximations. In a related study, Hossain et al. (1999)
considered non-Darcy convection heat and mass transfer along a vertical permeable
cylinder embedded in a porous medium for Prandtl number of unity.

10.7 NATURAL CONVECTION ABOUT SPHERES

Natural convection flow and heat transfer due to the presence of a heated sphere
embedded in a porous medium has motivated many researchers owing to its wide-
ranging applications in a number of fields such as chemical engineering, thermal
insulation systems, and nuclear waste management. Yamamoto (1974) was the first
to consider the natural convection problem around a sphere in a porous medium.
Asymptotic solutions for small Rayleigh numbers were obtained for steady natural
convection from a constant surface temperature sphere.
Sano and Okihara (1994) analyzed natural convection around a sphere embedded in
a porous medium for small Rayleigh numbers. The sphere was suddenly heated and,
subsequently, maintained at a constant heat flux over the surface. Asymptotic solu-
tions were obtained for the transient and steady-state temperature distribution around
the sphere. The effects of viscous dissipation, Joule heating and heat source/sink
on non-Darcy MHD natural convection flow over an isoflux permeable sphere in a
porous medium are numerically analyzed byYih (2000). The governing equations are
transformed into the nonsimilar boundary layer equations and solved by the Keller box
method. Numerical results for the wall shear stress and the Nusselt number are pre-
sented for the dimensionless coordinate along the surface, the Forchheimer number,