Begell House
Journal of Porous Media
Journal of Porous Media
1091-028X
5
3
2002
Heat and Mass Transfer in Tubes: An Analysis Using the Method of Volume Averaging
In this study, we use the method of volume averaging to predict the exchange coefficient associated with steady laminar flow in a tube. This allows us to compare theory with an exact solution. Good agreement is obtained between the theory and the exact solution for the asymptotic condition, and this provides support for the simplifications that are made in the closure problem for transport processes in porous media.
Fabrice
Golfier
Institut de Mecanique des Fluides de Toulouse, 31400 Toulouse, and Institut Francais du Petrole, 92506 Rueil-Malmaison Cedex, France
Stephen
Whitaker
Department of Chemical Engineering and Material Science, University of California, Davis, California, USA
Michel
Quintard
Université de Toulouse; INPT, UPS; IMFT (Institut de Mécanique des Fluides de Toulouse); Allée Camille Soula, F-31400 Toulouse, France and CNRS; IMFT; F-31400 Toulouse, France
18
Effects of Throughflow and Internal Heat Generation on Convective Instabilities in an Anisotropic Porous Layer
Convective instabilities caused by a nonunlform temperature gradient due to vertical through/low and internal heat generation were investigated in an anisotropic porous layer. The boundaries are taken to be either impermeable or porous and are perfect conductors of heat. The Forchheimer-extended Darcy model is used to describe the/low in the porous medium. The resulting eigenvalue problem is solved numerically by the Galerkin method with a modified external Rayleigh number as the eigenvalue. Both anisotropic parameters (i.e., effective thermal diffusivity, h, and permeability, x) appear through their ratio h/xonly. We found that an increase in h/x increases the stability of the system. Furthermore, we observed that in the absence of internal heat generation, throughflow stabilizes when the boundaries are symmetric and destabilizes when they are asymmetric. However, if an internal heat source exists, throughflow destabilizes the system irrespective of the boundary types considered. A more precise control of the buoyancy-driven instability may be achieved by tuning the anisotropy parameters and internal heat source strength.
A.
Khalili
Max-Planck Institute for Marine Microbiology, Celsiusstr. 1,28359 Bremen, Germany
M.
Huettel
Max-Planck Institute for Marine Microbiology, Celsiusstr. 1,28359 Bremen, Germany
12
Viscous Flow Through Straight Pore Channels
Steady laminar viscous 2-D flow through straight cylindrical tubes is studied. By comparison of the film-type Averyanov flow in an annular domain and the common Poiseuille flow in a circular tube, it is deduced why at high suctions sands are less conductive than clays. Flows in noncircular tubes with cusps modeling contact zones of solid particles are considered. Using conformal mappings, the Poisson equation in the physical plane is reduced to the Laplace equation in an auxiliary disk. The Dirichlet problem in this disk is solved by the Poisson integral formula. The value of maximal velocity at the center of the tube and the total flow rate (conductivity) are calculated.
I. R.
Kayumov
Institute of Mathematics and Mechanics, Kazan University, Kazan, Russia
Anvar R.
Kacimov
Department of Soil and Water Sciences, Sultan Qaboos University, P.O. Box 34, Al-Khod 123, Sultanate of Oman
10
The Effect of AnisotropicThermoconvective Currents on the Onset of Double-Diffusive Convection in a Sparsely Packed Porous Medium
The effect of anisotropic thermoconvective current on the onset of double-diffusive convection in a sparsely packed porous medium is investigated fir the case in which a large coupled diffusion effect is present. The Brinkman extension of the Darcy equation is chosen as the momentum equation with effective Brinkman viscosity different from the fluid viscosity. The normal mode analysis is used to find the condition for the onset of convection. The effect of'the porous parameter F, ratio of dtffusivities, and a separation parameter are presented graphically. It is found that the thermoconvective currents have a stabilizing effect as well as a destabilizing effect with respect to the case in which these currents are absent. The viscous case results and the Darcy results are obtained as a limiting case of the porous parameter F tending to zero and Infinity, respectively.
M.S.
Malashetty
Gulbarga University
S . N.
Gaikwad
Department of Mathematics, Gulbarga University, Jnana Ganga, Gulbarga-585106, India
11
Comments on "Natural Convection from a Vertical Plate in a Saturated Porous Medium: Nonequilibrium Theory" by A. A. Mohamad
Ioan
Pop
Department of Mathematics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania
Andrew
Rees
University of Bath
3