Begell House Inc.
Journal of Porous Media
JPM
1091-028X
7
1
2004
Analysis of Free Surface Enhancement in a Medium with Variable Porosity
8
M. R.
Shahnazari
Faculty of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran
Abbas
Abbassi
Department of Mechanical Engineering, Amirkabir University of Technology (Tehran
Polytechnic), 424 Hafez Ave., P.O. Box 15875-4413, Tehran, Iran
In this article, a mathematical model is presented to analyze the momentum transfer during the surface enhancement of nonhomogeneous porous media. The flow regime is assumed as non-Darcian with porosity (ε), permeability coefficient (K) are being variable. To consider the flow domain a new technique for the marker-and-cell method (MAC) with a variable grid system is employed. The effect of different Darcy numbers on the surface enhancement position at different Reynolds numbers is studied. In addition, the effect of variable permeability (K) in media with different porosities is considered and the results are presented.
Effect of Suspended Particles on Couple-Stress Fluid Heated and Soluted from Below in Porous Medium
10
Sunil
Department of Mathematics, National Institute of Technology, Hamirpur, (H.P.) 177005, India
R. C.
Sharma
Department of Mathematics, Himachal Pradesh University, Summer Hill, Shimla 171 005, India
Rajender Singh
Chandel
Department of Mathematics, Government Degree College, Palampur, (H.P.) 177 061, India
A layer of a couple-stress fluid permeated with suspended particles, heated and soluted from below in a porous medium, is considered. For the case of stationary convection, the stable solute gradient and couple-stress have stabilizing effects on the onset of convection, whereas the suspended particles and medium permeability have destabilizing effects on the couple-stress fluid permeated with suspended particles, heated and soluted from below in a porous medium. Graphs have been plotted by giving numerical values to the parameters, to depict the stability characteristics. The stable solute gradient is found to introduce oscillatory modes in the system, which were nonexistent in its absence. A sufficient condition for the nonexistence of overstability is obtained.
Thermally Developing Forced Convection in a Porous Medium: Parallel-Plate Channel or Circular Tube with Isothermal Walls
10
D A
Nield
University of Auckland
Auckland, New Zealand
Andrey V
Kuznetsov
Department of Mechanical and Aerospace Engineering, North Carolina State University, Campus Box 7910, Raleigh, NC 27695-7910, USA
Ming
Xiong
Department of Mechanical and Aerospace Engineering, North Carolina State University, Campus Box 7910, Rayleigh, North Carolina 27695-7910, USA
The classical Graetz methodology is applied to investigate the thermal development of forced convection in a parallel-plate channel or a circular tube filled by a saturated porous medium, with walls held at constant temperature. The Brinkman model is employed. The analysis leads to expressions for the local Nusselt number and average Nusselt number, as functions of the dimensionless longitudinal coordinate and the Darcy number.
Fingering Instabilities in Miscible Displacement Flows of Non-Newtonian Fluids
12
Jalel
Azaiez
Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, Calgary, Alberta, Canada T2N1N4
Full nonlinear simulation of the viscous fingering instability of miscible flow displacements in porous media that involve two non-Newtonian fluids has been conducted. The development of the fingering instability was studied in a rectilinear Hele-Shaw cell that models fluid flow in a porous media of constant permeability, and both the displacing and displaced fluids are considered to be non-Newtonian. The non-Newtonian fluids are assumed to be pseudo-plastic and are modeled using the Carreau-Yasuda model. A modified Darcy’s law is derived and is solved numerically using a pseudo-spectral method based on the Hartley transform. New mechanisms of viscous fingering not previously observed in the case of similar Newtonian flow displacements have been identified. These mechanisms, which are reminiscent of the fractal patterns observed in experimental studies, were interpreted in terms of the velocity-dependent mobility of the flow.
Soret and Double Diffusive Convection in a Porous Cavity
18
N.
Boutana
Ecole Polytechnique, C.P. 6079, Succ "Centre Ville," Montreal, Quebec, H3C 3A7, Canada
Ali
Bahloul
Départment de Génie Mécanique École Polytechnique de Montréal C.P. 6079, Succ. Centre-ville, Montréal, Québec H3C 3A7 Canada
Patrick
Vasseur
Ecole Polytechnique, Université de Montréal, C.P. 6079, Succ. "Centre ville", Montréal,
Québec H3C 3A7, Canada
F.
Joly
Ecole Polytechnique, C.P. 6079, Succ "Centre Ville," Montreal, Quebec, H3C 3A7, Canada; and Universite Paris-Sud, Orsay, France
Natural convection in a rectangular porous medium filled with a binary fluid is studied analytically and numerically. The two vertical walls of the cavity are subject to constant gradients of temperature while the two horizontal ones are adiabatic and impermeable. Solutal gradients are assumed to be induced either by the imposition of constant gradients of concentration on the vertical walls (double-diffusive convection, a = 0) or by the Soret effect (a = 1). Governing parameters of the problem under study are the thermal Rayleigh number RT, buoyancy ratio φ, Lewis number Le, and aspect ratio of the cavity, A. An analytical solution, based on the parallel flow approximation, is reported for tall enclosures. The analysis reveals that there is a range of buoyancy ratios φ which yields up to three analytical solutions for a given set of governing parameters. The range of buoyancy ratios for the existence of multiple solutions is found to depend on the type of convection induced by the solutal gradients, i.e., on the constant a. In the range of the governing parameters considered in this study, good agreement is observed between the analytical predictions and a numerical solution of the full governing equations.
Effect of Turbulence on Forced Convection in a Composite Tube Partly Filled with a Porous Medium
6
An engineering approach to modeling turbulent fluid flow and heat transfer in composite porous/fluid domains is suggested. Comparisons of critical values of the Reynolds number for the clear fluid and porous domains shows that if the permeability of the porous region is sufficiently small (which is probably true for most practical porous media), the flow in the porous region remains laminar even if the flow in the clear fluid region is turbulent. The problem is then reduced to matching the laminar flow solution in the porous region with the turbulent flow solution in the clear fluid region. The major assumption of this approach is that the flow in the porous domain is laminar. This assumption must be checked for a particular flow situation before the suggested method can be utilized.
Combined Effect of Magnetic Field and Lateral Mass Transfer on Non-Darsy Axisymmetric Free Convection in a Power-Law Fluid Saturated Porous Medium
7
Mohamed F.
El-Amin
Mathematics Department, Aswan Faculty of Science, South Valley University, Aswan, 81258; King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Kingdom of Saudi Arabia
M. A.
EL-Hakiem
Mathematics Department, Aswan Faculty of Science, South Valley University, Aswan, Egypt
M. A.
Mansour
Department of Mathematics, Assuit University, Faculty of Science, Assuit, Egypt
In this article, a boundary-layer analysis is presented to study the effect of transverse magnetic field of a non-Newtonian power-law fluid on non-Darcy axisymmetric free convection over a horizontal surface embedded in a porous medium in the presence of surface transpiration (lateral mass flux). The Ostwald-de Waele power-law model is used to characterize the non-Newtonian fluid behavior. Similarity solutions are obtained when the surface temperature varies as the square root of the radial distance or when heat flux is constant. The effects of the magnetic and non-Darcy parameters as well as the power-law index n and mass flux parameter on the velocity, temperature, and the boundary-layer thickness are shown on graphs. The numerical values of the rate of heat transfer through the boundary layer in terms of the Nusselt number are entered in a table.