Begell House Inc.
Journal of Porous Media
JPM
1091-028X
10
4
2007
Heat and Mass Transports in a One-Dimensional Porous Wick Driven by a Gas-Phase Diffusion Flame
327-342
10.1615/JPorMedia.v10.i4.10
Mandhapati P.
Raju
Department of Mechanical and Aerospace Engineering, Case Western Reserve University, Cleveland, OH 44106, USA
James S.
T'ien
Department of Mechanical and Aerospace Engineering, Case Western Reserve University, Cleveland, OH 44106, USA
A one-dimensional stagnation point diffusion flame stabilized next to a porous wick is studied using a numerical model. The bottom end of the one-dimensional wick is dipped inside a liquid fuel (ethanol) reservoir. The liquid is drawn toward the surface of the wick through capillary action against gravity. The model combines heat and mass transfer equations in the porous media with phase change and gas-phase combustion equations to investigate the steady state flow structure in the porous wick and the flame characteristics in the gas phase. In this one-dimensional system the only steady solution in the porous wick that is stable is found to be in the funicular regime. There are two regions in the wick: a vapor-liquid two-phase region near the surface exposed to the flame and a purely liquid region below it. The coupling between the flame and the porous transport involves three different length scales: flame standoff distance from the wick surface, wick height above the reservoir, and capillary rise. Attempt is made to study the effect of the nondimensional numbers that contain these scales. Thus a simplified similitude [based on these nondimensional numbers] has been identified.
Inertial Effects on Rotating Flow in a Porous Layer
343-356
10.1615/JPorMedia.v10.i4.20
Daniel N.
Riahi
School of Mathematical and Statistical Science, University of Texas Rio Grande Valley,
Edinburg, Texas 78539, USA
Inertial effects on flow instabilities in a horizontal reactive porous layer with a deformed upper boundary are studied using a linear stability analysis and under the condition that the porous layer, which is also referred to as a dendrite or mushy layer, is rotating about an inclined axis during the solidification of a binary alloy. The linear stability analysis leads to new results about the effects of the inertial force on the existence and the number of the oscillatory modes and on the preference of either left- or right-traveling longitudinal rolls, which can depend on the angle of inclination γ of the rotation axis with respect to the vertical axis. For some 0° < γ < 90° and for the rotation rate beyond some particular value, the preferred flow solution in the form of left-traveling rolls can be replaced by the one in the form of right-traveling rolls or vice versa. The preferred flow pattern, the period of oscillation of the flow solution, the critical Rayleigh number, and the shape and structure of the deformed upper boundary of the layer are found to depend on the inertial effect.
New Viscous Fingering Mechanisms at High Viscosity Ratio and Peclet Number Miscible Displacements
357-376
10.1615/JPorMedia.v10.i4.30
M. N.
Islam
Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, Alberta T2N 1N4, Canada
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 a rectilinear Hele-Shaw cell are conducted using a hybrid numerical algorithm. The algorithm allowed the modeling of the flow at relatively high values of the mobility ratio and Peclet number, representing the ratio of convective and dispersive forces. New finger structures, some reminiscent of fractal patterns observed in previous experimental studies, are reported. An explanation of the mechanisms responsible for the new finger structures is presented based on the development of the flow velocity field. The flow is also characterized qualitatively through a spectral analysis of the average concentration and an analysis of the variations of the relative finger width and relative contact area. General observations regarding the conditions for the development of complex finger structures are presented.
Reactive Contaminant Transport with Space-Dependent Dispersion and Time-Dependent Concentration Source
377-390
10.1615/JPorMedia.v10.i4.40
Ali J.
Chamkha
Mechanical Engineering Department, Prince Sultan Endowment for Energy and
Environment, Prince Mohammad Bin Fahd University, Al-Khobar 31952, Saudi Arabia; RAK Research and Innovation Center, American University of Ras Al Khaimah, P.O. Box
10021, Ras Al Khaimah, United Arab Emirates
Jasem
Al-Humoud
Civil Engineering Department, Kuwait University, Safat 13060, Kuwait
This work is focused on the modeling of a one-dimensional contaminant transport in a uniform porous medium with a spatially dependent dispersion coefficient and time-dependent source concentration in the presence of a first-order reaction. Two types of source concentration boundary conditions are employed. These are the type I and type III boundary conditions with an increasing time-dependent power law function multiplied by a decaying time-dependent exponential function. The variable dispersion coefficient is represented by an exponentially increasing function with the downstream distance. Various analytical solutions for special cases of the problem are presented, and the general nonlinear problem is solved numerically by an implicit finite difference method. The numerical method is validated by various comparisons with the analytical solutions and is found to be in excellent agreement. A parametric study of all physical parameters is conducted, and the results are presented graphically to illustrate interesting features of the solutions.
Exact Solution for the Magnetohydrodynamic Flows of an Oldroyd-B Fluid through a Porous Medium
391-399
10.1615/JPorMedia.v10.i4.50
Masood
Khan
Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan
S. B.
Khan
Department of Mathematics, Quaid-i-Azam University, Islamabad, 45320, Pakistan
Exact analytical solutions are obtained for the problem of unsteady flows of a magnetohydrodynamic Oldroyd-B fluid through a porous medium between two infinite plates. A modified Darcy's law is used in the flow modeling. The bottom plate moves in the presence of a uniform magnetic field. Graphs have been plotted for the velocity by giving numerical values to the parameters of interest. It is found that the velocity profile increases with an increase of retardation time and permeability, while it decreases as both the relaxation time and the magnetic parameter increase.
Certain Inverse Solutions of a Second-Grade Magnetohydrodynamic Aligned Fluid Flow in a Porous Medium
401-408
10.1615/JPorMedia.v10.i4.60
S.
Islam
Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, China
Chaoying
Zhou
Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, China
Inverse solutions are derived for the equations of a class of second-grade magnetohydrodynamic aligned, electrically conducting fluid flows in a porous medium that undergoes isochoric motion by assuming certain conditions on the stream function. Expressions for streamlines, velocity components, and pressure distribution are obtained. Exact solutions are derived for both finite and infinite electrically conducting cases.
Fully Developed Forced Convection of Three Fluids with Variable Therm o physical Properties Flowing through a Porous Medium Channel Heated Asymmetrically with Large Temperature Differences
409-419
10.1615/JPorMedia.v10.i4.70
The steady laminar flow in a fluid-saturated porous medium channel bounded by two parallel plates with constant but unequal temperatures is studied. For the porous medium the Brinkman-Darcy-Forchheimer model is used. The investigation concerns engine oil, water, and air, taking into account the variation of their physical properties with temperature. The results are obtained with the direct numerical solution of the governing equations and cover large temperature differences. It is found that dynamic viscosity and, in some cases, density and thermal conductivity play an important role in the results, which depart significantly from those of a fluid with constant properties when the temperature difference between the plates is large.
ERRATUM: Chebyshev Finite Difference Method for Hydromagnetic Free Convection from a Cone and a Wedge Through Porous Media with Radiation by M.A. Seddeek was published in Volume 10, Issue 1, pages 99-108 of Journal of Porous Media
420
10.1615/JPorMedia.v10.i4.80
The following corrections should be noted for the article.
Table 1, page 104
Table heading reads Da it should read 1/Da
Table heading reads (Elbarbary, 2005) it should read (Varjravelu et al. 1992)
Table 2, page 104 should be Table 3
Table 3, page 106 should be Table 2
Table heading reads Da it should read 1/Da
Table heading reads (Varjravelu et al., 2005) it should read (Varjravelu et al. 1992)