Begell House
Journal of Porous Media
Journal of Porous Media
1091-028X
15
9
2012
EFFECT OF A VERTICAL MAGNETIC FIELD ON NONLINEAR CONVECTION IN A MUSHY LAYER
The problem of nonlinear steady convection in a horizontal mushy layer during alloy solidification and in the presence of a vertical magnetic field is considered. Under a near-eutectic approximation and the limit of large far-field temperature, the steady solutions to the weakly nonlinear problem and their stability by using a perturbation technique and stability analysis are determined. It is found, in particular, that only a steady solution in the form of either subcritical down-hexagons with down-flow at the cells' centers and up-flow at the cells' boundaries or subcritical up-hexagons with up-flow at the cells' centers and down-flow at the cells' boundaries or supercritical rolls can be stable. The magnetic field reduces the domain in the parameter regime for the presence of steady modes. Under a certain parameter regime, the strength of the magnetic field can change the form of the stable steady flow pattern from up-hexagons to down-hexagons. The magnetic field enhances the subcritical domain of stable up-hexagons and the supercritical domain of stable rolls but narrows down the subcritical domain for the stable down-hexagons.
Daniel N.
Riahi
School of Mathematical and Statistical Sciences,
One West University Boulevard, University of Texas Rio Grande Valley, Brownsville, Texas 78520 USA
805-821
MODELING OF FLOW THROUGH A REACTIVE POROUS PLUG AS RELATED TO BIOLOGICAL APPLICATIONS
The present numerical study addresses flow through a reactive porous matrix for various pertinent parameters. Such parameters include the reaction constant, Reynolds number, and the width of the porous plug. The transport equations were solved using the finite-element formulation based on the Galerkin method of weighted residuals. The validity of the numerical code used was ascertained by comparing the results with previously published results. The results revealed that the reaction constant, Reynolds number, and the width of the porous plug have a significant effect on the streamlines and isoconcentration contours. The species concentration and the axial velocity along the centerline of the channel were reduced substantially with an increase in the reaction constant and width of the porous plug. In addition, the results showed that an increase in the Reynolds number reduced the species concentration and the axial velocity. An optimum width of the porous plug was obtained and is discussed. Further increase in the width beyond the optimum value did not affect the species concentration.
Alia
Marafie
Mechanical Engineering Department, Kuwait University, Al-Safat, Kuwait
823-833
AUGMENTATION OF A HEAT REJECTION MECHANISM IN A VENTILATED ENCLOSURE FILLED PARTIALLY WITH A POROUS LAYER
Heat rejection augmentation in a ventilated cavity filled partially with a porous medium is studied numerically using the finite-element method. Analyses were performed in a mixed convection heat transfer regime. Results were obtained using various pertinent dimensionless parameters; namely; the effects of the solid-to-fluid thermal conductivity ratio (1−100), Darcy number (10−3−10−6), Richardson number (0.01−10), location of the porous layer (0.1−0.9), and width of the porous layer (0.1−0.9) on the streamlines, and the isotherms, average Nusselt number and the bulk average fluid temperature are analyzed in this investigation. The generalized model of the momentum equation, which is also known as the Forchheimer-Brinkman extended Darcy model, is employed in modeling the fluid motion inside the porous layer. In addition, the local thermal equilibrium condition was assumed to be valid for the range of the thermophysical parameters considered in the present investigation. The results of this investigation reveal that the location and width of the porous layer play a significant role in the pattern of the streamlines and isotherms within the enclosure. Moreover, the average Nusselt number and the bulk average fluid temperature are found to increase as the porous layer moves toward the exit port. However, the Nusselt number is found to decrease while the average temperature increases as the width of porous layer increases. Finally, the contribution of the conduction and convection heat transfer regimes to the overall energy transport within the enclosure revealed some interesting optimization scenarios.
A.
Al-Amiri
Department of Mechanical Engineering, United Arab Emirates University, Al Ain, United Arab Emirates
khalil
Khanafer
University of Michigan Ann Arbor
835-848
STOKES FLOW PAST AN ASSEMBLAGE OF AXISYMMETRIC POROUS SPHEROIDAL PARTICLE-IN-CELL MODELS
The steady axisymmetric Stokes flow of an incompressible viscous fluid past an assemblage of porous concentric spheroidal particle-in-cell models is studied. Stokes equations are employed inside the fluid envelope and Brinkman equations are used inside the porous region. Continuity of velocity and stress at the porous fluid interface is used, while at the fluid interface of the envelope, different feasible boundary conditions have been used. The same small departure from a sphere is considered for each spheroidal surface. In the four models, the expressions for the pressure and stream functions in both flow regions are completely determined to the first order in a small parameter characterizing the deformation of the spheroidal surface from the spherical shape. As an application, both types of spheroids, prolate and oblate, are considered. In each case, the corresponding expression for the drag acting on the porous particle is derived and, hence, the particle mobility is obtained. The special cases of the expression for drag on the porous sphere in the fictitious spherical envelope, the porous spheroid in the case of uniform streaming in an unbounded fluid, and the impermeable solid spheroid-in-cell model are obtained.
El-Sayed Ibrahim
Saad
Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, Egypt ; Department of Mathematics, Faculty of Science, Shaqra University, Dawadmi, Saudi Arabia
849-866
EFFECTS OF POROSITY CHANGES ON THE SELF-HEATING CHARACTERISTICS OF COAL STOCKPILES
The oxidation process occurring in a coal stockpile is a serious economic and safety problem. In this research, heat and fluid flow within and around a heat generating porous material (coal stockpile) are numerically investigated by both a FORTRAN code and the commercially available software CFD-ACE for a self-heating medium. Transient variation of the maximum temperature inside the coal stockpile, as the main parameter to study self-heating and spontaneous self-ignition is monitored and a threshold is presented. It is shown that the maximum temperature inside the pile may reduce/increase depending on the stockpile average porosity and permeability.
Arash
Ejlali
School of Mechanical and Mining Engineering, The University of Queensland, Qld 4072, Australia
Kamel
Hooman
School of Mechanical and Mining Engineering, The University of Queensland, Qld 4072, Australia
Basil
Beamish
School of Mechanical and Mining Engineering, The University of Queensland, Qld 4072, Australia
869-876
DOUBLE DIFFUSIVE FREE CONVECTION INDUCED BY VERTICAL WAVY SURFACE IN A DOUBLY STRATIFIED DARCY POROUS MEDIUM UNDER THE INFLUENCE OF SORET AND DUFOUR EFFECT
A combined heat and mass transfer process by natural convection along a vertical wavy surface immersed in a thermal and mass stratified Darcy porous medium under the influence of Soret and Dufour effects have been analyzed. The governing partial differential equations are transformed into a set of coupled boundary layer equations based on non-similarity transformation deduced by scale analysis and are solved numerically by a finite-difference scheme following the Keller-box approach. Detailed simulations are carried out to investigate the effect of varying parameters such as: the wave amplitude (a), buoyancy ratio (B ), Lewis number (Le), Soret (Sr ) and Dufour (Df ) effect coefficients, and the presence of thermal (ST ) and mass (SC ) stratification. Local and average Nusselt (Nu) number and Sherwood (Sh) number plots are presented in all cases.
B. V. Rathish
Kumar
Department of Mathematics and Statistics, Indian Institute of Technology, India
Somanchi V S S N V G
Krishna Murthy
Department of Applied Mathematics, Defence Institute of Advanced Technology, Gririnagar, Pune 411025, India
877-890