Begell House Inc.
Journal of Porous Media
JPM
1091-028X
20
8
2017
UNSTEADY MHD FLOW OF SECOND-GRADE FLUID OVER AN OSCILLATING VERTICAL PLATE WITH ISOTHERMAL TEMPERATURE IN A POROUS MEDIUM WITH HEAT AND MASS TRANSFER BY USING THE LAPLACE TRANSFORM TECHNIQUE
671-690
10.1615/JPorMedia.v20.i8.10
Farhad
Ali
City University of Science and Information Technology, Peshawar
Nadeem Ahmad
Sheikh
Computational Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City,
Vietnam; Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City,
Vietnam; Department of Mathematics, City University of Science and Information Technology, Peshawar, Khyber Pakhtunkhwa, Pakistan
Muhammad
Saqib
Computational Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City,
Vietnam; Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City,
Vietnam; Department of Mathematics, City University of Science and Information Technology, Peshawar, Khyber Pakhtunkhwa, Pakistan
Ilyas
Khan
Ton Duc Thang University
exact solutions
MHD flow
oscillating plate
second-grade fluid
heat and mass transfer
radiation
A problem describing the oscillating flow of an incompressible magnetohydrodynamic second-grade fluid in a porous medium with combined effect of heat and mass transfer in the presence of radiation is investigated. Exact solutions for cosine oscillations are obtained via the Laplace transform method. The obtained starting solutions are explicitly expressed as the sum of steady state and transient solutions. It is shown that previous results for a nonporous medium and hydrodynamic fluid are the limiting cases of the present problem. The effects of different parameters for velocity are plotted and discussed physically.
ONSET OF DARCY-BRINKMAN CONVECTION IN A ROTATING POROUS LAYER INDUCED BY PURELY INTERNAL HEATING
691-706
10.1615/JPorMedia.v20.i8.20
Dhananjay
Yadav
Faculty of Science and Technology, Athabasca University, 1 University Drive, Athabasca, AB
T9S 3A3, Canada
Junye
Wang
Faculty of Science and Technology, Athabasca University, 1 University Drive, Athabasca, AB
T9S 3A3, Canada
Jinho
Lee
School of Mechanical Engineering, Yonsei University, Seoul 120-749, Korea
convection
internal heating
Brinkman model
porous medium
rotation
The influence of rotation and Darcy number on the criterion for the onset of convection induced by purely internal
heating in a porous layer is investigated. The boundaries are considered to be free-free, rigid-rigid, lower-rigid, and upper-free boundaries and subjected to two sets of thermal boundary conditions, namely, case (i) both boundaries isothermal and case (ii) lower insulated and upper isothermal. The Darcy-Brinkman model, with fluid viscosity different from effective viscosity, is used to characterize the fluid motion in porous medium. The coupled governing partial differential equations are transformed into ordinary differential equations by use of linear stability analysis and solved numerically using the higher order Galerkin method with the internal Darcy-Rayleigh number as the eigenvalue. Results indicate that the nature of boundaries, Darcy number, and speed of rotation significantly influence the stability characteristics of the system. Convection, when it occurs for case (i) where both boundaries are isothermal, is concentrated in the upper portion of the layer; whereas for case (ii) with lower insulated and upper isothermal boundaries, it is concentrated in the whole layer. The effect of increasing rotation parameter inhibits the onset of convection, while
Darcy number shows dual behavior on the criterion for the onset of convection in the presence of rotation. Some known
results are also recovered as special cases of the present study.
TRANSIENT PRESSURE BEHAVIOR OF A FRACTURED VERTICAL WELL WITH A FINITE-CONDUCTIVITY FRACTURE IN TRIPLE MEDIA CARBONATE RESERVOIR
707-722
10.1615/JPorMedia.v20.i8.30
Yong
Wang
School of Sciences, Southwest Petroleum University, Chengdu, Sichuan 610500, China;
State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum
University, Chengdu, Sichuan 610500, China
Xiangyi
Yi
State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Chengdu University
of Technology, Chengdu, Sichuan 610059, China
acid fracture
fractured vertical well
finite-conductivity fracture
transient pressure analysis
triple media carbonate reservoir
Carbonate reservoir is one of the most important reservoirs in the world. Because of the characteristics of carbonate reservoir, vertical well and acid fracturing have become the key technology for efficiently developing carbonate
reservoir. Establishing corresponding mathematical models and analyzing transient pressure behaviors of this type of
well-reservoir configuration can provide a better understanding of fluid flow patterns in formation as well as estimations of important parameters. A coupling mathematical model for a fractured vertical well in triple media carbonate reservoir by conceptualizing vugs as spherical shapes is presented in this paper, in which the finite conductivity of the acid fracture is taken into account. A semi-analytical solution is obtained in the Laplace domain by using source function theory, Laplace transformation, discretization of fracture, and the superposition principle. Analysis of transient pressure responses indicates that several characteristic flow periods of fractured vertical wells in triple media carbonate reservoir can be identified. Parametric analysis shows that fracture conductivity and fracture length can significantly influence the transient pressure responses of fractured vertical wells in triple media carbonate reservoir. The model presented in this paper can be applied to obtain important parameters pertinent to reservoir or fracture by type curve matching, and it can also provide useful information for optimizing fracture parameters.
SLIP-BRINKMAN FLOW THROUGH CORRUGATED CHANNEL WITH STATIONARY RANDOM MODEL
723-748
10.1615/JPorMedia.v20.i8.40
M. S.
Faltas
Department of Mathematics and Computer Science, Faculty of Science, Alexandria University,
Alexandria, Egypt
H. H.
Sherief
Department of Mathematics and Computer Science, Faculty of Science, Alexandria University,
Alexandria, Egypt
M. A.
Mansour
Department of Mathematics and Computer Science, Faculty of Science, Alexandria University,
Alexandria, Egypt
Brinkman flow
velocity slip
corrugations
random model
This paper applies the Brinkman-extended Darcy model to investigate the flow in micro-channels between two parallel
corrugated walls. The stationary random model is used to imitate the stochastic surface roughness of the walls. The
channel is filled with a sparse porous medium. A boundary perturbation method is used to obtain the stochastic volume
flow rates and the pressure gradients up to the second order of the normalized amplitude of the corrugations. The
present study is based on using a linear slip of Basset-type boundary condition at the impermeable surfaces of the
corrugated channel. The parallel and perpendicular flows to the corrugations are investigated. Also, in-phase and out-of-phase cases are considered. The effect of wall roughness, slip at the channel walls, and the permeability of the medium on the rate of flow and pressure gradient are discussed. The particular cases of Stokes and Darcy's flows and the no-slip case are also discussed.
TRANSVERSE FLOW OVER AN ARRAY OF CYLINDERS EMBEDDED IN A POROUS MEDIUM
749-759
10.1615/JPorMedia.v20.i8.50
C. Y.
Wang
Department of Mathematics and Mechanical Engineering, Michigan State University, East
Lansing, Michigan 48824, USA
Darcy-Brinkman
cylinder arrays
effective permeability
transverse flow
Transverse flow or cross flow with the main flow direction perpendicular to cylinder arrays embedded in a porous
medium is studied. The fourth order governing equation for the stream function is solved by eigenfunction expansion
and point match on the repeating boundary. Recirculation eddies exist for the square array of larger cylinder radius
and lower porous media factor. Effective permeabilities of the cylinder array-porous medium system are determined.
The single cylinder approximation and the Darcy approximation are valid only for very small cylinder radii and very large porous media factors.
COMPUTATIONAL MODELING OF FLOW AND SPECIES DISTRIBUTION IN A MEMBRANELESS FUEL CELL WITH POROUS ELECTRODES
761-767
10.1615/JPorMedia.v20.i8.60
Fadhel A.
Azeez
Department of Chemical Engineering, Kuwait University, Safat 13060, Kuwait
Khalil
Khanafer
Mechanical Engineering Department, Australian College of Kuwait, Safat 13015, Kuwait
Yusuf I.
Ali
Department of Chemical Engineering, Kuwait University, Safat 13060, Kuwait
fuel cell
porous electrode
membraneless
laminar flow
In this paper, a computational model of flow and species distribution in a microfluidic fuel cell with a flow-through
porous electrode was carried out for various parameters. Such parameters include the Reynolds number and the channel
height. The governing transport equations within the porous media were written according to the volume-average
theory. The governing equations were solved using a finite element formulation based on the Galerkin method of
weighted residuals. The results of this investigation illustrated that the channel height and Reynolds number have a profound effect on the flow and species characteristics within the fuel cell. This preliminary work shows that inertial effects can play a significant role in enhancing the performance of a microfluidic device.