Begell House Inc.
Journal of Porous Media
JPM
1091-028X
15
11
2012
MIXED CONVECTION FLOW IN A VERTICAL POROUS CHANNEL WITH BOUNDARY CONDITIONS OF THE THIRD KIND WITH HEAT SOURCE/SINK
989-1007
10.1615/JPorMedia.v15.i11.10
Jawali C.
Umavathi
Department of Mathematics, Gulbarga University, Gulbarga-585 106, Karnataka, India
J. Prathap
Kumar
Department of Mathematics, Gulbarga University, Gulbarga, Karnataka, India
Jaweriya
Sultana
Department of Mathematics, Gulbarga University, Gulbarga 585 106, Karnataka, India
mixed convection
perturbation method
Runge−Kutta method
porous medium
boundary conditions of the third kind
A numerical study of mixed convection in a vertical channel filled with a porous medium, including the effects of inertia forces, is studied by taking into account the effects of viscous and Darcy dissipations with heat source or sink. The flow is modeled using the Brinkman Forchheimer−extended Darcy equations. The plate exchanges heat with an external fluid. Both conditions of equal and of different reference temperatures of the external fluid are considered. The governing equations are solved using Runge−Kutta fourth-order method with shooting technique for extended Darcy model and analytically using the perturbation series method for the Darcy model. The velocity and temperature fields are obtained for various porous parameters, inertia effect, and perturbation parameters for equal and unequal Biot numbers and are shown graphically. It is also found that both analytical and numerical solutions agree to a great extent with the small values ofthe perturbation parameter in the absence ofinertial forces.
ANALYTICAL DETERMINATION OF THE PERMEABILITY FOR SLOW FLOW PAST PERIODIC ARRAYS OF CYLINDERS WITH DIFFERENT CROSS SECTIONS
1009-1018
10.1615/JPorMedia.v15.i11.20
A.Cihat
Baytaş
istanbul technical university
D.
Erdem
Faculty of Aeronautics and Astronautics, Istanbul Technical University, 34469 Maslak, Istanbul, Turkey
H.
Acar
Faculty of Aeronautics and Astronautics, Istanbul Technical University, 34469 Maslak, Istanbul, Turkey
O.
Cetiner
Faculty of Aeronautics and Astronautics, Istanbul Technical University, 34469 Maslak, Istanbul, Turkey
H.
Basci
Faculty of Aeronautics and Astronautics, Istanbul Technical University, 34469 Maslak, Istanbul, Turkey
porous media
permeability
analytical solution
periodic arrays
circular rod
square rod 45° rotated square rod
This study proposes analytical methods for determining the permeability of porous media that are composed of periodic arrays of rods with different cross sections. The cylindrical rods used for modeling the porous media are in circular, square, and 45° rotated square cross sections, respectively. Analytical determination of the permeability has been carried out for porous media composed of different rod geometries, and results have been obtained for a wide porosity range. Furthermore, the analytical permeability determination method has been supported by auxiliary information obtained from computational solutions performed using a commercial CFD code. The permeability values obtained by the proposed analytical method have been compared with prior empirical and analytical studies. These comparisons indicated good agreement of the proposed model with the existing ones. Moreover, the analytical permeability determination methods proposed for square and 45° rotated square cross-sectioned rods can be evaluated as the contribution of this study since throughout the literature search no other analytical method has been encountered for these types of geometries.
MEASUREMENT OF THE CHEMICAL POTENTIAL OF A LIQUID IN POROUS MEDIA
1019-1029
10.1615/JPorMedia.v15.i11.30
Jean-Claude
Benet
Laboratoire de Mecanique et Genie Civil, Universite de Montpellier 2, CNRS, Cc 048, Place Eugene Bataillon, 34095 Montpellier CEDEX 5, France
A.
Ramirez-Martinez
Laboratoire de Mecanique et Genie Civil, Universite de Montpellier 2, CNRS, Cc 048, Place Eugene Bataillon, 34095 Montpellier CEDEX 5, France
F.
Ouedraogo
Laboratoire de Mecanique et Genie Civil, Universite de Montpellier 2, CNRS, Cc 048, Place Eugene Bataillon, 34095 Montpellier CEDEX 5, France
F.
Cherblanc
Laboratoire de Mecanique et Genie Civil, Universite de Montpellier 2, CNRS, Cc 048, Place Eugene Bataillon, 34095 Montpellier CEDEX 5, France
chemical potential
tensiometry
sorption isotherm
capillarity
hygroscopicity
soils
gels
agroproducts
This study deals with experimental methods dedicated to the determination of the liquid chemical potential in heterogeneous media. Various measurement techniques are proposed, including a new mechanical method based on the expansion of the air−vapor atmosphere surrounding a sample. From the large range of materials under investigation (soil, wood, gel, agroproduct, biological tissue), various microstructures are investigated. Thus liquid−solid interactions occurring at the interface scale involve several physicochemical phenomena that can all be interpreted through the concept of chemical potential. The dependence of the liquid chemical potential on the liquid content is established over the whole range of energy. Eventually, extrapolation of the results toward the low values of chemical potential is analyzed, and a modeling approach is proposed. Even if the results presented concern essentially a water phase, the principles are applicable to several other fluids.
SOLUTE DISPERSION BETWEEN TWO PARALLEL PLATES CONTAINING POROUS AND FLUID LAYERS
1031-1047
10.1615/JPorMedia.v15.i11.40
J. Prathap
Kumar
Department of Mathematics, Gulbarga University, Gulbarga, Karnataka, India
Jawali C.
Umavathi
Department of Mathematics, Gulbarga University, Gulbarga-585 106, Karnataka, India
Ali J.
Chamkha
Faculty of Engineering, Kuwait College of Science and Technology, Doha District, Kuwait;
Center of Excellence in Desalination Technology, King Abdulaziz University, P.O. Box 80200,
Jeddah 21589, Saudi Arabia; 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
Ashok
Basawaraj
Department of Mathematics, Gulbarga University, Gulbarga 585106, Karnataka, India
Taylor dispersion
immiscible fluids
horizontal channel
porous medium
This paper presents an analytical solution for the dispersion of a solute between two parallel plates consisting of two regions, one region filled with porous matrix and another region filled with purely viscous fluid. The Brinkman model is used to define the flow through the porous matrix. The fluids in both regions of the parallel-plate channel are incompressible, and their transport properties are assumed to be constant. The closed-form solutions are obtained in both fluids regions of the channel. The results are tabulated for various values of porous parameter, viscosity ratio, and pressure gradient on the effective dispersion coefficient and volumetric flow rate. It is found that the effective Taylor dispersion coefficient decreases as the porous parameter increases. The validity of the results obtained for a two-fluid model is compared with the available one-fluid model in the presence of porous matrix, and the values agree very well. The effective dispersion coefficient and volumetric flow rate are also found for a two-fluid model in the absence of porous matrix and are verified with the available one-fluid model, and the results are in good agreement.
ANALYTICAL SOLUTION OF UNSTEADY MHD PERIODIC FLOW OF A NON-NEWTONIAN FLUID THROUGH A POROUS CHANNEL
1051-1059
10.1615/JPorMedia.v15.i11.50
A.
Taklifi
MAPNA Group, Tehran, Iran
A.
Aliabadi
MAPNA Group, Tehran, Iran
transient MHD flow
generalized Maxwell fluid
porous media
radiation
Darcy number
The unsteady magnetohydrodynamic (MHD) periodic flow of a non-Newtonian fluid through a porous channel analytically has been investigated. The unsteady one-dimensional equations of motion and energy considering the MHD, Darcian porous media, and radiation terms are used. The constitutive equation for generalized Maxwell fluids is considered. After nondimensionalizing the governing equations, an analytical solution has been developed. The effects of the rheological behavior of fluid on velocity and shear stress profiles along channel width at different time periods have been discussed and depicted. The effect of porosity on velocity and shear stress profiles and the combined effect of viscoelasticity and porosity has been studied. Results show that by increasing the Deborah number for generalized Maxwell fluid, the average velocity through the porous media increases. It is found that the fluid maximum velocity point could be changed along the channel width by normalized relaxation time variations of the fluid. It also could be seen that the effect of Darcy number variations on the velocity and shear stress is more considerable in the generalized Maxwell fluids than in Newtonian fluids.
A NOVEL TWO-PARAMETER RELATIVE PERMEABILITY MODEL
1061-1066
10.1615/JPorMedia.v15.i11.60
Eshragh
Ghoodjani
Sharif University of Technology
Seyed Hamed
Bolouri
Shahid Bahonar University of Kerman
relative permeability model
LU model (correlation)
multiphase flow
The relative permeability curves are key factors for assessment of reservoir performance by numerical simulators. The widely used one-parameter models are not sufficiently flexible for fitting laboratory measured relative permeability data. These models only show a concave upward trend and cannot represent the S-shape behavior of relative permeability. The other three-parameter models are too complex to use in practical reservoir engineering calculations. In this paper, a novel two-parameter model is proposed that maintains the simplicity of previous models while having great flexibility over a full range of saturation. The two parameters L and U control the shape of the lower and upper part of the curve, respectively; hence it is called the LU model. For testing its strength, relative permeabilities from literature are fitted with LU. The comparison results show that LU models are more accurate than previous one- and two-parameter models and that their performance is almost as good as three-parameter LET models.
THE DISPERSION ON PERISTALTIC FLOW OF MICROPOLAR FLUID IN A POROUS MEDIUM
1067-1077
10.1615/JPorMedia.v15.i11.70
Habtu
Alemayehu
Department of Mathematics, National Institute of Technology, Warangal 506 004, India
G
Radhakrishnamacharya
peristalsis
dispersion
chemical reaction
porous medium
micropolar fluid
The paper presents an analytical solution for dispersion of a solute in the peristaltic motion of a micropolar fluid in a porous medium in the presence of both homogeneous and heterogeneous chemical reactions. The average effective dispersion coefficient has been found using Taylor's limiting condition under long wavelength approximation. The effects of various relevant parameters on the average coefficient of dispersion have been studied. The average effective dispersion coefficient decreases with porosity parameter but increases with amplitude ratio and micropolar parameters for the case of a homogeneous chemical reaction. But in the case of combined homogeneous and heterogeneous reactions, dispersion increases with the cross-viscosity coefficient and heterogeneous reaction rate parameter.