Begell House
Journal of Porous Media
Journal of Porous Media
1091-028X
15
10
2012
FLOW IN AN ANNULAR CHANNEL FILLED WITH A POROUS MEDIUM OF VARIABLE PERMEABILITY
Fully developed laminar flow of a viscous incompressible fluid in an annular region between two coaxial cylindrical tubes filled with a porous medium of variable permeability is studied when the permeability of the porous medium varies with the radial distance. Analytical solutions of the problem for three special cases of permeability variation are derived, and relevant quantities such as velocity, volumetric flow rate, and average velocity and stress on the boundaries are obtained and exhibited graphically. The influence of the various parameters on the flow are discussed. It is found that the variation of permeability has considerable influence on the flow quantities. The authors have not come across such results in the existing literature.
Vineet Kumar
Verma
Department of Mathematics and Astronomy University of Lucknow, Lucknow, INDIA-226007
Sunil
Datta
Department of Mathematics and Astronomy, University of Lucknow, Lucknow, India-226007
891-899
EXACT SOLUTION FOR RAYLEIGH−STOKES PROBLEMS OF AN OLDROYD-B FLUID IN A POROUS MEDIUM AND ROTATING FRAME
The aim of this paper is to determine the exact solution of unsteady magnetohydrodynamic (MHD) flow of a rotating Oldroyd-B fluid in a porous medium over a suddenly moved flat plate. This is achieved by using the Fourier sine and Laplace transforms method. The use of this method provides a means to get a new additional term appearing in the final solution. Many interesting existing results in the literature are obtained as the special and limiting cases of our solution. Finally, some graphical results of the velocity profiles are presented for different values of the material constants. It is shown that the porosity of the medium, the rotation, and the magnetisation of the fluid have an effect on the velocity fields.
Faisal
Salah
UTM Centre for Industrial and Applied Mathematics, 81310 Universiti Teknologi Malaysia; Department of Mathematics, Faculty of Science, University of Kordofan, North Kordofan State, El-Obeid 51111, Sudan
Zainal Abdul
Aziz
Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
Norsarahaida Saidina
Amin
Department of Mathematics, Faculty of Science, University Technology Malaysia, 81300 Skudai, Johor, Malaysia
Dennis Ling Chuan
Ching
Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
901-908
ANALYTICAL AND NUMERICAL STUDY OF DOUBLE DIFFUSIVE NATURAL CONVECTION IN A CONFINED POROUS MEDIUM SUBJECTED TO HEAT AND MASS FLUXES
We are interested in the theoretical and numerical study of coupled heat and mass transfer in a porous medium saturated by a binary fluid in a two-dimensional rectangular cavity. Uniform and constant heat and mass fluxes are imposed on the horizontal walls, whereas the vertical walls are considered impermeable and adiabatic. We used the model of Darcy to establish the mathematical model describing the phenomenon of double diffusion natural convection within the porous medium. In the case of an elongated cavity subjected to uniform and constant heat and mass fluxes, it is possible to use the parallel flow hypothesis to obtain an analytical solution describing the fields of stream function, temperature, and concentration. The obtained results showed an excellent agreement between the analytical solution and the numerical simulation and allowed the evaluation of the effects of control parameters on the flow structure and on the heat and mass transfer.
Smail
Benissaad
Laboratory of Applied Energy and Pollution, Mechanical Engineering Department, University Mentouri, Constantine, Algeria
Nabil
Ouazaa
Laboratory of Applied Energy and Pollution, Mechanical Engineering Department, University Mentouri, Constantine, Algeria
909-926
GAS FLOW IN A CHANNEL SEMIOBSTRUCTED BY A POROUS MEDIUM
An experimental study of a gas flow in a narrow channel partially obstructed by a regular array of wires is presented. The velocity profile along the channel was measured by means of a hot-wire anemometer, inside and outside the obstructed region. Flow instabilities were found in the free zone adjacent to the porous region, which were characterized by the standard deviation and the power spectrum of the signal of the anemometer. The experimental profiles were compared with numerical simulations using a two-dimensional Lattice Boltzmann model.
Diego
Dalponte
CNEA-CONICET and Universidad National del Centro, Pinto 399, 7000 Tandil, Argentina
N.
Silin
CONICET-CNEA, Av. Bustillo 9500, 8400 Bariloche, Argentina
A.
Clausse
CNEA-CONICET and Universidad National del Centro, Pinto 399, 7000 Tandil, Argentina
927-936
UTILIZATION OF MEMORY CONCEPT TO DEVELOP HEAT TRANSFER DIMENSIONLESS NUMBERS FOR POROUS MEDIA UNDERGOING THERMAL FLOODING WITH EQUAL ROCK AND FLUID TEMPERATURES
Enhanced oil recovery (EOR) techniques are regaining interest as high oil prices have rendered such techniques economically attractive. Thermal EOR processes, which involve injection of heat into the reservoir, cause continuous alteration of the thermal characteristics of both reservoir rock and fluids that are seldom modeled in the heat and momentum transfer equations. In this study, the memory concept is employed to develop new dimensionless numbers that can characterize convective heat transfer between the rock and fluids in a continuous alteration phenomenon. The energy balance equation is employed to develop the heat transfer coefficient with the assumption that the rock achieves the fluid temperature instantaneously. The final form of the equation is written in terms of Peclet number and the three proposed dimensionless numbers. The results show that the proposed dimensionless numbers are sensitive to the absolute and effective thermal conductivities of the solid and fluids, average system heat capacity, and the hydraulic diffusivity of the fluid-saturated porous medium. One of the new numbers correlates with the Nusselt and Prandtl numbers, while the local Peclet number is found to be sensitive to memory. Since heat convection and conduction in porous media can now be explained through the proposed numbers with the memory concept, these numbers help characterize the rheological behavior of the rock−fluid system. This work will enhance understanding the effect of heat transfer on alteration of thermal conductivity during thermal recovery operations in a hydrocarbon reservoir.
M. Enamul
Hossain
King Fahd University of Petroleum & Minerals (KFUPM), Dhahran, Saudi Arabia; Memorial University of Newfoundland, St. John's, Newfoundland and Labrador, Canada
Sidqi A.
Abu-Khamsin
Department of Petroleum Engineering, King Fahd University of Petroleum and Minerals, Dhahran 31261, Kingdom of Saudi Arabia
937-953
DEVELOPMENT OF DIMENSIONLESS NUMBERS FOR HEAT TRANSFER IN POROUS MEDIA USING A MEMORY CONCEPT
Various dimensionless numbers such as the Nusselt, Prandtl, and Peclet numbers, play a significant role in the analysis of heat transfer in any non-isothermal physical system. This transport phenomenon is modeled by a very complex set of differential equations that could involve a large number of variables and for which analytical solutions may be unattainable. Therefore, the model equations are often linearized by neglecting one or more terms (such as convection) or by employing simplifying assumptions. With the advent of advanced computational tools, it is possible to tackle such mathematical challenges numerically. Using a mathematical model based on nonlinear energy balance equations, new dimensionless numbers were developed to describe the role of various heat transport mechanisms (such as conduction and convection) in thermal recovery processes in porous media. The results show that the proposed numbers are sensitive to most of the reservoir rock/fluid properties such as porosity, permeability, densities, heat capacities, etc. Therefore, the proposed dimensionless numbers help to characterize the rheological behavior of the rock−fluid system. This work will enhance the understanding of the effect of heat transfer on the alteration of effective permeability during thermal recovery operations in a hydrocarbon reservoir.
M. Enamul
Hossain
King Fahd University of Petroleum & Minerals (KFUPM), Dhahran, Saudi Arabia; Memorial University of Newfoundland, St. John's, Newfoundland and Labrador, Canada
Sidqi A.
Abu-Khamsin
Department of Petroleum Engineering, King Fahd University of Petroleum and Minerals, Dhahran 31261, Kingdom of Saudi Arabia
957-973
CONVECTIVE FLOW BETWEEN A CORRUGATED AND A SMOOTH WALL
The fully developed mixed convective flow in a long vertical channel containing porous and fluid layers bounded by corrugated and smooth walls is studied. Non-linear equations governing the motion have been solved by the linearization technique wherein the flow is assumed to be in two parts; a mean part and a perturbed part. Exact solutions are obtained for the mean part and the perturbed part is solved using long wave approximation. Separate solutions are matched at the interface using suitable matching conditions. It is found that the Grashof number, width ratio, conductivity ratio, and wall temperature ratio promote velocity parallel to the flow direction and reduce velocity perpendicular to the flow direction. The presence of a porous matrix and the viscosity ratio suppresses velocity parallel to the flow direction and promotes velocity perpendicular to the flow direction.
Jawali
Umavathi
Gulbarga University
J. Prathap
Kumar
Department of Mathematics, Gulbarga University, Gulbarga-585 106, Karnataka
M
Shekar
Department of Mathematics, Gulbarga University, Gulbarga 585 106, Karnataka, India
975-988