Flow of Two-Immiscible Fluids in Porous and Nonporous Channels

1999 ◽  
Vol 122 (1) ◽  
pp. 117-124 ◽  
Author(s):  
Ali J. Chamkha
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Oil Recovery ◽  
Flow Direction ◽  
Immiscible Fluids ◽  
Local Thermal Equilibrium ◽  
Physical Parameters ◽  
Electrical Insulator ◽  
Thermal Buoyancy ◽  
Different Temperatures

This study considers steady, laminar flow of two viscous, incompressible, electrically-conducting and heat-generating or absorbing immiscible fluids in an infinitely-long, impermeable parallel-plate channel filled with a uniform porous medium. A magnetic field of uniform strength is applied normal to the flow direction. The channel walls are assumed to be electrically nonconducting and are maintained at two different temperatures. When present, the porous medium is assumed to act as an electrical insulator and that it is in local thermal equilibrium with the fluid. The transport properties of both fluids are assumed to be constant. This study is expected to be useful in understanding the influence of the presence of slag layers on the flow and heat transfer aspects of coal-fired Magnetohydrodynamic (MHD) generators when the porous medium is absent and the effects of thermal buoyancy and a magnetic field on enhanced oil recovery and filtration systems where the porous medium is present. The problem is formulated by employing the balance laws of mass, linear momentum, and energy for both phases. Continuous conditions for the velocity and temperature as well as the shear stress and heat flux of both phases at the interface are employed. The resulting governing ordinary differential equations are solved numerically subject to the boundary and interface conditions for the velocity and temperature distributions of both fluids in the channel. Analytical solutions for a special case of the problem where the porous medium is absent or only its inertia effect is neglected are obtained. Comparisons with previously reported velocity profiles are performed and excellent agreements are obtained. A parametric study illustrating the influence of the physical parameters involved in the problem is conducted and the results are presented graphically and discussed. [S0098-2202(00)02101-5]

Influence of an inclined magnetic field on the Poiseuille flow of immiscible micropolar–Newtonian fluids in a porous medium

2018 ◽  
Vol 96 (9) ◽  
pp. 1016-1028 ◽  
Author(s):  
Pramod Kumar Yadav ◽  
Sneha Jaiswal
Keyword(s):  
Magnetic Field ◽  
Rotational Velocity ◽  
Immiscible Fluids ◽  
Newtonian Fluids ◽  
Porous Channel ◽  
Physical Parameters ◽  
Inclined Magnetic Field ◽  
Two Phase ◽  
Flow Through ◽  
Newtonian Viscous Fluid

The present problem is concerned with two-phase fluid flow through a horizontal porous channel in the presence of uniform inclined magnetic field. The micropolar fluid or Eringen fluid and Newtonian viscous fluid are flowing in the upper and lower regions of the horizontal porous channel, respectively. In this paper, the permeability of each region of the horizontal porous channel has been taken to be different. The effects of various physical parameters like angles of inclination of magnetic field, viscosity ratio, micropolarity parameter, etc., on the velocities, micro-rotational velocity of two immiscible fluids in horizontal porous channel, wall-shear stress, and flow rate have been discussed. The result obtained for immiscible micropolar–Newtonian fluids are compared with the results of two immiscible Newtonian fluids. The obtained result may be used in production of oil from oil reservoirs, purification of contaminated ground water, etc.

Reaction Kinetics of In-Situ Combustion: Part 1-Observations

1984 ◽  
Vol 24 (04) ◽  
pp. 399-407 ◽  
Author(s):  
Mohammad Reza Fassihi ◽  
William E. Brigham ◽  
Henry J. Ramey
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Reaction Mechanism ◽  
Crude Oil ◽  
Oil Recovery ◽  
Burning Front ◽  
Burning Zone ◽  
Different Temperatures ◽  
Air Compression

Abstract Continuous analysis of produced gases from a small packed bed reactor, at both isothermal and linearly increasing temperatures, has shown that combustion of crude oil in porous media follows several consecutive reactions. Molar carbon dioxide/carbon monoxide (CO2/CO) and apparent hydrogen/carbon (H/C) ratios were used to observe the transition between these reactions at different temperature levels. A new kinetic model for oxidation of crude oil in porous media is presented in Part 2 of this paper (Page 408) Introduction The quantity of fuel consumed and the reaction rate within the burning zone have been studied intensively for two reasons. First, the maximum oil recovery is the difference of the original oil in place (OOIP) at the start of the operation and the oil consumed as fuel. Second, one of the most important factors in the economic evaluation of any in-situ combustion project is the cost of air compression. Excessive fuel deposition causes a slow rate of advance of the burning front and large air compression costs. However, if the fuel concentration is too low, the heat of combustion will not be sufficient to raise the temperature of the rock and the contained fluids to a level of self-sustained combustion. This may lead to combustion failure. Thus, it is necessary to understand the reactions occurring at different temperatures as the combustion front moves in the porous medium. The most crucial and yet least understood zone of insitu combustion oil recovery is the burning front, where temperature reaches a maximum value. The velocity of the burning front is controlled by the chemical reactions involved. However, since crude oil is a mixture of hydrocarbons, it is necessary to consider a global description of the reaction mechanism. Reaction Mechanism The reaction between fuel and oxygen in a forward combustion process is a heterogeneous flow reaction. Injected oxidant gas must pass through the burning zone to make the burning front move. Within the burning zone, four known transport processes occur:oxygen diffuses from the bulk gas stream to the fuel interface; then, perhaps,the oxygen absorbs and reacts with the fuel;then combustion products desorb; andproducts finally transfer into the bulk gas stream. If any of these steps is inherently much slower than the remaining ones, the overall rate will be controlled by that step. Also, the rate of each series of steps must be equal in the steadystate condition. However, there are no useful correlations for computing absorption and desorption of oxygen in a porous medium. Consequently, consideration of these phenomena becomes extremely difficult for even simple reactions. Theoretical expressions for postulated mechanisms often contain 10 or more arbitrary constants. Because of the large number of arbitrary constants, sever-al expressions developed for widely different mechanisms often will match experimental data equally well. In general, the combustion rate, Rc, of crude oil in a porous medium can be described as dCm m nRc = - ------ = kpo2 Cm,............................(1)dt whereCm = instantaneous concentration of fuel, k = rate constant, Po2 = partial pressure of oxygen, andm, n = reaction orders. The reaction constant, k, is often a function of temperature, T, as expressed by k=w exp(– E/RT).......................................(2) where E is the activation energy, w is the Arrhenius constant, and R is the universal gas constant. For heterogeneous reactions, the constant w is a function of the surface area of the rock. Early studies of crude oil oxidation in a porous medium were mostly qualitative. Differential thermal analysis (DTA) was performed on samples of crude oil, and the resulting thermograms represented the thermal history of each sample as it was heated at a uniform rate (usually 18 degrees F/min [10 degrees C/min]) in a constant air flow (usually 277 mL/min [277 cm3/min]). These thermograms indicated the presence of a number of exothermic reactions. Another method of analysis is thermogravimetric analysis (TGA). Here, a sample of crude oil is weighed continuously as it is heated at a constant rate. The resulting curve of weight change vs. time or temperature indicates the occurrence of at least two reactions at different temperatures. SPEJ P. 399^

scholarly journals Unsteady Bioconvection Squeezing Flow in a Horizontal Channel with Chemical Reaction and Magnetic Field Effects

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Qingkai Zhao ◽  
Hang Xu ◽  
Longbin Tao
Keyword(s):  
Magnetic Field ◽  
Chemical Reaction ◽  
Oil Recovery ◽  
Oil And Gas ◽  
Sedimentary Basins ◽  
Squeezing Flow ◽  
Physical Parameters ◽  
Magnetic Field Effects ◽  
Parallel Plates ◽  
Similarity Transformations

The time-dependent mixed bioconvection flow of an electrically conducting fluid between two infinite parallel plates in the presence of a magnetic field and a first-order chemical reaction is investigated. The fully coupled nonlinear systems describing the total mass, momentum, thermal energy, mass diffusion, and microorganisms equations are reduced to a set of ordinary differential equations via a set of new similarity transformations. The detailed analysis illustrating the influences of various physical parameters such as the magnetic, squeezing, and chemical reaction parameters and the Schmidt and Prandtl numbers on the distributions of temperature and microorganisms as well as the skin friction and the Nusselt number is presented. The conclusion is drawn that the flow field, temperature, and chemical reaction profiles are significantly influenced by magnetic parameter, heat generation/absorption parameter, and chemical parameter. Some examples of potential applications of such bioconvection could be found in pharmaceutical industry, microfluidic devices, microbial enhanced oil recovery, modeling oil, and gas-bearing sedimentary basins.

scholarly journals MHD CASSON NANOFLUID FLOW OVER A STRETCHING SURFACE EMBEDDED IN A POROUS MEDIUM: EFFECTS OF THERMAL RADIATION AND SLIP CONDITIONS

2021 ◽  
Vol 51 (4) ◽  
pp. 229-239
Author(s):  
Sameh E. Ahmed ◽  
R.A Mohamed ◽  
A.M Ali ◽  
A.J Chamkha ◽  
M.S Soliman
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Thermal Radiation ◽  
Numerical Study ◽  
Physical Parameters ◽  
Radiation Parameter ◽  
Two Phase ◽  
Casson Nanofluid ◽  
Non Linear ◽  
The Magnetic Field

This article presents a numerical study for a magnetohydrodynamic flow of a non-Newtonian Casson nanofluid over a stretching sheet embedded in a porous medium under the impacts of non-linear thermal radiation, heat generation/absorption, Joule heating and slips boundary conditions. A two-phase nanofluid model is applied to represent the nanofluid mixture. The porous medium is represented via the Darcy model. A similar solution is obtained for the governing equations and a numerical treatment based on the Runge-Kutta method is conducted to the resulting system of equations.  In this study, the controlling physical parameters are the Casson fluid parameter , the magnetic field , the radiation parameter , the Brownian motion parameter  and the thermophoresis parameter . The obtained results reveal that an increase in the Casson parameter enhances both of the local Nusselt and the Sherwood number while they are reduced as the non-linear radiation parameter increases. In addition, an increase in the magnetic field parameter supports the skin friction coefficient regardless the value of the Casson parameter.

FERROFLUID FLOW WITH MAGNETIC FIELD-DEPENDENT VISCOSITY DUE TO ROTATING DISK IN POROUS MEDIUM

2012 ◽  
Vol 04 (04) ◽  
pp. 1250041 ◽  
Author(s):  
PARAS RAM ◽  
VIKAS KUMAR
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Differential Equations ◽  
Rotating Disk ◽  
Physical Parameters ◽  
Highly Nonlinear ◽  
Displacement Thickness ◽  
Field Dependent ◽  
Magnetic Field Dependent Viscosity ◽  
Dependent Viscosity

The present study is carried out to examine the effects of magnetic field-dependent viscosity on steady axi-symmetric ferrofluid flow due to rotating disk in porous medium. The momentum equations give rise to highly nonlinear partial differential equations, which are converted to a system of nonlinear coupled ordinary differential equations on using Karman's similarity transformation. Then a numerical technique, which is the combination of finite difference and shooting methods, is employed in MATLAB environment to get the numerical solution of the problem. Beside the velocity and pressure profiles, the effect of MFD viscosity parameter and porosity parameter are also examined on radial, tangential skin frictions and on boundary layer displacement thickness. The results thus obtained numerically over the entire range of physical parameters are presented graphically.

HEAT TRANSFER IN A SLIP FLOW OF PERISTALTIC TRANSPORT OF A MAGNETO-NEWTONIAN FLUID THROUGH A POROUS MEDIUM

2009 ◽  
Vol 02 (03) ◽  
pp. 299-309 ◽  
Author(s):  
AYMAN MAHMOUD SOBH
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Porous Medium ◽  
Slip Flow ◽  
Transverse Magnetic ◽  
Physical Parameters ◽  
Long Wavelength ◽  
Governing System ◽  
Long Wavelength Approximation ◽  
Wavelength Approximation

In this paper, we study the interaction of peristalsis with heat transfer for the flow of a viscous fluid through a porous medium in uniform and nonuniform channels. The flow is subjected to constant transverse magnetic field. Long wavelength approximation (that is, the wavelength of the peristaltic wave is large compared with the radius of the channel) is used to solve the governing system. Closed form expressions are derived for the pressure–flow relationship, temperature, and heat transfer coefficient. The effects of various physical parameters are discussed through graphs.

scholarly journals Peristaltic Flow with Heat Transfer for Nano-Coupled Stress Fluid through Non-Darcy Porous Medium in the Presence of Magnetic Field

Coatings ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 910
Author(s):  
Wael Abbas ◽  
Nabil T. M. Eldabe ◽  
Rasha A. Abdelkhalek ◽  
Nehad A. Zidan ◽  
Samir. Y. Marzouk
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Porous Medium ◽  
Couple Stress ◽  
Fluid Velocity ◽  
Fluid Motion ◽  
Physical Parameters ◽  
Linear Partial Differential Equations ◽  
Nanoparticles Concentration ◽  
Coupled Stress

In this paper, the peristaltic motion of nano-coupled stress fluid through non-Darcy porous medium is investigated, and the heat transfer is taken into account. The system is stressed by an external magnetic field. The Ohmic and viscous couple stress dissipations, heat generation and chemical reaction are considered. This motion is modulated mathematically by a system of non-linear partial differential equations, which describe the fluid velocity, temperature and nanoparticles’ concentration. These equations are transformed to non-dimensional form with the associated appropriate boundary conditions. The homotopy perturbation method is used to find the solutions of these equations as a function of the physical parameters of the problem. The effects of the parameters on the obtained solutions are discussed numerically and illustrated graphically. It is found that these parameters play an important role to control the solutions. Significant outcomes from graphical elucidation envisage that the inclusion of more magnetic field strength increases the resistance of the fluid motion. Intensification of the couple stress parameter attenuates the temperature values, while it increases with increasing thermophoresis parameter.

scholarly journals Magnetohydrodynamics Peristaltic Flow of a Couple- Stress with Varying Temperature and concentration for Jeffrey Fluid through a Flexible Porous Medium

2021 ◽  
Vol 26 (4) ◽  
pp. 466-484
Author(s):  
Saif Razzaq Al-Waily ◽  
Dheia G. Salih Al-Khafajy
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Couple Stress ◽  
Internal Heat ◽  
Peristaltic Flow ◽  
Jeffrey Fluid ◽  
Physical Parameters ◽  
Peristaltic Motion ◽  
Velocity Equation ◽  
Effects Of Temperature

The topic of this paper is the peristaltic motion of a non-Newtonian Jeffrey fluid with couple stress across a porous medium inside a horizontal conduit. The unit is strained by a uniform magnetic field. It is taken into account the effects of viscous dissipation, internal heat generation, and radiation. This approach solves the equations of momentum, temperature, and velocity. The numerical formulas for temperature, axial velocity, and velocity are calculated as functionsof the problem's physical parameters. Numerical calculations, as well as the effects of temperature and the inclined slanted magnetic field and concentration on the velocity equation, were conducted for this formula, and the results were shown on the channel wall. The results of the problem's physical parameters In a series of statistics, the effects of this formula are explained numerically and graphically.

scholarly journals An integral equation for immiscible fluid isplacement in a two-dimensional porous medium or Hele-Shaw cell

1984 ◽  
Vol 26 (1) ◽  
pp. 14-30 ◽  
Author(s):  
M. R. Davidson
Keyword(s):  
Integral Equation ◽  
Porous Medium ◽  
Interfacial Tension ◽  
Immiscible Fluids ◽  
Physical Parameters ◽  
Immiscible Fluid ◽  
Normal Velocity ◽  
Two Dimensional ◽  
Flat Interface ◽  
Hele Shaw Cell

AbstractAn integral equation for the normal velocity of the interface between two immiscible fluids flowing in a two-dimensional porous medium or Hele-Shaw cell (one fluid displaces the other) is derived in terms of the physical parameters (including interfacial tension), a Green's function and the given interface. When the displacement is unstable, ‘fingering’ of the interface occurs. The Saffman-Taylor interface solutions for the steady advance of a single parallel-sided finger in the absence of interfacial tension are seen to satisfy the integral equation, and the error incurred in that equation by the corresponding Pitts approximating profile, when interfacial tension is included, is shown. In addition, the numerical solution of the integral equation is illustrated for a sinusoidal and a semicircular interface and, in each case, the amplitude behaviour inferred from the velocity distribution is consistent with conclusions based on the stability of an initially flat interface.

scholarly journals Effect of magnetic field and heat source on Upper-convected-maxwell fluid in a porous channel

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 917-928 ◽  
Author(s):  
Zeeshan Khan ◽  
Haroon Ur Rasheed ◽  
Tawfeeq Abdullah Alkanhal ◽  
Murad Ullah ◽  
Ilyas Khan ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Differential Equations ◽  
Heat Source ◽  
Ordinary Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Maxwell Fluid ◽  
Deborah Number ◽  
Physical Parameters ◽  
Fluid Temperature

Abstract The effect of magnetic field on the flow of the UCMF (Upper-Convected-Maxwell Fluid) with the property of a heat source/sink immersed in a porous medium is explored. A shrinking phenomenon along with the permeability of the wall are considered. The governing equations for the motion and transfer of heat of the UC MF along with boundary conditions are converted into a set of coupled nonlinear mathematical equations. Appropriate similarity transformations are used to convert the set of nonlinear partial differential equations into nonlinear ordinary differential equations. The modeled ordinary differential equations have been solved by the Homotopy Analysis Method (HAM). The convergence of the series solution is established. For the sake of comparison, numerical (ND-Solve method) solutions are also obtained. Special attention is given to how the non-dimensional physical parameters of interest affect the flow of the UCMF. It is observed that with the increasing Deborah number the velocity decreases and the temperature inside the fluid increases. The results show that the velocity and temperature distribution increases with a porous medium. It is also observed that the magnetic parameter has a decelerating effect on velocity while the temperature profiles increases in the entire domain. Due to the increase in Prandtl number the temperature profile increases. It is also observed that the heat source enhance the thermal conductivity and increases the fluid temperature while the heat sink provides a decrease in the fluid temperature.

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