Abstract: Considering the numerous applications of the study of
the flow due to leakage in a buried pipe
in unsaturated porous media, finding a proper model to explain the
influence of the effective factors is of great importance.There are
various important factors involved in this type of flow such as: pipe
leakage size and location, burial depth, the degree of the saturation of
the surrounding porous medium, characteristics of the porous
medium, fluid type and pressure of the upstream.In this study, the
flow through unsaturated porous media due to leakage of a buried
pipe for up and down leakage location is studied experimentally and
numerically and their results are compared. Study results show that
Darcy equation together with BCM method (for calculating the
relative permeability) have suitable ability for predicting the flow due
to leakage of buried pipes in unsaturated porous media.
Abstract: The present study is concerned with the free
convective two dimensional flow and heat transfer, within the
framework of Boussinesq approximation, in anisotropic fluid filled
porous rectangular enclosure subjected to end-to-end temperature
difference have been investigated using Lattice Boltzmann method
fornon-Darcy flow model. Effects of the moving lid direction (top,
bottom, left, and right wall moving in the negative and positive x&ydirections),
number of moving walls (one or two opposite walls), the
sliding wall velocity, and four different constant temperatures
opposite walls cases (two surfaces are being insulated and the
twoother surfaces areimposed to be at constant hot and cold
temperature)have been conducted. The results obtained are discussed
in terms of the Nusselt number, vectors, contours, and isotherms.
Abstract: The steady mixed convection boundary layer flow from
a vertical cone in a porous medium filled with a nanofluid is
numerically investigated using different types of nanoparticles as Cu
(copper), Al2O3 (alumina) and TiO2 (titania). The boundary value
problem is solved by using the shooting technique by reducing it
into an ordinary differential equation. Results of interest for the local
Nusselt number with various values of the constant mixed convection
parameter and nanoparticle volume fraction parameter are evaluated.
It is found that dual solutions exist for a certain range of mixed
convection parameter.
Abstract: This paper presents an analytical method to solve
governing consolidation parabolic partial differential equation (PDE)
for inelastic porous Medium (soil) with consideration of variation of
equation coefficient under cyclic loading. Since under cyclic loads,
soil skeleton parameters change, this would introduce variable
coefficient of parabolic PDE. Classical theory would not rationalize
consolidation phenomenon in such condition. In this research, a
method based on time space mapping to a virtual time space along
with superimposing rule is employed to solve consolidation of
inelastic soils in cyclic condition. Changes of consolidation
coefficient applied in solution by modification of loading and
unloading duration by introducing virtual time. Mapping function is
calculated based on consolidation partial differential equation results.
Based on superimposing rule a set of continuous static loads in
specified times used instead of cyclic load. A set of laboratory
consolidation tests under cyclic load along with numerical
calculations were performed in order to verify the presented method.
Numerical solution and laboratory tests results showed accuracy of
presented method.
Abstract: The present work is concerned with the free
convective two dimensional flow and heat transfer, in isotropic fluid
filled porous rectangular enclosure with differentially heated walls for
steady state incompressible flow have been investigated for non-
Darcy flow model. Effects of Darcy number (0.0001 £Da£ 10),
Rayleigh number (10 £Ra£ 5000), and aspect ratio (0.25 £AR£ 4), for
a range of porosity (0.4 £e£ 0.9) with and without moving lower wall
have been studied. The cavity was insulated at the lower and upper
surfaces. The right and left heated surfaces allows convective
transport through the porous medium, generating a thermal
stratification and flow circulations. It was found that the Darcy
number, Rayleigh number, aspect ratio, and porosity considerably
influenced characteristics of flow and heat transfer mechanisms. The
results obtained are discussed in terms of the Nusselt number,
vectors, contours, and isotherms.
Abstract: The paper presents an analytical solution for dispersion
of a solute in the peristaltic motion of a couple stress fluid
through a porous medium with slip condition in the presence of both
homogeneous and heterogeneous chemical reactions. The average
effective dispersion coefficient has been found using Taylor-s limiting
condition and long wavelength approximation. The effects of various
relevant parameters on the average coefficient of dispersion have been
studied. The average effective dispersion coefficient tends to increase
with permeability parameter but tends to decrease with homogeneous
chemical reaction rate parameter, couple stress parameter, slip parameter
and heterogeneous reaction rate parameter.
Abstract: The effect of variable chemical reaction on heat and mass transfer characteristics over unsteady stretching surface embedded in a porus medium is studied. The governing time dependent boundary layer equations are transformed into ordinary differential equations containing chemical reaction parameter, unsteadiness parameter, Prandtl number and Schmidt number. These equations have been transformed into a system of first order differential equations. MATHEMATICA has been used to solve this system after obtaining the missed initial conditions. The velocity gradient, temperature, and concentration profiles are computed and discussed in details for various values of the different parameters.
Abstract: In this paper, the effects of radiation, chemical
reaction and double dispersion on mixed convection heat and mass
transfer along a semi vertical plate are considered. The plate is
embedded in a Newtonian fluid saturated non - Darcy (Forchheimer
flow model) porous medium. The Forchheimer extension and first
order chemical reaction are considered in the flow equations. The
governing sets of partial differential equations are nondimensionalized
and reduced to a set of ordinary differential
equations which are then solved numerically by Fourth order Runge–
Kutta method. Numerical results for the detail of the velocity,
temperature, and concentration profiles as well as heat transfer rates
(Nusselt number) and mass transfer rates (Sherwood number) against
various parameters are presented in graphs. The obtained results are
checked against previously published work for special cases of the
problem and are found to be in good agreement.
Abstract: The effect of porous medium on the capillary instability of a cylindrical interface in the presence of axial electric field has been investigated using viscous potential flow theory. In viscous potential flow, the viscous term in Navier-Stokes equation vanishes as
vorticity is zero but viscosity is not zero. Viscosity enters through normal stress balance in the viscous potential flow theory and tangential stresses are not considered. A dispersion relation that accounts for the growth of axisymmetric waves is derived and stability is discussed theoretically as well as numerically. Stability criterion is given by critical value of applied electric field as well as critical wave number. Various graphs have been drawn to show the effect of various physical parameters such as electric field, viscosity ratio, permittivity ratio on the stability of the system. It has been observed that the axial electric field and porous medium both have stabilizing effect on the stability of the system.
Abstract: Resins are used in nuclear power plants for water
ultrapurification. Two approaches are considered in this work:
column experiments and simulations. A software called OPTIPUR
was developed, tested and used. The approach simulates the onedimensional
reactive transport in porous medium with convectivedispersive
transport between particles and diffusive transport within
the boundary layer around the particles. The transfer limitation in the
boundary layer is characterized by the mass transfer coefficient
(MTC). The influences on MTC were measured experimentally. The
variation of the inlet concentration does not influence the MTC; on
the contrary of the Darcy velocity which influences. This is consistent
with results obtained using the correlation of Dwivedi&Upadhyay.
With the MTC, knowing the number of exchange site and the relative
affinity, OPTIPUR can simulate the column outlet concentration
versus time. Then, the duration of use of resins can be predicted in
conditions of a binary exchange.
Abstract: In this paper, we have applied the homotopy perturbation
method (HPM) for obtaining the analytical solution of unsteady
flow of gas through a porous medium and we have also compared the
findings of this research with some other analytical results. Results
showed a very good agreement between results of HPM and the
numerical solutions of the problem rather than other analytical solutions
which have previously been applied. The results of homotopy
perturbation method are of high accuracy and the method is very
effective and succinct.
Abstract: The stability analysis of Marangoni convection in porous media with a deformable upper free surface is investigated. The linear stability theory and the normal mode analysis are applied and the resulting eigenvalue problem is solved exactly. The Darcy law and the Brinkman model are used to describe the flow in the porous medium heated from below. The effect of the Crispation number, Bond number and the Biot number are analyzed for the stability of the system. It is found that a decrease in the Crispation number and an increase in the Bond number delay the onset of convection in porous media. In addition, the system becomes more stable when the Biot number is increases and the Daeff number is decreases.
Abstract: We report the results of an lattice Boltzmann
simulation of magnetohydrodynamic damping of sidewall convection
in a rectangular enclosure filled with a porous medium. In particular
we investigate the suppression of convection when a steady magnetic
field is applied in the vertical direction. The left and right vertical
walls of the cavity are kept at constant but different temperatures
while both the top and bottom horizontal walls are insulated. The
effects of the controlling parameters involved in the heat transfer and
hydrodynamic characteristics are studied in detail. The heat and mass
transfer mechanisms and the flow characteristics inside the enclosure
depended strongly on the strength of the magnetic field and Darcy
number. The average Nusselt number decreases with rising values of
the Hartmann number while this increases with increasing values of
the Darcy number.
Abstract: We report the results of an lattice Boltzmann
simulation of magnetohydrodynamic damping of sidewall convection
in a rectangular enclosure filled with a porous medium. In particular
we investigate the suppression of convection when a steady magnetic
field is applied in the vertical direction. The left and right vertical
walls of the cavity are kept at constant but different temperatures
while both the top and bottom horizontal walls are insulated. The
effects of the controlling parameters involved in the heat transfer and
hydrodynamic characteristics are studied in detail. The heat and mass
transfer mechanisms and the flow characteristics inside the enclosure
depended strongly on the strength of the magnetic field and Darcy
number. The average Nusselt number decreases with rising values of
the Hartmann number while this increases with increasing values of
the Darcy number.
Abstract: Fluid flow and heat transfer of vertical full cone
embedded in porous media is studied in this paper. Nonlinear
differential equation arising from similarity solution of inverted cone
(subjected to wall temperature boundary conditions) embedded in
porous medium is solved using a hybrid neural network- particle
swarm optimization method.
To aim this purpose, a trial solution of the differential equation is
defined as sum of two parts. The first part satisfies the initial/
boundary conditions and does contain an adjustable parameter and
the second part which is constructed so as not to affect the
initial/boundary conditions and involves adjustable parameters (the
weights and biases) for a multi-layer perceptron neural network.
Particle swarm optimization (PSO) is applied to find adjustable
parameters of trial solution (in first and second part). The obtained
solution in comparison with the numerical ones represents a
remarkable accuracy.
Abstract: Multiphase flow transport in porous medium is very common and significant in science and engineering applications. For example, in CO2 Storage and Enhanced Oil Recovery processes, CO2 has to be delivered to the pore spaces in reservoirs and aquifers. CO2 storage and enhance oil recovery are actually displacement processes, in which oil or water is displaced by CO2. This displacement is controlled by pore size, chemical and physical properties of pore surfaces and fluids, and also pore wettability. In this study, a technique was developed to measure the pressure profile for driving gas/liquid to displace water in pores. Through this pressure profile, the impact of pore size on the multiphase flow transport and displacement can be analyzed. The other rig developed can be used to measure the static and dynamic pore wettability and investigate the effects of pore size, surface tension, viscosity and chemical structure of liquids on pore wettability.
Abstract: A steady two-dimensional magnetohydrodynamics
flow and heat transfer over a stretching vertical sheet influenced by
radiation and porosity is studied. The governing boundary layer
equations of partial differential equations are reduced to a system of
ordinary differential equations using similarity transformation. The
system is solved numerically by using a finite difference scheme
known as the Keller-box method for some values of parameters,
namely the radiation parameter N, magnetic parameter M, buoyancy
parameter l , Prandtl number Pr and permeability parameter K. The
effects of the parameters on the heat transfer characteristics are
analyzed and discussed. It is found that both the skin friction
coefficient and the local Nusselt number decrease as the magnetic
parameter M and permeability parameter K increase. Heat transfer
rate at the surface decreases as the radiation parameter increases.
Abstract: The problem of natural convection about a cone embedded in a porous medium at local Rayleigh numbers based on the boundary layer approximation and the Darcy-s law have been studied before. Similarity solutions for a full cone with the prescribed wall temperature or surface heat flux boundary conditions which is the power function of distance from the vertex of the inverted cone give us a third-order nonlinear differential equation. In this paper, an approximate method for solving higher-order ordinary differential equations is proposed. The approach is based on a rational Chebyshev Tau (RCT) method. The operational matrices of the derivative and product of rational Chebyshev (RC) functions are presented. These matrices together with the Tau method are utilized to reduce the solution of the higher-order ordinary differential equations to the solution of a system of algebraic equations. We also present the comparison of this work with others and show that the present method is applicable.
Abstract: In this study, the effect of greywater irrigation on airwater interfacial area is investigated. Several soil column experiments were conducted for different greywater irrigation to develop the pressure-saturation curves. Surface tension was measured for different greywater concentration and fitted for Gibbs adsorption equation. Pressure-saturation curves show that the reduction of capillary rise stops when it reaches its critical micelle concentration (CMC). A simple theory is derived from pressure-saturation curves for calculating air-water interfacial area in porous medium during greywater irrigation by introducing a term 'hydraulic radius' for the pores. This term diminishes any effect of pore shapes on the air-water interfacial area. The air-water interfacial area was calculated using the pressure-saturation curves and found that it decreases with increasing moisture content. But no significant effect was observed on air-water interfacial area for different greywater irrigation. A maximum of 10% variation in interfacial area was observed at the residual saturation zone.
Abstract: The flow and heat transfer characteristics for natural
convection along an inclined plate in a saturated porous medium with
an applied magnetic field have been studied. The fluid viscosity has
been assumed to be an inverse function of temperature. Assuming
temperature vary as a power function of distance. The transformed
ordinary differential equations have solved by numerical integration
using Runge-Kutta method. The velocity and temperature profile
components on the plate are computed and discussed in detail for
various values of the variable viscosity parameter, inclination angle,
magnetic field parameter, and real constant (λ). The results have also
been interpreted with the aid of tables and graphs. The numerical
values of Nusselt number have been calculated for the mentioned
parameters.