Begell House Inc.
Journal of Porous Media
JPM
1091-028X
20
6
2017
RADIAL BASIS FUNCTION PSEUDO-SPECTRAL SOLUTION OF THE NON-DARCY MODEL IN A POROUS MEDIUM
479-490
10.1615/JPorMedia.v20.i6.10
Bengisen
Pekmen
TED University, Basic Sciences Unit, Ankara, Turkey
radial basis function approximation
natural convection
porous medium
Brinkman-Forchheimer-extended Darcy model
In this study, the radial basis function pseudo-spectral (RBF-PS) method is applied for solving natural convective flow in a square cavity and in a curved pipe filled with a porous medium. RBF-PS constructs differentiation matrices by the coordinate matrix formed by radial distances using multiquadric radial basis function (MQ-RBF) √(r2 + c2). The direct implementation of the problem and the cheap computational cost using the small number of grid points make the proposed method captivating. The governing dimensionless equations are solved in terms of stream function, vorticity, and temperature. The results are given for several values of Rayleigh (Ra) number, Darcy (Da) number, and porosity εp in terms of average Nusselt number, or streamlines, isotherms, and vorticity contours. Physically the decrease in Darcy number suppresses the heat transfer while the convective heat transfer becomes prominent with the increase in Ra, and in εp.
MIXED CONVECTION IN A VERTICALLY LAYERED FLUID-POROUS MEDIUM ENCLOSURE WITH TWO INNER ROTATING CYLINDERS
491-511
10.1615/JPorMedia.v20.i6.20
Muneer A.
Ismael
Mechanical Engineering Department, Engineering College, University of Basrah, Basrah
61004, Iraq
Fatih
Selimefendigil
Mechanical Engineering Department, Celal Bayar University, Manisa, 45140, Turkey
Ali J.
Chamkha
Department of Mechanical Engineering, Prince Sultan Endowment for Energy and
Environment, Prince Mohammad Bin Fahd University, Al-Khobar 31952, Kingdom of Saudi
Arabia; RAK Research and Innovation Center, American University of Ras Al Khaimah, P.O. Box
10021, Ras Al Khaimah, United Arab Emirates
mixed convection
two rotating cylinders
porous medium
computational fluid dynamics
In this study, mixed convection in a vertically half partitioned cavity with two rotating adiabatic cylinders is numerically investigated. The horizontal walls are thermally insulated. The left vertical wall is kept isothermally at high temperature while the right vertical wall is kept isothermally at lower temperature. The Galerkin weighted residual finite element method is used to solve the governing equations. The numerical study is performed for various values of Rayleigh numbers (between 103 and 106), angular rotational speed of the cylinders (between −5000 and 5000), Darcy numbers (between 10−5 and 10−2), horizontal positions of the cylinder centers (between 0.4 and 0.6) and cylinder sizes (between 0.1 and 0.4). It is observed that angular velocity of the cylinders and cylinder sizes have a profound effect on the heat transfer enhancement along the hot vertical wall. The averaged heat transfer enhancements are 354.65% and 45.24% at a Rayleigh number of 106 compared to the case at a Rayleigh number of 103 for cylinder sizes of R = 0.1 and R = 0.4. Large variations in the local heat transfer are seen for various angular velocities of the cylinder, and cylinder rotation brings averaged heat transfer enhancement for sizes of R = 0.3 and R = 0.4. The averaged heat transfer enhances by 235.10% for a Darcy number of 10−2 compared to a Darcy number of 10−5 using cylinder sizes of R = 0.1. The horizontal movement of the cylinder centers increases the averaged heat transfer by 34.08% for (D1 = D2 = 0.6) compared to configuration at (D1 = D2 = 0.4) for angular rotational speed of Ω = −5000.
THROUGHFLOW EFFECT ON WEAKLY NONLINEAR OSCILLATORY CONVECTION IN A VISCOELASTIC FLUID SATURATING POROUS MEDIUM UNDER TEMPERATURE MODULATION
513-529
10.1615/JPorMedia.v20.i6.30
Beer S.
Bhadauria
Department of Applied Mathematics, School for Physical Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, India; Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, India
throughflow
temperature modulation
weak nonlinear theory
non-Newtonian fluid
The effect of vertical throughflow and temperature modulation on a viscoelastic fluid-saturated porous medium has been investigated. A sinusoidal profile is taken to modulate the walls' temperature. The amplitudes of temperature modulation at the lower and upper surfaces are considered to be very small, and the disturbances are expanded in terms of power series of amplitude of convection. A weak nonlinear stability analysis has been performed for the oscillatory mode of convection, and heat transport in terms of Nusselt number, which is governed by the nonautonomous complex Ginzburg-Landau equation, is calculated. The effect of vertical throughflow is found to stabilize the system irrespective of the direction of throughflow in the case of permeable boundary conditions. The time relaxation λ has a destabilizing effect, whereas the time retardation parameter e has stabilizing effect on the system. The effects of amplitude and frequency of modulation on heat transport have been analyzed and depicted graphically. The study establishes that the heat transport can be controlled effectively by a mechanism that is external to the system. Furthermore, it is also found that heat transfer is more in the oscillatory mode of convection than in the stationary mode of convection.
FOULING AND WETTING STUDIES RELATING TO THE VACUUM MEMBRANE DISTILLATION PROCESS FOR BRACKISH AND GREY WATER TREATMENT
531-547
10.1615/JPorMedia.v20.i6.40
Mohammad
Ramezanianpour
Department of Engineering and Architectural Studies, Ara Institute of Canterbury,
Christchurch, New Zealand
Muttucumaru
Sivakumar
School of Civil, Mining and Environmental Engineering, Faculty of Engineering and Information Sciences, University of Wollongong, Wollongong, Australia
brackish water
fouling
grey water
hydrophobic membrane
vacuum membrane distillation
wetting phenomena
Membrane distillation (MD) has two major problems: wetting and fouling. MD is rarely employed in wastewater reclamation since the active surfactant in the detergents contained in such water promotes feed water penetration through the membrane. Another difficulty is that the membrane lifetime and the performance of the MD process are both influenced by fouling. The main aim of this paper is to determine the effectiveness of the linear alkylbenzene sulfonate (LAS) concentration in the reduction of contact angle and the prediction of the flux decline with variation of the influent salt concentration. Contact angle was measured for different concentrations of LAS solution as well as different samples of brackish and grey water. The tests were performed with three different types of hydrophobic membranes. A simple empirical model was proposed, and related coefficients were calibrated based on experimental data for contact angles measured for different solutions with the hydrophobic membrane. Flux decline trends during pore wetting was investigated by monitoring the permeate quality through the treatment of synthetic grey water. The effect of membrane fouling during vacuum membrane distillation (VMD) was also studied under different operating conditions. A variety of temperature and pressure combinations as well as several salinity concentrations has been examined. The mathematical based model developed for the permeate flux was used to predict the flux rate of different salinity solutions. It was found that the flux decline could be attributed to the mass transfer resistance of the salt crystals.
VISUAL STUDY OF TURBULENT FILTRATION IN POROUS MEDIA
549-557
10.1615/JPorMedia.v20.i6.50
Aleksei R.
Evseev
Kutateladze Institute of Thermophysics, 1 Lavrentiev Avenue, Novosibirsk, 630090, Russia
turbulent filtration flow
refractive-index matching technique
visual studies
packing of spheres
The effect of pore geometry and Reynolds number (1000−20000) on the flow structure, formation of vortex zones, and their scale in a stationary layer of spheres was studied visually in the turbulent developed regime of filtration using the refractive-index matching technique. Three types of packing with different porosity were realized in the experiments: a cubic packing with through channels, octahedral packing with blocked channels, and random packing. For the regular packing in the turbulent regime, the shape and size of the resulting vortex structures are determined by the packed bed geometry, and do not depend on the Reynolds number in the considered range. Vortex structures are usually formed near the contact points of spheres; their sizes do not exceed the pore scale. In the random packing of spheres in the filtration turbulent flow, the small zones of separation are formed first, where the vortex structure stabilizes quickly. The further increase in the Reynolds number leads to formation of the larger vortex regions of recirculation, which, however, do not occupy the entire shadow area behind the sphere.
MHD COUETTE FLOW OF POWELL-EYRING FLUID IN AN INCLINED POROUS SPACE IN THE PRESENCE OF A TEMPERATURE-DEPENDENT HEAT SOURCE WITH CHEMICAL REACTION
559-575
10.1615/JPorMedia.v20.i6.60
R.
Muthuraj
Department of Mathematics,
P.S.N.A. College of Engineering & Technology,
Dindigul-624622, India
D. Lourdu
Immaculate
Department of Mathematics, Bharathiar University, Coimbatore, India, and Department of Mathematics, The American College, Madurai, India
Suripeddi
Srinivas
Department of Mathematics, School of Sciences and Languages, VIT-AP University,
Amaravati - 522 237, India
Couette flow
heat and mass transfer
chemical reaction
inclined channel
porous medium
The present study investigates the MHD Couette flow of Powell-Eyring fluid in an inclined porous space in the presence of chemical reaction with thermal diffusion and diffusion thermo effects. The highly nonlinear coupled differential equations governing the problem are solved by using the homotopy analysis method (HAM). The homotopy solutions are validated with the numerical solutions obtained by NDSolve in Mathematica. It was found that there is an excellent agreement between analytical and numerical solutions. The effects of involved parameters on the flow, heat, and mass transfer characteristics such as velocity, temperature, concentration distribution, flow rate, total heat rate added to the fluid, and total species rate added to the fluid are shown graphically and discussed in detail. Further, variations on coefficient of skin friction, Nusselt number, and Sherwood number for different values of interesting parameters are tabulated.