Begell House Inc.
Journal of Porous Media
JPM
1091-028X
19
9
2016
AXISYMMETRIC AND ASYMMETRIC INSTABILITIES OF A NON-NEWTONIAN LIQUID JET MOVING IN AN INVISCID STREAMING GAS THROUGH POROUS MEDIA
751-769
10.1615/JPorMedia.v19.i9.10
Mohamed
El-Sayed
Ph. D.
Galal M.
Moatimid
Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
F. M. F.
Elsabaa
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Roxy 11757, Cairo, Egypt
M. F. E.
Amer
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Roxy 11757, Cairo, Egypt
hydrodynamic stability
non-Newtonian fluids
three-dimensional disturbances
liquid jets
flows through porous media
In this paper, a linear stability analysis is presented for a non-Newtonian liquid jet moving in a streaming inviscid gas through porous media with three-dimensional disturbances. The dispersion relation between the non-dimensional growth rate and the non-dimensional wave number is derived using appropriate boundary conditions, and it is solved numerically via a new technique using Mathematica software. The effects of different parameters on the stability behavior of the system are discussed in detail. The instability behavior of the jet is influenced by the interaction of liquid viscosity, porous medium parameters, and elasticity. It is shown that non-Newtonian liquid jets are more than their Newtonian counterparts, and that Squire's theorem is in general no longer applicable. It is shown also that the elasticity, Reynolds, Weber numbers; gas to liquid density ratio, and the jet velocity have destabilizing effects; while the porosity of porous medium, medium permeability, surface tension, jet viscosity, and the deformation retardation time to stress relaxation time ratio have stabilizing influences. The dynamic viscosity of the gas to the zero shear viscosity of the liquid and the Ohnesorge number are found to have dual roles on the stability of the considered system. Moreover, it is found that the system is more unstable in the presence of porous medium than in its absence.
IMPACT OF POST-PROCESSING METHODS ON ACCURACY OF DARCIAN AND FORCHHEIMER PERMEABILITIES DETERMINATION
771-782
10.1615/JPorMedia.v19.i9.20
Eddy
El-Tabach
Univ. Orléans, INSA-CVL, PRISME, EA 4229, 63 avenue de Lattre de Tassigny, F18020,
Bourges, France
Nicolas
Gascoin
Univ. Orléans, INSA-CVL, PRISME, EA 4229, 88 boulevard Lahitolle, F18022, Bourges,
France
Marc
Bouchez
MBDA-France, 18 rue Le Brix, 18000 Bourges, France
Guillaume
Fau
PRISME Laboratory, INSA-Centre Val de Loire, 88 boulevard Lahitolle, 18000 Bourges, France
permeation
porous medium
methods comparison
CMC characterization
Getting the Darcian and Forchheimer permeabilities is required by a number of applications to characterize porous materials. In the meantime, ensuring the reliability of these numerical values is essential. While a number of studies aim at developing appropriate test benches, the quantitative importance of post-processing methods is often underestimated. Yet, they play a major role in terms of accuracy and reliability, in addition to the test benches and test methods themselves. The present work uses experimental data obtained in the framework of transpiration cooling of high-speed cooled structures. It presents a comparison between six methodologies which are found in the literature to post-process the experimental raw data. Their accuracy is found to be influenced by several parameters (Darcian and Forchheimer permeabilities orders of magnitude, operating range, and flow nature). This work intends to quantify these methods and to suggest which method to choose to minimize the uncertainty. Above 10−17 m2, the Darcian description should be replaced by the Brinkman one and the ISO 4022 method is generally the best processing method (best correlation factor) over the entire range of test. The Multiple Linear regression method shows a clear advantage over the Simple Linear Regression one without rebutting computation cost.
NATURAL CONVECTION OF HEAT TRANSFER FOR NANOFLUID IN A PARTIALLY OPEN CAVITY WITH INTERNAL HEAT GENERATION: NON-DARCY EFFECT
783-797
10.1615/JPorMedia.v19.i9.30
N.
Nithyadevi
Department of Mathematics, Bharathiar University, Coimbatore 641046, Tamilnadu, India
Muthu
Rajarathinam
Department of Science and Humanities, Karpagam College of Engineering, Coimbatore
641 032, India
porous medium
nanofluid
partially open cavity
internal heat generation
In this work, unsteady laminar convection in a partially open porous cavity filled by Cu-water nanofluid with internal heat generation has been numerically studied using the Darcy−Brinkman−Forchheimer model. The numerical solution of the governing equations are obtained from finite volume method together with power law scheme. The SIMPLE algorithm is used for continuity and momentum equations. Numerical simulations are carried out to find the true effects of Darcy number (10−5 ≤ Da ≤ 10−1), heat generation parameter (0 ≤ Q ≤ 15), solid volume fraction (0% ≤ Φ ≤ 5%), and three different opening positions, while the Marangoni and Rayleigh numbers are fixed at 100 and 104. It is found that the heat transfer rate increases with Da and Φ but decreases with Q. Also, the heat transfer has a significant effect due to the ventilation position.
ENTROPY ANALYSIS OF THERMALLY RADIATING MAGNETOHYDRODYNAMIC SLIP FLOW OF CASSON FLUID IN A MICROCHANNEL FILLED WITH SATURATED POROUS MEDIA
799-810
10.1615/JPorMedia.v19.i9.40
Oluwole Daniel
Makinde
Faculty of Military Science, Stellenbosch University, Private Bag X2, Saldanha 7395, South
Africa
Adetayo S.
Eegunjobi
Department of Mathematics and Statistics, Namibia University of Science and Technology, Windhoek, Namibia
Casson fluid
porous medium
thermal radiation
slip flows
entropy generation
In this paper, we have investigated the influence of thermal radiation, magnetic field, wall suction/injection, and porous media permeability on inherent irreversibility in magnetohydrodynamic (MHD) forced convective flow of an electrically conducting Casson fluid in a horizontal microchannel with boundary slip and saturated with porous medium. The nonlinear model problem is tackled numerically using fourth−fifth order Runge−Kutta−Fehlberg method and the computed results for velocity and temperature fields are utilized to determine the skin friction, Nusselt number, entropy generation rate, and Bejan number. Pertinent results are displayed graphically and the physical aspects are discussed. It is observed that the impact of magnetic field and Casson fluid parameter have significant effect on the entropy generation rate.
VALIDITY OF PARAMETRIC RESTRICTIONS TO THE MODIFIED BUCKLEY-LEVERETT EQUATIONS
811-819
10.1615/JPorMedia.v19.i9.50
Gabriel
de Moraes
Programa de Pos-Graduacao em Engenharia de Defesa, Instituto Militar de Engenharia, Praca General Tiburcio 80, Rio de Janeiro, RJ 22290-270, Brazil
Renan
de S. Teixeira
Programa de Pos-Graduacao em Engenharia de Defesa, Instituto Militar de Engenharia, Praca General Tiburcio 80, Rio de Janeiro, RJ 22290-270, Brazil; Current address: Lacad - Dinam - INMETRO, Av. Nossa Senhora das Gracas 50, Predio 06, Duque de Caxias, RJ 25250-020, Brazil
Leonardo S.
de B. Alves
Laboratorio de Mecanica Teorica e Aplicada, Departamento de Engenharia Mecanica, Universidade Federal Fluminense, Rua Passo da Patria 156, bloco E, sala 216, Niteroi, RJ 24210-240, Brazil
total variation diminishing schemes
Runge-Kutta schemes
strong stability preserving properties
A modified version of the regularized Buckley-Leverett equation is studied. It is shown that adequate numerical schemes with nonlinear numerical stability properties should be employed to capture the different compressible and under-compressive shock waves, as well as rarefaction waves, present in this model. Otherwise, unphysical non-monotonic behavior will be artificially produced, which might lead to an incorrect physical interpretation of the problem under study. An example is shown where this oscillatory behavior led to the imposition of an unnecessary restriction on the possible values of the regularization parameter of this model. The schemes presented here can and have been extended to more complex flow models.
COMBINED EFFECT OF HEAT AND MASS TRANSFER IN MHD FLOW OF A NANOFLUID BETWEEN EXPANDING/CONTRACTING WALLS OF A POROUS CHANNEL
821-839
10.1615/JPorMedia.v19.i9.60
Muhammad Farooq
Iqbal
Centre for Advanced Studies in Pure and Applied Mathematics, (CASPAM), Bahauddin
Zakariya University, (BZU), Multan, 608000 Pakistan
Shahzad
Ahmad
Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya
University, Multan, Pakistan, 75500
Kashif
Ali
Center for Advanced Studies in Pure and Applied Mathematics (CASPAM),
Bahauddin Zakariya University, 60800-BZU, Multan-60000, Pakistan
Muhammad
Ashraf
Department of Mathematics, Faculty of Science, University of Sargodha, Sargodha, 40100, Pakistan
heat transfer
porous channel
aluminium dioxide nanoparticles
wall expansion ratio
permeability Reynolds number
We consider an incompressible laminar viscous nanofluid in a porous channel with expanding/contracting walls. The governing equations of flow and heat transfer are reduced into a set of nonlinear coupled ordinary differential equations (ODEs). A combination of an iterative (successive over relaxation) and a direct method is employed for solving the sparse systems of linear algebraic equations arising from the finite difference discretization of the linearized self-similar ODEs. We have noticed that the permeability Reynolds number increases both the shear stress and the heat transfer rate when the porous walls of the channel are moving away, whereas the viscous dissipation always increases the heat transfer rate at the walls, irrespective of the wall movement.