Begell House Inc.
Journal of Porous Media
JPM
1091-028X
15
1
2012
THERMAL INSTABILITY IN SUPERPOSED POROUS AND FLUID LAYERS IN THE PRESENCE OF A MAGNETIC FIELD USING THE BRINKMAN MODEL
1-10
10.1615/JPorMedia.v15.i1.10
Hanadi
Banjer
Department of Mathematical Sciences, Umm Al-Qura University, P.O. Box 6337, Makkah, Saudi Arabia
Abdullah A.
Abdullah
Department of Mathematical Sciences, Umm Al-Qura University, Makkah 24382, Saudi
Arabia
superposed porous and fluid layers
thermal convection
Brinkman model
magnetic field
Chebyshev tau method
Thermal convection in a two-layer system consisting of a horizontal fluid layer overlying a layer of porous medium saturated with the same fluid, with uniform heating from below and in the presence of a vertical magnetic field, is investigated. The flow in the porous medium is assumed to be governed by the Brinkman model. The onset of convection is seen to have a bimodal nature in which convection may be dominated by the porous medium or by the fluid, depending on the depth of the relative layers and the strength of the magnetic field. Numerical results are obtained for different
values of the parameter d (= depth of fluid layer/depth of porous layer) and for different values of the magnetic parameter Q. A comparison between the critical Rayleigh numbers in Brinkman and Darcy models reveals that in the absence of a magnetic field, the critical Ram for the Brinkman model is always greater than the corresponding one in the Darcy model; however, in the presence of a magnetic field when d ≥ 0.33, the critical Ram for the Darcy model is larger.
NANOFLUID BIOCONVECTION IN A HORIZONTAL FLUID-SATURATED POROUS LAYER
11-27
10.1615/JPorMedia.v15.i1.20
Andrey V
Kuznetsov
Department of Mechanical and Aerospace Engineering, North Carolina State University, Campus Box 7910, Raleigh, NC 27695-7910, USA
nanofluid bioconvection
gyrotactic microorganisms
Brownian motion
thermophoresis
natural convection
horizontal layer
The theory of nanofluid bioconvection in porous media is presented. The major motivation of using bioconvection is to enhance mixing and mass transfer in microvolumes, but before this goal can be implemented in practical microdevices, nanofluid bioconvection must be understood at the fundamental level. The developed theory is applied to investigating the onset of nanofluid bioconvection in a horizontal porous layer heated from below. The cases of non-oscillatory and oscillatory convection are investigated. The obtained results indicate that the effect of microorganisms on the stability of the suspension may depend on the value of bioconvection Peclet number.
POROUS CURVILINEAR SQUEEZE FILM BEARING WITH ROUGH SURFACES LUBRICATED BY A POWER-LAW FLUID
29-49
10.1615/JPorMedia.v15.i1.30
Anna
Walicka
Department of Mechanics and Design of Machines, University of Zielona Gora, 65-516 Zielona Gora, Poland
curvilinear bearing
surface roughness effect
porous wall
squeeze film
power-law fluid
The flow of a power-law lubricant in a squeeze film bearing with one porous wall is considered. The bearing is modeled by two curvilinear rough surfaces and the porous wall adheres to the curved nonporous surface. The flow in the bearing clearance is considered without inertia and the momentum and Poisson equations are uncoupled by using the Morgan-Cameron approximation. A closed-form solution is obtained by using the Christensen stochastic model of surface roughness. A step bearing and a spherical bearing are discussed as examples. It is shown that the power-law exponent and the roughness influence the bearing performance considerably.
STUDY OF THE MIXED CONVECTION IN A CHANNEL WITH POROUS LAYERS USING A THERMAL NONEQUILIBRIUM MODEL
51-62
10.1615/JPorMedia.v15.i1.40
S.
Jaballah
LETTM Laboratory, Department of Physics, Faculty of Sciences of Monastir, 5019 Monastir, Tunisia
Habib
Sammouda
LabEM, LR11ES34, Sousse University,Tunisa, ESSTHS, rue LamineAbbassi, 4011-H.Sousse-Tunisia
Rachid
Bennacer
L2MGC F-95000, University of Cergy-Pontoise, 95031 Cergy-Pontoise Cedex, Paris, France; ENS-Cachan Dpt GC/LMT/CNRS UMR 8535, 61 Ave. du Président Wilson, 94235 Cachan Cedex, France; Tianjin Key Lab of Refrigeration Technology, Tianjin University of Commerce, 300134
solar sensor
PV cells
mixed convection
local thermal nonequilibrium
porous medium
heat exchanger
With the aim of cooling the PV cells and recovering maximum heat dissipated by joule effect on the solar sensor, and thus to contribute to the improvement of the effectiveness of such a system, we are interested in the present study in the nonequilibrium thermal transfer of heat occurring between the coolant fluid and the exchanger (channel) partially filled by successive porous matrices. The coolant fluid saturating the porous medium is injected at different values of velocity and temperature. The model of the local thermal nonequilibrium (LTNE) is used to analyze the effects of some characteristic parameters such as the ratio of fluid and solid heat transfer coefficient Rs and the thermal conductivity ratio Rλ on the stability and flow mode and on the output of such exchange. Compromise values of these coefficients Rs and Rλ are necessary for obtaining a high-temperature outlet of the channel.
A NEW APPROACH FOR POROSITY ESTIMATION IN A MULTILAYER POROUS CHANNEL USING NONLINEAR CONJUGATE GRADIENTS METHOD
63-72
10.1615/JPorMedia.v15.i1.50
Farshad
Kowsary
Department of Mechanical Engineering, University College of Engineering, University of Tehran, Tehran 515-14395, Iran
Mohsen
Nazari
Department of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran
thermal nonequilibrium
conjugate gradients method
porosity estimation
In this paper, the possibility of estimating the porosity distribution in a porous medium using inverse heat conduction method is explored. The thermal model is a one-dimensional porous medium enclosed by parallel plates for which the porosity is variable in space and the condition of nonthermal equilibrium between the fluid and solid phases prevails. The conjugate gradients method (CGM) along with the differential adjoint equations have been used under nonthermal equilibrium conditions between two phases to estimate the variant configuration of porous layers inside a channel. Derivation of the adjoint differential equations in the case of nonuniform porosity and calculation of gradient function from the coupled adjoint equations are presented in detail in the paper. Estimation of the porosity in the porous channel using measured temperature data leads to a nonlinear inverse heat transfer problem in which the direct heat conduction problem, sensitivity equations, and adjoint differential equations are coupled together. Different porosity distributions in the channel are examined to evaluate the performance of the presented inverse heat transfer method.
DETERMINATION OF COEFFICIENTS IN THE ANALYTICAL SOLUTION OF COUPLED DIFFERENTIAL EQUATIONS OF HEAT AND MASS TRANSFER DURING CONVECTIVE DRYING OF HEAT-TREATED WOOD
75-82
10.1615/JPorMedia.v15.i1.60
Aleksandar Dj.
Dedic
Faculty of Forestry, University of Belgrade, 11030 Belgrade, Serbia
wood
drying
temperature
moisture content
analytical solution
coefficients
This paper describes one possible solution of temperature distribution during wood drying in the analytical form. The proposed solution of the coupled differential equations is in the form of a nondimensional expression. It was proved that the solution assumption satisfied the initial and boundary conditions. In this way, a final solution in the form of a boundless row was suggested. The coefficients in the row were determined using experimental values of the distribution of temperature of wood and before calculating the values of the coefficients of heat and mass transfer. Additionally, the values obtained for the coefficients of thermo-wood during drying and heating enable the prediction of nondimensional temperature at any place on the sample at any time.
ANALYTICAL SOLUTION OF MHD STAGNATION-POINT FLOW IN POROUS MEDIA BY MEANS OF THE HOMOTOPY PERTURBATION METHOD
83-94
10.1615/JPorMedia.v15.i1.70
Ahmet
Yildirim
Department of Mathematics, Ege University, 35100 Bornova-Izmir, Turkey; Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA
Sefa Anil
Sezer
Science Faculty, Department of Mathematics, Istanbul Medeniyet University, Kadikoy-Istanbul, Turkey
homotopy perturbation method
heat transfer
boundary layer
magnetohydrodynamic
stagnation flow
porous media
In this study, the steady two-dimensional laminar forced magnetohydrodynamic Hiemenz flow against a flat plate with variable wall temperature in a porous medium is solved analytically by using the homotopy perturbation method (HPM). The nonlinear boundary layer equations were transformed, and the resulting ordinary differential equations were solved by HPM. The skin friction coefficient and the rate of heat transfer given by the HPM are in good agreement with the numerical solutions of the Keller box method.
NUMERICAL MODELING OF CONTAMINANT TRANSPORT IN SETS OF PARALLEL FRACTURES WITH FRACTURE SKIN
95-100
10.1615/JPorMedia.v15.i1.80
Vinish V.
Nair
Department of Civil Engineering, National Institute of Technology Calicut, Kozhikode, Kerala 673 601, India
Santosh G.
Thampi
Department of Civil Engineering, National Institute of Technology Calicut, Kozhikode, Kerala 673 601, India
contaminant transport
fractured rocks
fracture skin
numerical model
solute velocity
A fully implicit finite difference method-based numerical model is developed to simulate reactive solute transport in a fractured formation. The formulation of the model is based on a triple continuum approach, with fracture, fracture skin, and the rock matrix as three continuums. Simulations carried out using this model show that fracture skin significantly affects the contaminant transport in fractured formations and that the contaminant penetration along the fracture increases with increase in flow velocity. Small solute velocities lead to conditions favorable for contaminant diffusion through the fracture skin. The analysis of influence of flow velocity on contaminant transport for different fracture aperture sizes and fracture skin thicknesses has demonstrated that contaminant transport is affected more by change in fracture aperture than by change in skin thickness.