Begell House
Journal of Porous Media
Journal of Porous Media
1091-028X
16
1
2013
NON-DARCY AND LOCALIZED HEATING EFFECTS ON BENARD CONVECTION IN POROUS ENCLOSURE
Benard convection in a porous medium using the non-Darcy model with localized heating is studied numerically in the present paper. The Forchheimer−Brinkman-extended Darcy model is used in the mathematical formulation for the porous layer. The governing parameters considered are the heater size (0.2 ≤ H ≤ 1), the Rayleigh number (102 ≤ Ra ≤ 105), the porosity of the porous medium (0.4 ≤ ε ≤ 0.99), the Darcy number (10−5 ≤ Da ≤ 10−2), and the thermal conductivity ratio of solid matrix to fluid (1 ≤ ka/kf ≤ 10). The Prandtl number is fixed at Pr = 1. It is found that an extremum heat transfer rate occurs about H = 0.8 for any value of the porosity and any porous material considered.
H.
Saleh
Centre for Modelling & Data Analysis, School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor, Malaysia
I
Hashim
1-10
EXPLAINING LONGITUDINAL HYDRODYNAMIC DISPERSION USING VARIANCE OF PORE SIZE DISTRIBUTION
Hydrodynamic dispersion is responsible for spreading of dissolved mass within a single phase in porous media. It typically arises because of variability in local flow velocities. Because the pattern of spreading by dispersion is similar to Fickian diffusion, dispersion has been traditionally modeled as a pseudo-diffusive process that depends on the concentration gradient. However, there is no physical basis for this dependence of dispersion on concentration gradient. This unphysical formulation of dispersive flux has led to a number of major shortcomings including (a) lack of a self-consistent, mechanistic, and independent approach for predicting dispersion coefficient; and (b) dependence of the dispersion coefficient on transport distance. In this paper we show that the shape of dispersive spreading can be described using a model based on a variably sized bundle of capillaries and purely advective transport. The model suggests that dispersion can be described in terms of the variance of the pore size distribution only. Breakthrough curves of the proposed model can be exactly matched with the traditional diffusive-type dispersion model. By utilizing this equivalence, we derived relationships between the traditional dispersivity coefficient, pore size variance, and transport distance. The plausibility of the proposed expressions was tested using three illustrative examples that compare aspects of the proposed model with measurements obtained from the literature.
Juan Lopez
Arriaza
Life and Environmental Sciences, School of Natural Sciences, University of California, Merced
Teamrat A.
Ghezzehei
Life and Environmental Sciences, School of Natural Sciences, University of California, Merced
11-19
PIV MEASUREMENTS OVER A PERMEABLE AND AN IMPERMEABLE BED
In this study, the characteristics of turbulent flow in an open channel with permeable (vegetation) and impermeable bed were studied experimentally using two-dimensional (2D) particle image velocimetry (PIV). The experiments were conducted for both impermeable and permeable beds in a channel 6.5 m in length, 7.5 cm in width, and 25 cm in height. For the simulation of the permeable bed two types of grass-like vegetation with different heights (2 and 6 cm) but with the same porosity (ε = 0.80) were used. These conditions are typical of flows encountered in sediment transport problems. Hydraulic characteristics such as distribution of velocities, turbulent intensities, and Reynolds stress are investigated at a fine resolution using the PIV. Velocity is measured above the vegetation for the permeable bed and above the impermeable bed for the same different total heights. Results show that velocity over the vegetation region is a function of the vegetation height and the total flow depth; velocity decreases as the vegetation height increases. In addition, we show that velocities above the vegetation region are much lower than velocities above an impermeable bed. This is due to the drag resistance of the vegetation. This result shows that 50% of the vegetation behaves like an impermeable bed. The measurements of mean velocity indicate the effect of the permeable bed on the flow characteristics. Also, the presence of the vegetation influences significantly the variation of longitudinal turbulent intensity u'/U* and vertical turbulent intensity v'/U*.
Evangelos
Keramaris
Division of Hydraulic and Environmental Engineering, Department of Civil Engineering,
University of Thessaly, Pedion Areos, 38334, Volos, Greece
George
Pechlivanidis
Department of Civil Engineering T.E., Alexander Educational Institute of Thessaloniki, 57400, Sindos, Thessaloniki, Greece
21-28
AN ANALYTICAL EXPRESSION FOR THE DISPERSION COEFFICIENT IN POROUS MEDIA USING CHANG'S UNIT CELL
Mathematical modeling of transport phenomena in hierarchical systems is often carried out by means of effective medium equations resulting from upscaling techniques. For the case of convection and diffusion taking place at the pore scale, the upscaled model is expressed in terms of a total dispersion tensor, which encompasses the essential features from the microscale. Several theoretical and experimental works have evidenced that the dispersion coefficient follows a power-law dependence with the particle Peclet number. In this work, we show that such functionality can be derived analytically using the method of volume averaging with Chang's unit cell. Our derivations lead to an expression for the dispersion coefficient that reduces to the classical result by Maxwell under purely diffusive conditions. Interestingly, the dispersivity is found to follow a nontrivial functionality with the particle Peclet number. The predictions from our analytical expression are compared with those obtained by solving the same closure problem in periodic unit cells showing, in general, good agreement, especially for homothetic unit cells.
Helen D.
Lugo-Mendez
Departamento de I.P.H., Universidad Autonoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, 09340, Mexico, D.F., Mexico
Francisco J
Valdes-Parada
UAM-Iztapalapa
J Alberto
Ochoa-Tapia
Departamento de I.P.H., Universidad Autonoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, 09340, Mexico, D.F., Mexico
29-40
CONJUGATE HEAT TRANSFER IN METAL FOAM: GRAVITY DRIVEN AND FORCED FLOW HEAT EXCHANGE COEFFICIENTS DETERMINATION
This paper presents an experimental and numerical study of heat and mass transfer in a porous channel crossed by a gravity driven or forced fluid flow. We measured mass flux and local and overall heat transfer coefficients. In the gravity driven case, a maximal mass flux is observed, for which a maximal heat flux is measured. We propose an analytical model based on the Forchheimer law to determine this mass flux. Pore scale numerical simulations were used to provide local quantities and provide complementary interpretation of experimental data. Finally, we have shown that only a part of the foam is efficient for heat transfer and we have determined a foam active length. We propose an analytical model to evaluate this active length.
J.-M.
Hugo
Laboratoire IUSTI CNRS UMR 6595, Aix-Marseille Universite, Technopole de Chateau-Gombert, 5, rue Enrico Fermi, 13453 Marseille Cedex 13, France; MOTA S.A. Cooling System, Zone Industrielle les Paluds, 225, rue du Douard, 13400 Aubagne, France
E.
Brun
ESRF, European Synchrotron Radiation Facility, 6 rue Jules Horowitz, BP 220,38043 Grenoble Cedex 9, France
Frederic
Topin
Polytech Marseille, Laboratoire IUSTI, UMR CNRS 7343, Technopole de Chateau Gombert, 5 rue Enrico Fermi, 13453 Marseille Cedex 13, France
Lounes
Tadrist
Laboratoire IUSTI CNRS UMR 6595, Aix-Marseille Universite, Technopole de Chateau-Gombert, 5, rue Enrico Fermi, 13453 Marseille Cedex 13, France
41-58
THE EFFECTS OF VARIABLE VISCOSITY ON THE PERISTALTIC FLOW OF NON-NEWTONIAN FLUID THROUGH A POROUS MEDIUM IN AN INCLINED CHANNEL WITH SLIP BOUNDARY CONDITIONS
The present paper investigates the peristaltic motion of an incompressible non-Newtonian fluid with variable viscosity through a porous medium in an inclined symmetric channel under the effect of the slip condition. A long wavelength approximation is used in mathematical modeling. The system of the governing nonlinear partial differential equation has been solved by using the regular perturbation method and the analytical solutions for velocity and pressure rise have been obtained in the form of stream function. In the obtained solution expressions, the long wavelength and low Reynolds number assumptions are utilized. The salient features of pumping and trapping phenomena are discussed explicitly. The flow is investigated in a wave frame of reference moving with velocity of the wave. The features of the flow characteristics are analyzed by plotting the graphs of various values of the physical parameters in detail.
Ambreen Afsar
Khan
Department of Mathematics & Statistics, FBAS, IIU, Islamabad, 44000, Pakistan
R.
Ellahi
Department of Mathematics and Statistics, FBAS, IIUI, Islamabad, Pakistan; Department of Mathematics, Faculty of Science, Taibah University, Al-Madeenah, Saudi Arabia
Muhammad
Usman
University of Dayton
59-67
ENTROPY GENERATION FOR PULSATING FLOW IN A CYLINDER FILLED WITH POROUS MEDIA INCLUDING VISCOUS DISSIPATION EFFECTS
The present paper deals with numerical investigation of heat transfer and entropy generation for pulsating flow within a cylinder filled with a fluid-saturated porous medium with a wall maintained at constant heat flux. In modeling the flow, the Brinkman−Lapwood−Forchheimer-extended Darcy model is incorporated in momentum equations. Furthermore, the local thermal equilibrium condition is assumed to be applicable for the current investigation. In the energy equation the viscous dissipation effects are included. The control volume-based finite element method is used to solve the governing equations with an unequal order velocity−pressure interpolation. A comprehensive analysis of the influence of the amplitude pulsation, the thermal conductivity ratio, the heat capacity ratio, the Darcy number, the Eckert number, the Brinkman number, and the dimensionless temperature difference on the heat transfer and entropy generation is investigated throughout this paper.
Hacen
Dhahri
Laboratoire d'Etudes des Systèmes Thermiques et Energétiques, Université de Monastir, Ecole Nationale d'Ingénieurs de Monastir, Rue Ibn Eljazzar, 5019 Monastir, Tunisia
A.
Boughamoura
Laboratoire d'Etudes des Systèmes Thermiques et Energétiques, Ecole Nationale d'Ingénieurs de Monastir, Rue Ibn Eljazzar, 5019 Monastir, Tunisie
Sassi Ben
Nasrallah
Laboratoire d'Études des Systèmes Thermiques et Énergétiques, Ecole Nationale d'Ingénieurs
de Monastir, Monastir 5019 Tunisie
69-87