Begell House
Journal of Porous Media
Journal of Porous Media
1091-028X
8
2
2005
Hot-Wire Method for Measuring Effective Thermal Conductivity of Porous Media
The effective thermal conductivity λe in porous media is often measured by the transient hot-wire method. This technique uses an identification method based on the Blackwell solution that makes some valuable assumptions (heat transfers are one-dimensional and by conduction only, and the sample is considered as an infinite medium), which are the origin of vagueness. A two-dimensional and dynamic model of heat transfer describing the functioning of the hot-wire method is developed. The numerical solution of the equations allows the tracing of the time-space evolution of the state variables (temperature, pressure, velocity) inside the porous medium and the determination of the validity domain of the Blackwell identification method. The results show that the Blackwell technique is accurate (better than 1%) for building materials where the wire is thin compared to the sample (γ < 5 × 10−3 ), the aspect ratio of the sample is ≥1.5, and the Rayleigh number is ≤100.
Latifa
Sassi
Laboratoire d'Etude des Systemes Thermiques et Energetiques, Ecole Nationale d'Ingenieurs de Monastir, Avenue Ibn El Jazzar, 5019 Monastir, Tunisia
Foued
Mzali
Laboratoire d'Etudes des Systèmes Thermiques et Energétiques, Ecole Nationaled'Ingénieurs de Monastir, Tunisia
Abdelmajid
Jemnia
Laboratoire d'Etude des Systemes Thermiques et Energetiques, Ecole Nationale d'Ingenieurs de Monastir, Tunisia
Sassi Ben
Nasrallah
Laboratoire d'Études des Systèmes Thermiques et Énergétiques, Ecole Nationale d'Ingénieurs
de Monastir, Monastir 5019 Tunisie
97-114
Theoretical and Experimental Investigation of the Channeling Effect in Fluid Flow through Porous Media
During fluid flow through a channel filled with porous fiber, due to the gap between the walls and the edge of fiber or the variation of porosity, permeability will become a variable. In this paper, an exponential model is assumed for porosity and permeability. Also, the two-dimensional momentum equation is solved by the finite difference method, using a maker and cell (MAC) scheme and variable grid size mesh. Also, in order to verify the theoretical results, an experimental apparatus is designed and constructed. The experimental results were used to determine the model parameters. The results showed good validity of the assumed exponential model for prediction of preformed fiber permeability with air gap, as a function of distance from the walls.
M. R.
Shahnazari
Faculty of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran
M. Zia Bashar
Hagh
Mechanical Engineering Department, K. N. Toosi University of Technology, Tehran, Iran
115-124
Analytical Solutions and Estimates for Microlevel Flows
Steady, two-dimensional, viscous, fully developed, laminar flows are studied by the methods of isoperimetric estimations, complex analysis, and asymptotic approximations. The Carman-Kozeny averaging of velocity over the cross-sectional area of a tube is shown to become meaningless for some fractures deviating from "normal" convex shapes. Permeability of constituting tubes is estimated from above and below using a novel characteristic, the momentum of the flow domain about its boundary. Poiseuille-type flows in double-connected and misconnected domains are discussed. Longitudinal and transversal flows through a nonplanar zigzag fracture composed of annular segments are studied by an asymptotic solution of the Poisson equation and an exact solution of the Navier-Stokes equation, correspondingly. The lubrication theory approximation is compared with the case of a nonparabolic velocity profile within the fracture. The influence of tortuosity on permeability is established by calculation of the flux ratio through curved and planar fractures. For the Stokes approximation, a double-periodic combination of plane fractures and circular enlargements is studied using the Rayleigh solution and its generalization. A two-dimensional Darcian flow through a system with regular square occlusions is studied and kinematic channeling is quantified by the travel time along the fastest streamline.
F. G.
Avkhadiev
Institute of Mathematics and Mechanics, Kazan University, Kazan, Russia
Anvar R.
Kacimov
Department of Soil and Water Sciences, Sultan Qaboos University, P.O. Box 34, Al-Khod 123, Sultanate of Oman
125-148
Natural Convection in Nonhomogeneous Heat-Generating Media: Comparison of Continuum and Porous-Continuum Models
The present work investigates the appropriateness of using a porous-continuum (PC) based model for simulating the flow and heat transfer within a fluid-filled enclosure containing a matrix of 16 evenly distributed, heat-generating solid blocks. This configuration aims at mimicking the pool storage of radioactive nuclear fuel elements. Results from the continuum (C) model, obtained by solving the transport equations within each (fluid and solid) constituent, are compared to results from the PC model, obtained by using volume-averaged, general transport equations. Streamline and isotherm distributions identify nuances particular to each model. An average Nusselt number along each surface of the enclosure indicates a large discrepancy between the two models, particularly along the top and bottom surfaces. Although much easier to implement and numerically more efficient, the PC model should be avoided when the Rayleigh number is low (Ra ≤ 105) and the porosity is high (φ ≥ 0.5), and when the Rayleigh number is high (Ra ≥ 10 ) and the porosity is low (φ < 0.5). Moreover, the PC model is inappropriate when the Rayleigh number and the porosity are high (e.g., for Ra = 106 and φ ≥ 0.9, and for Ra = 107 and φ ≥ 0.8) for failing to capture the unsteady regime observed when the more elaborated C model is used.
A. A.
Merrikh
Department of Mechanical Engineering, Eastern Mediterranean University, G. Magosa, T.R.N.C. Mersin 10, Turkey
Jose' L.
Lage
Southern Methodist University, Department of Mechanical Engineering,
POBox 750337, Dallas, TX 75275-0337, USA
149-163
Transient Forced Convection in an Isothermal Fluid-Saturated Porous-Medium Layer: Effective Permeability and Boundary Layer Thickness
Transient forced convection in an isothermal saturated porous-medium layer is analyzed analytically on the basis of the Forchheimer-Brinkman-extended Darcy equation. An analytical solution describing the transient regime is obtained by considering the ensemble average velocity of the fluid flow as much larger than the fluctuations in the fluid velocity. This solution provides a better knowledge of the features of the flow within the porous layer. Among other results is presented an expression for the effective porous-medium permeability, as a function of the Darcy number, of the Reynolds number, and of a "relaxation time" characteristic of the transient regime. The solution found also indicates that an appropriate periodic forcing of the pressure gradient may increase the effective permeability of the porous layer to fluid flow.
Antonio Ferreira
Miguel
Department of Physics, School of Sciences and
Technology, University of Evora, Institute of Earth Sciences (ICT) Pole of Evora,
Portugal
A. Heitor
Reis
Department of Physics, University of Évora, Rua Romão Ramalho, 59, 7000-671 Évora, Portugal; and Évora Geophysics Centre, Apartado 94, 7002-554 Évora, Portugal
165-174
Radon-222 Exhalation Rates from Phosphogypsum-Bearing Embankment Subjected to Constant Temperature and Fixed Activity Concentration
Stack or embankment disposal of phosphogypsum — a by-product from phosphate fertilizer industries-has given rise to environmental issues concerning 222Rn exhalation rates into the local atmosphere. Early models for radon transport in porous media have considered both diffusion and convection, although basically taking into account air flow driven by predefined pressure differences and Darcy's law. The present paper introduces buoyant effects and outlines a steady-state two-dimensional model for 222Rn transport through a phosphogypsum-bearing embankment, inside of which there are sources and sinks for this gaseous radionuclide. The embankment is treated as an open cavity filled with porous material and surrounded by isothermal and impermeable ground. Its top surface is subjected to fixed activity concentration and fixed lower temperature. Buoyancy-driven interstitial air flow is supposedly laminar and modeled according to Darcy-Brinkman-Boussinesq formulation. Governing equations are written in dimensionless form in order to account for concurrent effects of the various physical parameters involved, and three unconventional dimensionless groups are put forward apart from usual controlling parameters, such as Darcy, Grashof, Prandtl, and Schmidt numbers. An analytical solution regarding a strictly diffusive approach is inferred, whereas full model equations are solved numerically by adapting an existing finite-volume simulator. As a preliminary investigation, results are reported for Pr = 0.71 and Sc = 15, while Da and Gr are allowed to vary from 10−7 to 10−13 and from 107 to 109 , respectively. Results are also presented as a function of the modified Grashof number Grm = Gr·Da. For porous media with relatively low permeability (Da ≤ 10−9), 222Rn transport is diffusion dominated (i.e., natural convective effects play a minor role) and both Nusselt and Sherwood numbers prove to be insensitive to Grashof number. At approximately Grm ≈ 10, circulation cell splitting occurs within each embankment half, as the natural convective fluid flow increases its strength, which results in very low 222Rn concentration levels inside the porous matrix.
J. A.
Rabi
Faculty of Zootechny and Food Engineering, University of Sao Paulo, Av. Duque de Caxias Norte, 225, Pirassununga, SP, 13635-900, Brazil
175-191
Flow through a Tube with an Annual Porous Medium Layer
In this study, the boundary conditions necessary for continuum numerical modeling of flow involving a porous-medium-free-fluid interface are examined. In a region within the free flow adjacent to a porous medium interface, the momentum dispersion persists due to the extension of the spatial velocity fluctuation into the free flow. Consequently, at elevated flow rates, the viscous response to flow of the fluid in the region adjacent to a porous medium has to be modified due to the presence of such spatial velocity fluctuations caused by the porous medium. This influence decays exponentially and extends several pore sizes into the free fluid.
Experimental and numerical studies have shown that, at moderately high flow rates, the pressure drop through a porous bed is a quadratic function of the flow discharge rate. For flow through a straight tube containing no porous structures, the pressure drop is linearly related to the flow discharge rate in the laminar regime. However, experimental observation shows that when fluid flows through a tube with an annular porous medium ring, the qualitative trend of the pressure drop is similar to flow through a porous medium. This behavior confirms our expectations on the existence of momentum dispersion. An exponential decay model is proposed to account for the momentum dispersion variation.
Jacob H.
Masliyah
Department of Chemical Engineering, University of Alberta, Edmonton, Canada T6G 2G6
Artin
Afacan
Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Canada T6G 2G6
Shijie
Liu
Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Canada T6G 2G6
193-210
Groundwater Parameter Estimation by Optimization and Dual Reciprocity Finite Differences Method
A new solution method called the dual reciprocity finite differences method (DRFDM) is proposed. The method combines the finite differences method and optimization technique, and can be implemented in a spreadsheet to solve groundwater parameter estimation problems. In the DRFDM model, the hydraulic heads and transmissivities in the solution domain are obtained using limited hydraulic heads and/or transmissivities. The method is implemented as an objective function. Three different scenarios are examined. A set of transmissivities are used in the first scenario. In the second scenario, only hydraulic heads are used. In the third scenario, both transmissivities and hydraulic heads are used in an objective function. A spreadsheet solver is used as an optimization tool. Two examples taken from literature are used to verify the method; one of which has an analytical solution, and the other has not. Good agreement between the DRFDM model output and both analytical and observed values is obtained only when limited transmissivity values or both hydraulic heads and transmissivity values are known. The presented method was not effective in the studied cases in which only hydraulic heads were known.
Halil
KARAHAN
Pamukkale University
M. Tamer
Ayvaz
Pamukkale University, Faculty of Engineering, Department of Civil Engineering, 20017 Denizli, Turkey
211-223
Mixed-Convection Flow Adjacent to a Horizontal Surface in a Porous Medium with Variable Permeability and Surface Heat Flux
A nonsimilarity solution for mixed convection from impermeable horizontal surfaces in a saturated porous medium incorporating variation of permeability and thermal conductivity due to packing of particles is obtained for the case of variable heat flux in the form qw(x) = bxn. To cover the entire mixed-convection regime, two different transformations are used. In the first transformation the nonsimilarity parameter ζf= Rax⁄Pex2 is found to measure the buoyancy effect in the forced-flow-dominated mixed-convection regime, and in the second transformation the nonsimilarity parameter ζn = Rax⁄Pex1⁄2 is found to measure the forced-flow effect in the buoyancy-dominated mixed-convection regime. The two solutions provide results that cover the entire mixed-convection regime from pure forced- to pure free-convection limit. Numerical results for different values of surface heat flux variation, permeability K, and thermal diffusivity α are presented.
I. A.
Hassanien
Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
Gh. M.
Omer
Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
225-235
Effect of Variable Permeability and Viscous Dissipation on a Non-Darcy Natural-Convection Regime with Thermal Dispersion
The effect of variable permeability on non-Darcy natural-convection flow along an isothermal vertical wall embedded in a saturated porous medium is initiated. The flow field is divided into a non-Darcy regime G → 0, an intermediate regime G = 0(1), and a limit Darcy regime G → ∞ using the inertia buoyancy scales. Thermal dispersion effects are also taken into consideration. The effect of viscous dissipation increases as we move from a non-Darcy to a limit Darcy regime. The effect of viscous dissipation in non-Darcy, intermediate, and limit Darcy regimes is studied with and without thermal dispersion for uniform and variable permeability. The results show a significant decrease in the heat transfer rate with the inclusion of viscous effect. It is seen that as the value of the dispersion parameter increases, the effect of viscous dissipation increases in all three regimes and the percentage decrease in the value of Nu/Rax1/4 increases with the value of G.
I. A.
Hassanien
Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
Fouad S.
Ibrahim
Department of Mathematics, University College, Umm Al-Qura University, Makkah, Saudi
Arabia; Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
Gh. M.
Omer
Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
237-246