Transport Phenomena in Porous Media III

Transport Phenomena in Porous Media III

1st Edition - July 29, 2005

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  • Editors: Derek Ingham, Ioan Pop
  • eBook ISBN: 9780080543185

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Fluid and flow problems in porous media have attracted the attention of industrialists, engineers and scientists from varying disciplines, such as chemical, environmental, and mechanical engineering, geothermal physics and food science. There has been a increasing interest in heat and fluid flows through porous media, making this book a timely and appropriate resource.Each chapter is systematically detailed to be easily grasped by a research worker with basic knowledge of fluid mechanics, heat transfer and computational and experimental methods. At the same time, the readers will be informed of the most recent research literature in the field, giving it dual usage as both a post-grad text book and professional reference.Written by the recent directors of the NATO Advanced Study Institute session on 'Emerging Technologies and Techniques in Porous Media' (June 2003), this book is a timely and essential reference for scientists and engineers within a variety of fields.


Mechanical and civil engineers, materials scientists and environmental engineers.

Table of Contents

  • Contents

    1 The Double-Decomposition Concept for Turbulent Transport in Porous Media

    1.1 Introduction

    1.2 Instantaneous Local Transport Equations

    1.3 Time- and Volume-Averaging Procedures

    1.4 Time-Averaged Transport Equations

    1.5 The Double-Decomposition Concept

    1.5.1 Basic Relationships

    1.6 Turbulent Transport

    1.6.1 Momentum Equation

    1.7 Heat Transfer

    1.7.1 Governing Equations

    1.7.2 Turbulent Thermal Dispersion

    1.7.3 Local Thermal Equilibrium Hypothesis

    1.7.4 Macroscopic Buoyancy Effects

    1.8 Mass Transfer

    1.8.1 Mean and Turbulent Fields

    1.8.2 Turbulent Mass Dispersion

    1.9 Concluding Remarks


    2 Heat Transfer in Bidisperse Porous Media

    2.1 Introduction

    2.2 Determination of Transport Properties

    2.3 Two-Phase Flow and Boiling Heat Transfer

    2.4 Dispersion

    2.5 Two-Velocity Model

    2.6 Two-Temperature Model

    2.7 Forced Convection in A Channel Between Plane Parallel Walls

    2.7.1 Uniform Temperature Boundaries: Theory

    2.7.2 Uniform Flux Boundaries: Theory

    2.7.3 Uniform Temperature Boundaries: Results

    2.7.4 Uniform Flux Boundaries: Results

    2.7.5 Conjugate Problem

    2.7.6 Thermal Development

    2.8 Conclusions


    3 From Continuum To Porous-Continuum: The Visual Resolution Impact On Modeling Natural Convection in Heterogeneous Media

    3.1 Introduction

    3.2 Horizontal Heating

    3.2.1 Continuum Equations

    3.2.2 Porous-Continuum Equations

    3.2.3 Heat Transfer Comparison Parameters

    3.2.4 Results

    3.2.5 Internal Structure Effect

    3.3 Heat-Generating Blocks

    3.3.1 Mathematical Modeling

    3.3.2 Heat Transfer Comparison Parameters

    3.3.3 Results

    3.4 Conclusion


    4 in Integral Transforms for Natural Convection in Cavities Filled With Porous Media

    4.1 Introduction

    4.2 Two-Dimensional Problem

    4.3 Three-Dimensional Problem

    4.4 Results and Discussion

    4.5 Conclusions


    5 A Porous Medium Approach for The Thermal Analysis of Heat Transfer Devices

    5.1 Introduction

    5.2 Thermal Analysis of Microchannel Heat Sinks

    5.2.1 High-Aspect-Ratio Microchannels

    5.2.2 Low-Aspect-Ratio Microchannels

    5.3 Thermal Analysis of Internally Finned Tubes

    5.3.1 Mathematical Formulation and theoretical Solutions

    5.3.2 Velocity and Temperature Distributions

    5.3.3 Optimizationof thermal Performance

    5.3.4 Comments On The Averaging Direction

    5.4 Conclusions


    6 Local Thermal Non-Equilibrium in Porous Medium Convection

    6.1 Introduction

    6.2 Governing Equations

    6.3 Conditions for the Validity of LTE

    6.4 Free Convection Boundary Layers

    6.4.1 General Formulation

    6.4.2 Results for Stagnation Point Flow

    6.4.3 Results for A Vertical Flat Plate

    6.4.4 General Comments

    6.5 Forced Convection Past A Hot Circular Cylinder

    6.6 Stability of Free Convection

    6.7 Conclusions


    7 Three-Dimensional Numerical Models for Periodically Fully-Developed Heat and Fluid Flows Within Porous Media

    7.1 Introduction

    7.2 Three-Dimensional Numerical Model for Isotropic Porous Media

    7.2.1 Numerical Model

    7.2.2 Governing Equations and Periodic Boundary Conditions

    7.2.3 Method of Computation

    7.2.4 Macroscopic Pressure Gradient and Permeability

    7.3 Quasi-Three-Dimensional Numerical Model for Anisotropic Porous Media

    7.3.1 Periodic Thermal Boundary Conditions

    7.3.2 Quasi-Three-Dimensional Solution Procedure for Anisotropic Arrays of Infinitely Long Cylinders

    7.3.3 Effect of Cross Flow Angle On the Euler and Nusselt Numbers

    7.3.4 Effect of Yaw Angle On the Euler and Nusselt Numbers

    7.4 Large Eddy Simulation of Turbulent Flow in Porous Media

    7.4.1 Large Eddy Simulation and Numerical Model

    7.4.2 Velocity Fluctuations and Turbulent Kinetic Energy

    7.4.3 Macroscopic Pressure Gradient in Turbulent Flow

    7.5 Conclusions


    8 Entropy Generation in Porous Media

    8.1 Introduction

    8.2 A Short History of the Second Law of thermodynamics

    8.3 Governing Equations

    8.3.1 Continuity Equation

    8.3.2 Momentum Balance Equation

    8.3.3 Energy Equation

    8.3.4 Entropy Generation

    8.4 Entropy Generation in A Porous Cavity and Channel

    8.4.1 Entropy Generation in A Porous Cavity

    8.4.2 Entropy Generation in A Porous Channel

    8.5 Conclusions


    9 Thermodiffusion in Porous Media

    9.1 Introduction

    9.2 Literature Review

    9.2.1 Measurement Techniques of the Soret Coefficient

    9.2.2 Mathematical and Numerical Techniques

    9.3 Fundamental Equations of thermodiffusion

    9.3.1 Haase Model

    9.3.2 Kempers Model

    9.3.3 Firoozabadi Model

    9.4 Fundamental Equations in Porous Media

    9.5 Numerical Solution Technique

    9.6 Mesh Sensitivity Analysis

    9.7 Results and Discussion

    9.7.1 Comparison of Molecular and thermodiffusion Coefficients for Water Alcohol Mixtures

    9.7.2 Calculation of Molecular and thermodiffusion Coefficients for Hydrocarbon Mixtures

    9.7.3 Convection in A Square Cavity

    9.7.4 Convection in A Rectangular Cavity

    9.8 Conclusions


    10 Effect of Vibration On The Onset of Double-Diffusive Convection in Porous Media

    10.1 Introduction

    10.2 Mathematical Formulation

    10.2.1 Direct Formulation

    10.2.2 Time-Averaged Formulation

    10.2.3 Scale Analysis Method

    10.2.4 Time-Averaged System of Equations

    10.3 Linear Stability Analysis

    10.3.1 Infinite Horizontal Porous Layer

    10.3.2 Limiting Case of the Long-Wave Mode

    10.3.3 Convective Instability Under Static Gravity (No Vibration)

    10.4 Comparison of the Results With Fluid Media

    10.5 Numerical Method

    10.5.1 Vertical Vibration

    10.5.2 Horizontal Vibration

    10.6 The Onset of thermo-Solutal Convection Under The Influence of Vibration Without Soret Effect

    10.6.1 Linear Stability Analysis

    10.7 Conclusions


    11 Combustion in Porous Media: Fundamentals and Applications

    11.1 Introduction

    11.2 Previous Works

    11.3 Characteristics of Combustion in Porous Media

    11.4 Applications

    11.5 Porous Burners

    11.6 Mathematical Modeling

    11.7 Results and Discussion

    11.8 Radial Burner

    11.9 Conclusions

    11.10 Possible Future Work


    12 Reactive Transport in Porous Media—Concepts and Numerical Approaches

    12.1 Introduction

    12.2 Quantitative Geochemistry

    12.3 Analytical Description of Reactive Transport

    12.4 Examples

    12.4.1 Equilibrium Example 1

    12.4.2 Equilibrium Example 2

    12.4.3 Equilibrium and Kinetics Example 1

    12.4.4 Equilibrium and Kinetics Example 2

    12.5 Numerical Approaches

    12.5.1 Speciation Calculations

    12.5.2 Transport Modeling

    12.5.3 Transport and Reaction Coupling

    12.6 Numerical Errors

    12.7 Implementation in Matlab

    12.8 Example Models

    12.8.1 Three-Species Model

    12.8.2 Calcite Dissolution Test Case (ID)

    12.8.3 Two-Dimensional Modeling

    12.9 Conclusions


    13 Numerical and Analytical Analysis of the Thermosolutal Convection in An Annular Field: Effect of thermodiffusion

    13.1 Introduction

    13.2 Mathematical Model

    13.2.1 Numerical Solution

    13.3 Analytical Solution

    13.4 Results and Discussion

    13.5 Conclusions


    14 Pore-Scale Transport Phenomena in Porous Media

    14.1 Introduction

    14.2 Conjugated Transport Phenomena With Pore Structure

    14.2.1 Conjugated Phenomena in Sludge Drying

    14.2.2 Effect of Inner Evaporation On The Pore Structure

    14.3 Transport-Reaction Phenomena

    14.3.1 Reaction in A Porous Solid

    14.3.2 Experimental Investigation

    14.4 Boiling and Interfacial Transport

    14.4.1 Experimental Observations

    14.4.2 Static Description of Primary Bubble Interface

    14.4.3 Replenishment and Dynamic Behavior of the Interface

    14.4.4 Interfacial Heat and Mass Transfer At Pore Level

    14.5 Freezing and Thawing

    14.5.1 Experimental Facility

    14.5.2 Sludge Agglomerates During Freezing

    14.5.3 Botanical Tissues During Freezing

    14.6 Two-Phase Flow Behavior

    14.6.1 Experimental Observation

    14.6.2 Critical Diameter

    14.6.3 Transport of Small Bubbles

    14.6.4 Transport of Big Bubbles

    14.7 Conclusion


    15 Dynamic Solidification in A Water-Saturated Porous Medium Cooled From Above

    15.1 Introduction

    15.2 Mathematical Formulation

    15.2.1 Two-Dimensional Model

    15.2.2 A Reduced One-Dimensional Model

    15.3 Numerical Results

    15.3.1 Development of A Solid Layer and Convecting Flow

    15.3.2 Amplitude and Phase Lag of the Oscillating Solid-Liquid Interface

    15.4 Experimental Results

    15.4.1 Experimental Apparatus and Procedure

    15.4.2 Ice-Layer Thickness At Steady State

    15.4.3 Average Nusselt Number and Vertical Temperature Variation At Steady State

    15.4.4 Oscillating Cooling Temperature and the Response of Ice-Layer

    15.4.5 Amplitude and Phase Lag Against Oscillating Cooling Temperature

    15.5 Conclusion


    16 Application of Fluid Flows Through Porous Media in Fuel Cells

    16.1 Introduction

    16.2 Operation Principles of Fuel Cells

    16.3 Governing Equations for The Fluid Flows in Porous Electrodes

    16.3.1 Equations for The Fluid Flow and Mass Transfer in Fuel Cells

    16.3.2 Heat Generation and Transfer in Fuel Cells

    16.3.3 The Electric Field in Fuel Cells

    16.4 Multicomponent Gas Transport in Porous Electrodes

    16.4.1 Convective Transport

    16.4.2 Diffusive Transport

    16.5 CFD Model Predictions of Fuel Cells

    16.6 Concluding Remarks


    17 Modeling The Effects of Faults and Fractures On Fluid Flow in Petroleum Reservoirs

    17.1 Introduction

    17.2 Single and Multiphase Flow

    17.3 Modeling Flow in Petroleum Reservoirs Where Faults Act As Barriers

    17.3.1 Numerical Modeling of the Permeability of Fault Rocks

    17.3.2 Modeling Flow in Complex Damage Zones

    17.3.3 Incorporation of Fault Properties Into Production Simulation Models

    17.3.4 Knowledge Gaps and Future Directions

    17.4 Modeling Flow in Reservoirs Where Faults and Fractures Act As Conduits

    17.4.1 Overview of Existing Discrete Fracture Models

    17.4.2 Technical Description of the Methodology

    17.4.3 An Example of Flow Simulation in A Fractured Reservoir

    17.5 Discussion and Conclusions


Product details

  • No. of pages: 450
  • Language: English
  • Copyright: © Elsevier Science 2005
  • Published: July 29, 2005
  • Imprint: Elsevier Science
  • eBook ISBN: 9780080543185

About the Editors

Derek Ingham

Department of Applied Mathematics, Ingham Centre for Computational Fluid Dynamics, University of Leeds, Leeds, UK

Affiliations and Expertise

Department of Applied Mathematics, University of Leeds, Leeds, UK

Ioan Pop

Ioan Pop is a Professor of Applied Mathematics at the Faculty of Mathematics and Computer Science at Babes-Bolyai University, Romania. He has more than 50 years’ experience of research in fields including fluid mechanics and heat transfer with application to boundary layer theory, heat transfer in Newtonian and non-Newtonian fluids, magnetohydrodynamics, and convective flow in fluid-saturated porous media. In his career he has co-supervised more than 20 phd students, written 10 books, and co-authored over 850 research journal papers. He is the Director of the Centre for Excellence in Mechanics of the Romanian National Research Council, and serves on the editorial boards of 14 international scholarly journals, and has served on the organizing committee of over 27 conferences.

Affiliations and Expertise

Faculty of Mathematics and Computer Science, Babes-Bolyai University, Romania

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