Transport Phenomena in Porous Media III

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

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
References
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
References
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
References
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
References
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
References
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
References
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
References
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
References
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
References
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
References
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
References
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
References
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
References
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
References
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
References
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
References
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
References