Essentials of Heat and Fluid Flow in Porous Media

This textbook provides a general overview of porous media flow, and introduces various theoretical tools to characterize and predict the flow. It has been written for graduate and advanced graduate students in various engineering disciplines. It includes the topics such as fluid flow, conduction, convection, and radiation in porous media as well as porous medium aspects of biological systems. The concepts are supported by numerous solved examples to aid self-learning in students. The textbook also contains illustrated diagrams for better understanding of the concepts. This textbook will be useful for the core course of "Flow through Porous media" for graduate and advanced graduate students in various engineering disciplines. This textbook will also serve as a refresher course for researchers who are engaged in research related to porous media flow. Foreword by Prof. D. Andrew S. Rees Foreword by Prof. Pradip Dutta Preface Acknowledgements Contents About the Author 1 Basic Concepts 1.1 Porous Medium Definition 1.1.1 Non-traditional Examples 1.1.2 Bi-disperse Porous Medium (BDPM) 1.1.3 Porous Bio-materials 1.2 Porosity 1.2.1 Volumetric Porosity 1.2.2 Surface Porosity 1.3 Percolation and Tortuosity 1.3.1 Percolation 1.3.2 Tortuosity 1.4 Volume-Averaging Procedure 1.4.1 Homogeneous Porous Medium 1.4.2 Representative Elemental Volume 1.4.3 Some Clarifications on REVs 1.5 Problems 2 Heat Conduction in Porous Medium 2.1 Introduction 2.2 First Law of Thermodynamics 2.2.1 Local Thermal Equilibrium 2.2.2 Porous Medium Energy Equation 2.3 Second Law of Thermodynamics 2.4 Effective Stagnant Thermal Conductivity 2.4.1 Limiting Models 2.4.2 Other Models 2.4.3 Experimental Determination 2.4.4 Description of SGHP Apparatus 2.4.5 Determination of ke 2.5 Thermal Dispersion 2.6 Local Thermal Non-equilibrium Model 2.6.1 LTNE Formulation of PM Energy Equation 2.6.2 Interface Heat Transfer Coefficient 2.7 Transient Heat Conduction in Porous Medium 2.7.1 1D Transient PM Heat Conduction Under LTE 2.7.2 Lumped Capacitance Model 2.7.3 1D Transient PM Heat Conduction Under LTNE 2.8 Problems 3 Fluid Flow Through a Porous Medium 3.1 Introduction 3.2 Historical Overview 3.2.1 Darcy Model 3.2.2 Hazen–Dupuit–Darcy Model 3.3 Physics of Flow Through Porous Media 3.3.1 Inertialess Motion and the HDD Model 3.3.2 From Newton's Principia to the Nature of Form Drag 3.4 Extensions of the HDD Model 3.4.1 Brinkman Model 3.4.2 Generalized Momentum Equation 3.5 Permeability and Form Coefficient 3.5.1 Analytical Estimates 3.5.2 Fictitious Porous Media 3.5.3 Experimental Determination 3.5.4 Viscometry and Permeametry 3.5.5 Protocol for Permeability Measurement 3.6 Flow Transition 3.6.1 What Is Transition? 3.6.2 Characterization of the Transition 3.6.3 Prediction of Transition 3.6.4 PM Transition Flow and Turbulent Flow 3.7 Miscellaneous Topics 3.7.1 Hydrodynamic Boundary Layer 3.7.2 Wall Channelling 3.7.3 Porosity and Permeability 3.7.4 Secondary Effect in the Determination of K and C 3.7.5 Boundary and Interface Conditions 3.8 Problems 4 Forced Convection Through Porous Medium 4.1 Energy Equation with Flow 4.1.1 Local Thermal Non-equilibrium (LTNE) Situation 4.1.2 Local Thermal Equilibrium (LTE) Situation 4.2 Forced Convection in Porous Medium Over a Flat Plate 4.3 Forced Convection in Porous Medium Channel 4.3.1 Bulk Temperature 4.3.2 Nusselt Numbers 4.3.3 Channel Filled with Porous Medium 4.3.4 A Measurable Nu 4.4 Heat Transfer Enhancement Aspects 4.4.1 Basic Configurations 4.4.2 Heat Exchangers as Porous Media 4.4.3 Porous Medium Inter-connectors 4.5 Other Forced Convection Configurations 4.6 Viscous Dissipation Effects 4.7 Problems 5 Natural Convection Through Porous Medium 5.1 Natural Convection Boundary Layers 5.1.1 Vertical Wall 5.1.2 Horizontal Wall 5.2 Natural Convection with Vertical Thermal Gradient 5.2.1 Onset of Natural Convection 5.2.2 Experimental Results 5.3 Natural Convection with Horizontal Thermal Gradient 5.3.1 Isothermal Side-Wall Heated Configuration 5.3.2 Isoflux Side-Wall Heated Configuration 5.3.3 High Ra Results 5.4 Heatline Visualization 5.5 Non-Darcy, LTNE and Heat Generation Effects 5.5.1 Governing Equations 5.5.2 Boundary Conditions 5.5.3 Departure from Darcy Flow Effects 5.5.4 Heat Generation Effect 5.5.5 Prediction of Critical Internal Heat Generation 5.5.6 Correlation for Nu in Porous Annulus 5.6 Viscous Dissipation 5.7 Problems 6 Porous Medium Aspects of Biological Systems 6.1 Introduction to Bio-thermofluids 6.2 Porous Medium Modelling in Bio-heat Transport 6.2.1 Chen and Holmes Bio-heat Model 6.2.2 Porous Medium Bio-heat Model with LTNE 6.2.3 Other Recent Models 6.3 Modelling Drug Delivery 6.3.1 Transscleral Porous Medium Model 6.3.2 Governing Equations 6.3.3 Determination of Porosity and Permeability of the Sclera 6.3.4 Boundary Conditions 6.3.5 Anecortave Acetate Case Study 6.3.6 Effect of Choroidal Blood Flow on Drug Diffusion 6.3.7 Transdermal Drug Delivery 6.4 LDL Transport Across Arterial Tissues 6.5 Porous Medium Modelling in Bio-mass Transport 6.5.1 Mass Transport in Tissue Regeneration 6.5.2 Porous Medium Model for Lung Diffusion 6.5.3 Porous Medium Models of Microbial Transport 7 Radiation Heat Transfer in Porous Medium 7.1 The Radiative Transfer Equation (RTE) 7.2 The Energy Equation with Radiation 7.3 Radiative Property Measurement 7.4 Solving the RTE 7.5 Coupling of RTE with Other Heat Transfer Modes 8 Advanced Topics 8.1 Phase Change in Porous Media 8.1.1 Porous Medium LHTES Device 8.1.2 The Enthalpy Model and Governing Equations 8.1.3 Effective Properties and Boundary Conditions 8.1.4 Exergy Criterion and Optimum φ 8.1.5 Scale Analysis 8.2 Variable Viscosity Porous Medium Flows 8.2.1 Temperature-Dependent Viscosity Effects 8.2.2 Variable Viscosity and HDD Model 8.2.3 Limiting Case of the HDD Model 8.2.4 Modified HDD Model 8.2.5 M-HDD Model Coefficients 8.2.6 Hydrodynamics of μ(T) Flows 8.3 Flow and Convection in Bi-disperse Porous Media 8.3.1 Laminar Flow Through BDPM Channel 8.3.2 Governing Equations and Boundary Conditions 8.3.3 Effects of Internal Permeability (DaI) 8.3.4 Effects of Macro-pore Volume Fraction (φE) 8.3.5 Natural Convection in BDPM Enclosure 8.4 Two-Phase Flow Through Porous Media 8.4.1 Mixture Model Governing Equations 8.4.2 Mixture Variables and Coefficients 8.4.3 Constitutive Relations 8.4.4 Sample Result 8.5 LBM Formulation for Porous Medium Flows 8.5.1 Introduction 8.5.2 d2q9 Model 8.5.3 d2q9i Model 8.6 Combustion in Inert Porous Media Appendix Suggested Reading Appendix Porosity and Permeability Values Appendix Convection Results and Correlations Appendix Bibliography Index