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Physics - Classical Continuum Physics | Principles of Heat Transfer in Porous Media

Principles of Heat Transfer in Porous Media

Kaviany, Massoud

2nd ed. 1995, XXII, 712 p.

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Convective heat tranfer is the result of fluid flowing between objects of different temperatures. Thus it may be the objective of a process (as in refrigeration) or it may be an incidental aspect of other processes. This monograph reviews in a concise and unified manner recent contributions to the principles of convective heat transfer for single- and multi-phase systems: It summarizes the role of the fundamental mechanism, discusses the governing differential equations, describes approximation schemes and phenomenological models, and examines their solutions and applications. After a review of the basic physics and thermodynamics, the book divides the subject into three parts. Part 1 deals with single-medium transfer, specifically with intraphase transfers in single-phase flows and with intramedium transfers in two-phase flows. Part 2 deals with fluid-solid transfer processes, both in cases where the interface is small and in cases where it is large, as well as liquid-liquid transfer processes. Part 3 considers three media, addressing both liquid-solid-solid and gas-liquid-solid systems.

Content Level » Research

Keywords » convection - dynamics - fluid mechanics - heat transfer - mechanics - porous media - radiation - thermodynamics

Related subjects » Classical Continuum Physics

Table of contents 

1 Introduction.- 1.1 Historical Background.- 1.2 Length, Time, and Temperature Scales.- 1.3 Scope.- 1.4 References.- I Single-Phase Flow.- 2 Fluid Mechanics.- 2.1 Stokes Flow and Darcy Equation.- 2.2 Porosity.- 2.3 Pore Structure.- 2.4 Permeability.- 2.4.1 Capillary Models.- 2.4.2 Hydraulic Radius Model.- 2.4.3 Drag Models for Periodic Structures.- 2.5 High Reynolds Number Flows.- 2.5.1 Macroscopic Models.- 2.5.2 Microscopic Fluid Dynamics.- 2.5.3 Turbulence.- 2.6 Brinkman Superposition of Bulk and Boundary Effects.- 2.7 Local Volume-Averaging Method.- 2.7.1 Local Volume Averages.- 2.7.2 Theorems.- 2.7.3 Momentum Equation.- 2.8 Homogenization Method.- 2.8.1 Continuity Equation.- 2.8.2 Momentum Equation.- 2.9 Semiheuristic Momentum Equations.- 2.10 Significance of Macroscopic Forces.- 2.10.1 Macroscopic Hydrodynamic Boundary Layer.- 2.10.2 Macroscopic Entrance Length.- 2.11 Porous Plain Media Interfacial Boundary Conditions.- 2.11.1 Slip Boundary Condition.- 2.11.2 On Beavers-Joseph Slip Coefficient.- 2.11.3 Taylor-Richardson Results for Slip Coefficient.- 2.11.4 Slip Coefficient for a Two-Dimensional Structure.- 2.11.5 No-Slip Models Using Effective Viscosity.- 2.11.6 Variable Effective Viscosity for a Two-Dimensional Structure.- 2.11.7 Variable Permeability for a Two-Dimensional Structure.- 2.12 Variation of Porosity near Bounding Impermeable Surfaces.- 2.12.1 Dependence of Average Porosity on Linear Dimensions of System.- 2.12.2 Local Porosity Variation.- 2.12.3 Velocity Nonuniformities Due to Porosity Variation.- 2.12.4 Velocity Nonuniformity for a Two-Dimensional Structure.- 2.13 Analogy with Magneto-Hydrodynamics.- 2.14 References.- 3 Conduction Heat Transfer.- 3.1 Local Thermal Equilibrium.- 3.2 Local Volume Averaging for Periodic Structures.- 3.2.1 Local Volume Averaging.- 3.2.2 Determination of bf and bs.- 3.2.3 Numerical Values for bf and bs.- 3.3 Particle Concentrations from Dilute to Point Contact.- 3.4 Areal Contact Between Particles Caused by Compressive Force.- 3.4.1 Effect of Rarefaction.- 3.4.2 Dependence of Gas Conductivity on Knudsen Number.- 3.5 Statistical Analyses.- 3.5.1 A Variational Formulation.- 3.5.2 A Thermodynamic Analogy.- 3.6 Summary of Correlations.- 3.7 Adjacent to Bounding Surfaces.- 3.7.1 Temperature Slip for a Two-Dimensional Structure.- 3.7.2 Variable Effective Conductivity for a Two-Dimensional Structure.- 3.8 On Generalization.- 3.9 References.- 4 Convection Heat Transfer.- 4.1 Dispersion in a Tube—Hydrodynamic Dispersion.- 4.1.1 No Molecular Diffusion.- 4.1.2 Molecular Diffusion Included.- 4.1.3 Asymptotic Behavior for Large Elapsed Times.- 4.1.4 Turbulent Flow.- 4.2 Dispersion in Porous Media.- 4.3 Local Volume Average for Periodic Structures.- 4.3.1 Local Volume Averaging for ks = 0.- 4.3.2 Reduction to Taylor-Aris Dispersion.- 4.3.3 Evaluation of u’ and b.- 4.3.4 Results for ks = 0 and In-Line Arrangement.- 4.3.5 Results for ks ? 0 and General Arrangements.- 4.4 Three-Dimensional Periodic Structures.- 4.4.1 Unit-Cell Averaging.- 4.4.2 Evaluation of u’, b, and D.- 4.4.3 Comparison with Experimental Results.- 4.4.4 Effect of Darcean Velocity Direction.- 4.5 Dispersion in Disordered Structures—Simplified Hydrodynamics.- 4.5.1 Scheidegger Dynamic and Geometric Models.- 4.5.2 De Josselin De Jong Purely Geometric Model.- 4.5.3 Saffman Inclusion of Molecular Diffusion.- 4.5.4 Horn Method of Moments.- 4.6 Dispersion in Disordered Structures—Particle Hydrodynamics.- 4.6.1 Local Volume Averaging.- 4.6.2 Low Peclet Numbers.- 4.6.3 High Peclet Numbers.- 4.6.4 Contribution of Solid Holdup (Mass Transfer).- 4.6.5 Contribution Due to Thermal Boundary Layer in Fluid.- 4.6.6 Combined Effect of All Contributions.- 4.7 Properties of Dispersion Tensor.- 4.8 Experimental Determination of D.- 4.8.1 Experimental Methods.- 4.8.2 Entrance Effect.- 4.8.3 Effect of Particle Size Distribution.- 4.8.4 Some Experimental Results and Correlations.- 4.9 Dispersion in Oscillating Flow.- 4.9.1 Formulation and Solution.- 4.9.2 Longitudinal Dispersion Coefficient.- 4.10 Dispersion Adjacent to Bounding Surfaces.- 4.10.1 Temperature-Slip Model.- 4.10.2 No-Slip Treatments.- 4.10.3 Models Based on Mixing-Length Theory.- 4.10.4 A Model Using Particle-Based Hydrodynamics.- 4.10.5 Results of a Two-Dimensional Simulation.- 4.11 References.- 5 Radiation Heat Transfer.- 5.1 Continuum Treatment.- 5.2 Radiation Properties of a Single Particle.- 5.2.1 Wavelength Dependence of Optical Properties.- 5.2.2 Solution to Maxwell Equations.- 5.2.3 Scattering Efficiency and Cross Section.- 5.2.4 Mie Scattering.- 5.2.5 Rayleigh Scattering.- 5.2.6 Geometric- or Ray-Optics Scattering.- 5.2.7 Comparison of Predictions.- 5.3 Radiative Properties: Dependent and Independent.- 5.4 Volume Averaging for Independent Scattering.- 5.5 Experimental Determination of Radiative Properties.- 5.5.1 Measurements.- 5.5.2 Models Used to Interpret Experimental Results.- 5.6 Boundary Conditions.- 5.6.1 Transparent Boundaries.- 5.6.2 Opaque Diffuse Emitting/Reflecting Boundaries.- 5.6.3 Opaque Diffusely Emitting Specularly Reflecting Boundaries.- 5.6.4 Semitransparent Nonemitting Specularly Reflecting Boundaries.- 5.7 Solution Methods for Equation of Radiative Transfer.- 5.7.1 Two-Flux Approximations, Quasi-Isotropic Scattering.- 5.7.2 Diffusion (Differential) Approximation.- 5.7.3 Spherical Harmonics-Moment (P-N) Approximation.- 5.7.4 Discretc-Ordinates (S-N) Approximation.- 5.7.5 Finite-Volume Method.- 5.8 Scaling (Similarity) in Radiative Heat Transfer.- 5.8.1 Similarity Between Phase Functions.- 5.8.2 Similarity Between Anisotropic and Isotropic Scattering.- 5.9 Noncontinuum Treatment: Monte Carlo Simulation.- 5.9.1 Opaque Particles.- 5.9.2 Semitransparent Particles.- 5.9.3 Emitting Particles.- 5.10 Geometric, Layered Model.- 5.11 Radiant Conductivity Model.- 5.11.1 Calculation of F.- 5.11.2 Effect of Solid Conductivity.- 5.12 Modeling Dependent Scattering.- 5.12.1 Modeling Dependent Scattering for Large Particles.- 5.13 Summary.- 5.14 References.- 6 Mass Transfer in Gases.- 6.1 Knudsen Flows.- 6.2 Fick Diffusion.- 6.3 Knudsen Diffusion.- 6.4 Crossed Diffusion.- 6.5 Prediction of Transport Coefficients from Kinetic Theory.- 6.5.1 Fick Diffusivity in Plain Media.- 6.5.2 Knudsen Diffusivity for Tube Flows.- 6.5.3 Slip Self-Diffusivity for Tube Flows.- 6.5.4 Adsorption and Surface Flux.- 6.6 Dusty-Gas Model for Transition Flows.- 6.7 Local Volume-Averaged Mass Conservation Equation.- 6.8 Chemical Reactions.- 6.9 Evaluation of Total Effective Mass Diffusivity Tensor.- 6.9.1 Effective Mass Diffusivity.- 6.9.2 Mass Dispersion Tensor.- 6.10 Evaluation of Local Volume-Averaged Source Terms.- 6.10.1 Homogeneous Reaction.- 6.10.2 Heterogeneous Reaction.- 6.11 Local Chemical Noncquilibrium.- 6.12 Modifications to Energy Equation.- 6.13 References.- 7 Thermal Nonequilibrium Between Fluid and Solid Phases.- 7.1 Local Phase Volume Averaging for Steady Flows.- 7.1.1 Allowing for Difference in Average Local Temperatures.- 7.1.2 Evaluation of [b] and [?].- 7.1.3 Energy Equation for Each Phase.- 7.1.4 Example: Axial Travel of Thermal Pulses.- 7.2 Interfacial Convective Heat Transfer Coefficient hsf.- 7.2.1 Models Based on hsf.- 7.2.2 Experimental Determination of hsf.- 7.3 Distributed Treatment of Oscillating Flow.- 7.4 Chemical Reaction.- 7.4.1 Two-Dimensional Direct Simulation.- 7.4.2 Volume-Averaged Models.- 7.4.3 Interfacial Nusselt Number.- 7.4.4 Comparison of Results of Various Treatments.- 7.5 References.- II Two-Phase Flow.- 8 Fluid Mechanics.- 8.1 Elements of Pore-Level Flow Structure.- 8.1.1 Surface Tension.- 8.1.2 Continuous Phase Distribution.- 8.1.3 Discontinuous Phase Distributions.- 8.1.4 Contact Line.- 8.1.5 Thin Extension of Meniscus.- 8.2 Local Volume Averaging.- 8.2.1 Effect of Surface Tension Gradient.- 8.3 A Semiheuristic Momentum Equation.- 8.3.1 Inertial Regime.- 8.3.2 Liquid-Gas Interfacial Drag.- 8.3.3 Coefficients in Momentum Equations.- 8.4 Capillary Pressure.- 8.4.1 Hysteresis.- 8.4.2 Models.- 8.5 Relative Permeability.- 8.5.1 Constraint on Applicability.- 8.5.2 Influencing Factors.- 8.5.3 Models.- 8.6 Microscopic Inertial Coefficient.- 8.7 Liquid-Gas Interfacial Drag.- 8.8 Immiscible Displacement.- 8.8.1 Interfacial Instabilities.- 8.8.2 Buckley-Leverett Front.- 8.8.3 Stability of Buckley-Leverett Front.- 8.9 Fluid-Solid Two-Phase Flow.- 8.10 References.- 9 Thermodynamics.- 9.1 Thermodynamics of Single-Component Capillary Systems.- 9.1.1 Work of Surface Formation.- 9.1.2 First and Second Laws of Thermodynamics.- 9.1.3 Thickness of Interfacial Layer.- 9.2 Effect of Curvature in Single-Component Systems.- 9.2.1 Vapor Pressure Reduction.- 9.2.2 Reduction of Chemical Potential.- 9.2.3 Increase in Heat of Evaporation.- 9.2.4 Liquid Superheat.- 9.2.5 Change in Freezing Temperature.- 9.2.6 Change in Triple-Point Temperature.- 9.3 Multicomponcnt Systems.- 9.3.1 Surface Tension of Solution.- 9.3.2 Vapor Pressure Reduction.- 9.4 Interfacial Thermodynamics of Meniscus Extension.- 9.5 Capillary Condensation.- 9.5.1 Adsorption by Solid Surface.- 9.5.2 Condensation in a Mesoporous Solid.- 9.6 Prediction of Fluid Behavior in Small Pores.- 9.6.1 Phase Transition in Small Pores: Hysteresis.- 9.6.2 Stability of Liquid Film in Small Pores: Hysteresis.- 9.7 References.- 10 Conduction and Convection.- 10.1 Local Volume Averaging of Energy Equation.- 10.1.1 Averaging.- 10.1.2 Effective Thermal Conductivity and Dispersion Tensors.- 10.2 Effective Thermal Conductivity.- 10.2.1 Anisotropy.- 10.2.2 Correlations.- 10.3 Thermal Dispersion.- 10.3.1 Anisotropy.- 10.3.2 Models.- 10.3.3 Correlations for Lateral Dispersion Coefficient.- 10.3.4 Dispersion near Bounding Surfaces.- 10.4 References.- 11 Transport Through Bounding Surfaces.- 11.1 Evaporation from Heated Liquid Film.- 11.1.1 Simple Model for Transition Region.- 11.1.2 Inclusion of Capillary Meniscus.- 11.2 Mass Diffusion Adjacent to a Partially Saturated Surface.- 11.2.1 Large Knudsen Number Model.- 11.2.2 Small Knudsen Number Model.- 11.3 Convection from Heterogeneous Planar Surfaces.- 11.3.1 Mass Transfer from a Single Strip.- 11.3.2 Simultaneous Heat and Mass Transfer from Multiple Surface Sources.- 11.4 Convection from Heterogeneous Two-Dimensional Surfaces.- 11.4.1 A Simple Surface Model.- 11.4.2 Experimental Observation on Simultaneous Heat and Mass Transfer.- 11.5 Simultaneous Heat and Mass Transfer from Packed Beds.- 11.6 References.- 12 Phase Change.- 12.1 Condensation at Vertical Impermeable Bounding Surfaces.- 12.1.1 Thick Liquid-Film Region (?? / d ” 1).- 12.1.2 Thin Liquid-Film Region (?? / d ” 1).- 12.2 Evaporation at Vertical Impermeable Bounding Surfaces.- 12.3 Evaporation at Horizontal Impermeable Bounding Surfaces.- 12.3.1 Effect of Bond Number.- 12.3.2 A One-Dimensional Analysis for Bo ” 1.- 12.4 Evaporation at Thin Porous-Layer Coated Surfaces.- 12.5 Moving Evaporation or Condensation Front.- 12.5.1 Temperatures Equal to or Larger than Saturation Temperature.- 12.5.2 Temperatures Below Saturation Temperature.- 12.5.3 Condensation Front Moving into Dry Porous Media.- 12.6 Melting and Solidification.- 12.6.1 Single-Component Systems.- 12.6.2 Multicomponent Systems.- 12.7 References.- Nomenclature.- Citation Index.

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