Transport by Advection and Diffusion

Ted Bennett is Associate Professor of Mechanical and Environmental Engineering at the University of California – Santa Barbara. He received his PhD from UC Berkeley in 1996. He has taught the transport phenomena course for the last 9 years, and in 2000 was awarded the Distinguished Teaching Award.

• Chapter 1 Thermodynamic Preliminaries 11.1 The First and Second Laws of Thermodynamics 11.2 Fundamental Equations 21.3 Ideal Gas 71.4 Constant Density Solid or Liquid 81.5 Properties of Mixtures 91.6 Summary of Thermodynamic Results 91.7 Problems 10Chapter 2 Fundamentals of Transport 122.1 Physics of Advection and Diffusion 122.2 Advection Fluxes 142.3 Diffusion Fluxes 172.4 Reversible vs. Irreversible Transport 222.5 Looking Ahead 232.6 Problems 23Chapter 3 Index Notation 253.1 Indices 253.2 Representation of Cartesian Differential Equations 263.3 Special Operators 273.4 Operators in Non-Cartesian Coordinates 313.5 Problems 34Chapter 4 Transport by Advection and Diffusion 364.1 Continuity Equation 374.2 Transport of Species 394.3 Transport of Heat 424.4 Transport of Momentum 434.5 Summary of Transport Equations without Sources 444.6 Conservation Statements from a Finite Volume 444.7 Eulerian and Lagrangian Coordinates and the Substantial Derivative 464.8 Problems 48Chapter 5 Transport with Source Terms 505.1 Continuity Equation 515.2 Species Equation 515.3 Heat Equation (without Viscous Heating) 525.4 Momentum Equation 545.5 Kinetic Energy Equation 555.6 Heat Equation (with Viscous Heating) 575.7 Entropy Generation in Irreversible Flows 585.8 Conservation Statements Derived from a Finite Volume 595.9 Leibniz’s Theorem 625.10 Looking Ahead 635.11 Problems 64Chapter 6 Specification of Transport Problems 666.1 Classification of Equations 666.2 Boundary Conditions 676.3 Elementary Linear Examples 696.4 Nonlinear Example 736.5 Scaling Estimates 756.6 Problems 78Chapter 7 Transient One-Dimensional Diffusion 827.1 Separation of Time and Space Variables 837.2 Silicon Doping 897.3 Plane Wall With Heat Generation 937.4 Transient Groundwater Contamination 977.5 Problems 101Chapter 8 Steady Two-Dimensional Diffusion 1038.1 Separation of Two Spatial Variables 1038.2 Nonhomogeneous Conditions on Nonadjoining Boundaries 1058.3 Nonhomogeneous Conditions on Adjoining Boundaries 1078.4 Nonhomogeneous Condition in Governing Equation 1118.5 Looking Ahead 1158.6 Problems 115Chapter 9 Eigenfunction Expansion 1199.1 Method of Eigenfunction Expansion 1199.2 Non-Cartesian Coordinate Systems 1279.3 Transport in Non-Cartesian Coordinates 1309.4 Problems 139Chapter 10 Similarity Solution 14010.1 The Similarity Variable 14010.2 Laser Heating of a Semi-Infinite Solid 14210.3 Transient Evaporation 14610.4 Power Series Solution 14810.5 Mass Transfer with Time-Dependent Boundary Condition 15210.6 Problems 157Chapter 11 Superposition of Solutions 15911.1 Superposition in Time 15911.2 Superposition in Space 16411.3 Problems 169Chapter 12 Diffusion-Driven Boundaries 17212.1 Thermal Oxidation 17212.2 Solidification of an Undercooled Liquid 17412.3 Solidification of a Binary Alloy from an Undercooled Liquid 17812.4 Melting of a Solid Initially at the Melting Point 18312.5 Problems 186Chapter 13 Lubrication Theory 18813.1 Lubrication Flows Governed by Diffusion 18813.2 Scaling Arguments for Squeeze Flow 18913.3 Squeeze Flow Damping in an Accelerometer Design 19113.4 Coating Extrusion 19413.5 Coating Extrusion on a Porous Surface 19813.6 Reynolds Equation for Lubrication Theory 20213.7 Problems 203Chapter 14 Inviscid Flow 20614.1 The Reynolds Number 20714.2 Inviscid Momentum Equation 20814.3 Ideal Plane Flow 20914.4 Steady Potential Flow through a Box with Staggered Inlet and Exit 21014.5 Advection of Species through a Box with Staggered Inlet and Exit 21514.6 Spherical Bubble Dynamics 21714.7 Problems 221Chapter 15 Catalog of Ideal Plane Flows 22415.1 Superposition of Simple Plane Flows 22415.2 Potential Flow over an Aircraft Fuselage 22515.3 Force on a Line Vortex in a Uniform Stream 22715.4 Flow Circulation 22915.5 Potential Flow over Wedges 23115.6 Problems 233Chapter 16 Complex Variable Methods 23416.1 Brief Review of Complex Numbers 23416.2 Complex Representation of Potential Flows 23516.3 The Joukowski Transform 23616.4 Joukowski Symmetric Airfoils 23816.5 Joukowski Cambered Airfoils 24016.6 Heat Transfer between Nonconcentric Cylinders 24216.7 Transport with Temporally Periodic Conditions 24416.8 Problems 246Chapter 17 MacCormack Integration 24917.1 Flux-Conservative Equations 24917.2 MacCormack Integration 25017.3 Transient Convection 25517.4 Steady-State Solution of Coupled Equations 25917.5 Problems 262Chapter 18 Open Channel Flow 26518.1 Analysis of Open Channel Flows 26518.2 Simple Surface Waves 26718.3 Depression and Elevation Waves 26818.4 The Hydraulic Jump 26918.5 Energy Conservation 27118.6 Dam-Break Example 27318.7 Tracer Transport in the Dam-Break Problem 28018.8 Problems 280Chapter 19 Open Channel Flow with Friction 28419.1 The Saint-Venant Equations 28419.2 The Friction Slope 28619.3 Flow through a Sluice Gate 28719.4 Problems 293Chapter 20 Compressible Flow 29620.1 General Equations of Momentum and Energy Transport 29620.2 Reversible Flows 29820.3 Sound Waves 29920.4 Propagation of Expansion and Compression Waves 30020.5 Shock Wave (Normal to Flow) 30220.6 Shock Tube Analytic Description 30420.7 Shock Tube Numerical Description 30720.8 Shock Tube Problem with Dissimilar Gases 31120.9 Problems 312Chapter 21 Quasi-One-Dimensional Compressible Flows 31521.1 Quasi-One-Dimensional Flow Equations 31521.2 Quasi-One-Dimensional Steady Flow Equations without Friction 31821.3 Numerical Solution to Quasi-One-Dimensional Steady Flow 32321.4 Problems 330Chapter 22 Two-Dimensional Compressible Flows 33322.1 Flow through a Diverging Nozzle 33322.2 Problems 342Chapter 23 Runge-Kutta Integration 34423.1 Fourth-Order Runge-Kutta Integration of First-Order Equations 34423.2 Runge-Kutta Integration of Higher Order Equations 34723.3 Numerical Integration of Bubble Dynamics 34923.4 Numerical Integration with Shooting 35123.5 Problems 355Chapter 24 Boundary Layer Convection 35924.1 Scanning Laser Heat Treatment 35924.2 Convection to an Inviscid Flow 36324.3 Species Transfer to a Vertically Conveyed Liquid Film 36924.4 Problems 374Chapter 25 Convection into Developing Laminar Flows 37625.1 Boundary Layer Flow over a Flat Plate (Blasius Flow) 37625.2 Species Transfer across the Boundary Layer 38325.3 Heat Transfer across the Boundary Layer 38725.4 A Correlation for Forced Heat Convection from a Flat Plate 38925.5 Transport Analogies 39025.6 Boundary Layers Developing on a Wedge (Falkner-Skan Flow) 39225.7 Viscous Heating in the Boundary Layer 39425.8 Problems 396Chapter 26 Natural Convection 39926.1 Buoyancy 39926.2 Natural Convection from a Vertical Plate 40026.3 Scaling Natural Convection from a Vertical Plate 40126.4 Exact Solution to Natural Convection Boundary Layer Equations 40426.5 Problems 411Chapter 27 Internal Flow 41227.1 Entrance Region 41227.2 Heat Transport in an Internal Flow 41427.3 Entrance Region of Plug Flow between Plates of Constant Heat Flux 41527.4 Plug Flow between Plates of Constant Temperature 41727.5 Fully Developed Transport Profiles 41927.6 Fully Developed Heat Transport in Plug Flow between Plates of Constant Heat Flux 42127.7 Fully Developed Species Transport in Plug Flow Between Surfaces of Constant Concentration 42427.8 Problems 426Chapter 28 Fully Developed Transport in Internal Flows 42928.1 Momentum Transport in a Fully Developed Flow 42928.2 Heat Transport in a Fully Developed Flow 43028.3 Species Transport in a Fully Developed Flow 44128.4 Problems 444Chapter 29 Influence of Temperature-Dependent Properties 44729.1 Temperature-Dependent Conductivity in a Solid 44729.2 Temperature-Dependent Diffusivity in Internal Convection 45129.3 Temperature-Dependent Gas Properties in Boundary Layer Flow 45729.4 Problems 462Chapter 30 Turbulence 46530.1 The Transition to Turbulence 46630.2 Reynolds Decomposition 46830.3 Decomposition of the Continuity Equation 46930.4 Decomposition of the Momentum Equation 47030.5 The Mixing Length Model of Prandtl 47130.6 Regions in a Wall Boundary Layer 47330.7 Parameters of the Mixing Length Model 47630.8 Problems 477Chapter 31 Fully Developed Turbulent Flow 47931.1 Turbulent Poiseuille Flow Between Smooth Parallel Plates 48031.2 Turbulent Couette Flow between Smooth Parallel Plates 48531.3 Turbulent Poiseuille Flow in a Smooth-Wall Pipe 48831.4 Utility of the Hydraulic Diameter 49031.5 Turbulent Poiseuille Flow in a Smooth Annular Pipe 49031.6 Reichardt’s Formula for Turbulent Diffusivity 49531.7 Poiseuille Flow with Blowing between Walls 49731.8 Problems 504Chapter 32 Turbulent Heat and Species Transfer 50732.1 Reynolds Decomposition of the Heat Equation 50732.2 The Reynolds Analogy 50832.3 Thermal Profile Near the Wall 51032.4 Mixing Length Model for Heat Transfer 51332.5 Mixing Length Model for Species Transfer 51432.6 Problems 515Chapter 33 Fully Developed Transport in Turbulent Flows 51733.1 Chemical Vapor Deposition in Turbulent Tube Flow with Generation 51733.2 Heat Transfer in a Fully Developed Internal Turbulent Flow 52233.3 Heat Transfer in a Turbulent Poiseuille Flow between Smooth Parallel Plates 52333.4 Fully Developed Transport in a Turbulent Flow of a Binary Mixture 53233.5 Problems 543Chapter 34 Turbulence over Rough Surfaces 54534.1 Turbulence over a Fully Rough Surface 54634.2 Turbulent Heat and Species Transfer from a Fully Rough Surface 54734.3 Application of the Rough Surface Mixing Length Model 54934.4 Application of Reichardt’s Formula to Rough Surfaces 55334.5 Problems 563Chapter 35 Turbulent Boundary Layer 56535.1 Formulation of Transport in Turbulent Boundary Layer 56535.2 Formulation of Heat Transport in the Turbulent Boundary Layer 57535.3 Problems 580Chapter 36 The K-Epsilon Model of Turbulence 58136.1 Turbulent Kinetic Energy Equation 58136.2 Dissipation Equation for Turbulent Kinetic Energy 58536.3 The Standard K-Epsilon Model 58636.4 Problems 587Chapter 37 The K-Epsilon Model Applied to Fully Developed Flows 58937.1 K-Epsilon Model for Poiseuille Flow between Smooth Parallel Plates 58937.2 Transition Point between Mixing Length and K-Epsilon Models 59137.3 Solving the K and E Equations 59337.4 Solution of the Momentum Equation with the K-Epsilon Model 59737.5 Turbulent Diffusivity Approaching the Centerline of the Flow 59837.6 Turbulent Heat Transfer with Constant Temperature Boundary 60137.7 Problems 604Appendix A 606Index 611