Viscosity and the Mechanism of Momentum Transport. Newtou's Law of Viscosity "Example Calculation oi Momentum Flux, 7

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1 PART I MOMENTUM TRANSPORT Chapter 1 * 1.1 * 1.2 * Chapter 2 * 2.1 * 2.2 Viscosity and the Mechanism of Momentum Transport Newtou's Law of Viscosity "Example Calculation oi Momentum Flux, 7 Non-Newtonian Fluids Pressure and Temperature Dependence of Viscosity *Example Estimation oi Viscosity [rom Critical Properties, 18 *Example Effect oi Pressure on Gas Viscosity, 19 Theory of Viscosity of Gases at Low Density Example Computation oi the Viscosity oj a Gas at Low Density, 25 Example Prediction oi the Viscosity oi a Gas Mixture at Low Density, 25 Theory of Viscosity of Liquids Example Estimation oj the Viscosity oj a Pure Liquid, 29 Velocity Distributions in Laminar Flow Shell Mornentum Balances: Boundary Conditions Flow of a Falling Film *Example Calculation oj Film Velocity,41 Example Falling Film with Variable Viscosity, xl

2 xii * 2.3 * * 2.6 Chapter 3 * 3.1 * * 3.4 * * 3.7 Chapter 4 * Flow through a Circular Tube 42 *Example Determination of Viscosity from Capillary Flow Data, 48 Example Bingham Flow in a Circular Tube, 48 Flow through an Annulus 51 Adjacent Flow of Two Immiscible Fluids 54 Creeping Flow Around a Solid Sphere 56 "Example Determination of Viscosityfrom Terminal Velocity of a Falling Sphere, 60 lhe Equations of Change for Isothermal Systems 71 The Equation of Continuity 74 The Equation of Motion 76 The Equation of Mechanical Energy 81 The Equations of Change in Curvilinear Coordinates 82 Use of the Equations of Change to Set Up Steady Flow Problems 92 *Example Tangential A nnular Flow of a Newtonian Fluid,94 "Example Shape of the Surface of a Rotating Liquid, 96 Example Torque Relationships and Velocity Distribution in lhe Cone-and-Plate Viscometer, 98 The Equations of Change for Incompressible Non- Newtonian.Flow 101 Example Tangential Annular Flow of a Bingham Plastic, 104 Example Components of the Momenlum Flux Tensor For Non-Newtonian Radial Flow between Two Parallel Disks, 106 Dimensional Analysis of the Equations of Change 107 "Example Prediction of Vortex Deptb in an Agitated Tank, 108 Velocity Distributions with More lhan One Independent Variable 123 Unsteady Viscous Flow 123 "Example Flow Near a Wall Suddenly Set in Motion, 124 Example Unsteady Laminar Flow in a Circular TlIbe, 126 Steady Viscous Flow With Two Nonvanishing Velocity Components: The Stream Function 130 Example "Creeping Flow" Around a Sphere, 132

3 xiii 4.3 Steady Two-Dimensional Potential Flow 133 Example Ideal Flow Around a Cylinder, 136 Example Flow into a Rectangular Channel, Boundary-Layer Theory 140 Example Flow Near a Wall Suddenly Set in Motion, 140 Example Flow Near the Leading Edge of a Flat Plate, 142 Chapter 5 Velocity Distributions in Turbulent Flow 153 * 5.1 Fluctuations and Time-Smoothed Quantities 154 * 5.2 Time-Smoothing of the Equations of Change for an Incompressible Fluid 158 * 5.3 Semiempirical Expressions for the Reynolds Stresses 160 *Example Derivation of the Logarithmic Distribution Law for Tube Flow (Far from Wall), 161 "Example Velacity Distribution for Tube Flow (Near Wall), 163 "Example Relative Magnitude af Molecular and Eddy Viscosity, The Second-Order Correlation Tensor and Its Propagation (the von Kármán-Howarth Equation) 166 Example Decay of Turbulence Behind a Crid, 173 Chapter 6 Interphase Transport in Isothermal Systems 180 * 6.1 Definition of Friction Factors 181 * 6.2 Friction Factors for Flow in Tubes 183 *Example Pressure Drop Requireâ for a Civen Flow Rate, 188 *Example Flow Rate for a Civen Pressure Drop, 189 * 6.3 Friction Factors for Flow Around Spheres 190 "Example Determination af Diameter of a Falling Sphere, Friction Factors for Packed Columns 196 Chapter 7 Macroscopic Balances for Isothermal Systems 208 * 7.1 The Macroscopic l\lass Balance 209 * 7.2 The l\1acroscopic Momentum Balance 210 * 7.3 The Macroscopic l\lechanical Energy Balances (Bernoulli equation) 211 Example Derivation of Mechanical Energy Balance for Steady Incompressible Flow, 213 * 7.4 Estimation of the Friction Loss 214 *Example Pouer Requirements for Pipe-Line Flow, 217

4 xiv Conlenls * 7.5 Use of the Macroscopic Balances to Set Up Steady Flow Problems 219 "Example Pressure Rise and Friction Loss in a Sudden Expansion, 219 *Example Performance of a Liquid-Liquid Ejector, 220 *ExamPle Thrust on a Pipe Bend, 222 *Example I sothermal Flow of a Liquid through. an Orifice, Use of the l\1acroscopic Balances to Set Up Unsteady Flow Problems 226 Example Efflu«Time for Flowfrom a Funnel, 226 Example Oscillalion of a Damped Manometer, 229 PART \I ENERGY TRANSPORT Chapler 8 Thermal Conductivily and lhe Mechanism of Energy Transporl 243 * 8.1 Fourier's Law of Heat Conduction 244 *Example Measurement of Thermal Conductivity, 247 * 8.2 Temperature and Pressure Dependence of Thermal Conductivity in Gases and Liquids 249 *Example Effect of Pressure on Thermal Conductivity, Theory of Thermal Conductivity of Gases at Low Density 253 Example Computation of the Thermal Conductivity of a Monatomic Gas at Low Density, 258 Example Estimation of lhe Thermal Conductivity of a Polyatomic Gas at Low Density, 258 Example Prediction of lhe Thermal Conductivity of a Gas Mixture at Low Density, Theory of Thermal Conductivity of Liquids 260 Example Prediction of lhe Thermal Conductivity of a Liquid, Thermal Conductivity of Solids 262 Chapler 9 Temperalure Dislribulions in Solids and in Laminar Flow 265 * 9.1 Shell Energy Balances; Boundary Conditions 266 * 9.2 Heat Conduction with an Electrical Heat Source 267 "Example Voltage Requiredfor a Given Temperature Rise in a Wire Heated by an Eleclric Current, 271 Example Heating of an Electric Wire with Temperature- Dependent Electrical and Thermal Conductivity, 272

5 9.3 * * * 9.8 * 9.9 Heat Conduction with a Nuclear Heat Source Heat Conduction with a Viscous Heat Source Heat Conduction with a Chemical Heat Source Heat Conduction through Composite Walls: Addition of Resistances *Example Composite Cylindrical Walls, 286 Heat Conduction in a Cooling Fin Example Error in Thermocouple Measurement, 290 Forced Free Convection Convection xv ( Chapter 10 * 10.1 * 10.2 * 10.3 * 1O.4 * 1O.5 * 10.6 lhe Equations of Change for Nonisothermal Systems The Equations of Energy The Energy Equation in Curvilinear Coordinates The Equations of Motion for Forced and Free Convection in Nonisothermal Flow Summary of the Equations of Change Use of the Equations of Change to Set Up Steady-State Heat Transfer Problems "Example Tangential Flow in an Annulus with Viscous Heat Ceneration, 325 *Ex""ample Steady Flow of a Nonisothermal Film, 326 *Example Transpiration Cooling, 328 Example Free-Convection Heat Transfer from_a Vertical Plate, 330 Example One-Dimensional Compressible Flow: Velocity, Temperature, and Pressure Cradients in a Stationary Shock Wave, 333 *Example A diabatic Frictionless Processes in an Ideal Gas, 337 Dimensional Analysis of the Equations of Change *Example Forced-Convection Heat Transfer in an Agitated Tank, 339 *Example Surjace Temperature of an Electric Heating Coil, Chapter 11 * 11.1 lemperature Distributions with More lhan One Independent Variable Unsteady Heat Conduction in Solids *Example Heating of a Semi-Infinite Slab, 353 "Example Heating of a Finite Slab, 354 Example Cooling of a Sphere in Contact with a Well-Stirred Fluid,

6 xvi 11.2 Steady Heat Conduction in Laminar Flow of a Viscous Fluid 361 Example : Laminar Tube Flow with Constant Heat Flux ai Wall, 362 Example Laminar Tube Flow with Constant Heat Flux at Wall: Asymptotic Solutionfor Small Distances, Steady Two-Dirnensional Potential Flow of Heat in Solids 364 Example Temperature Distribution in a Walt, Boundary-Layer Theory 366 Example Heat Transfer in Forced-Convection Laminar Flow along a Heated Flat Plate, 367 Chapter 12 Temperature Oistributions in Turbulent Flow 375 * 12.1 Temperature Fluctuations and the Tirne-Smoothed Temperature 375 * 12.2 Time-Smoothing the Energy Equation 377 * 12.3 Semiempirical Expressions for the Turbulent Energy Flux 379 "Example Temperature Profiles in Steady Turbulent Flow in Smooth Circular Tubes, The Double Temperature Correlation and I ts Propagation: The Corrsin Equation 384 Example Decay Equationfor the Double Temperaiure Correlation, 386 Chapter 13 Interphase Transport in Nonisothermal Systems 389 * 13.1 Definition of the Heat-Transfer Coefficient 390 *Example Calculation of Heat- Transfer Coefficients from Experimental Data, 394 * 13.2 Heat-Transfer Coefficients for Forced Convection in Tubes 396 *Example Design of a Tubular Heater, 405 * 13.3 Heat- Transfer Coefficients for Forced Convection around Submerged Objects Heat-Transfer Coefficients for Forced Convection through Packed Beds 411 * 13.5 Heat-Transfer Coefficients for Free Convection 412 *Example Heat Loss by Free Convection from a Horizontal Pipe, Heat-Transfer Coefficients for Condensation of Pure Vapors on Solid Surfaces 415 Example Condensation of Steam on a Vertical Surface, 418

7 contentr Chapter 14 * 14.1 * 14.2 * 14.3 * 14.4 * Chapter 15 * 15.1 * 15.2 * 15.3 * xvii Energy Transport by Radiation 426 The Spectrum of Electromagnetic Radiation 427 Absorption and Emission a t Solid Surfaces 429 Planck's Distribution Law, Wien's Displacement Law, and the Stefan-Boltzrnann Law 433 *Example Temperature and Radiant-Energy Emission of the Sun, 437 Direct Radiation between Black Bodies in Vacuo at Different Temperatures 437 *Example Estimation of the Solar Constant, 443 *Exdmple Radiant Heat Transfer between Disks, 444 Radiation between Nonblack Bodies at Different Temperatures 445 "Example Radiation Shields, 446 *Example Radiation and Free-Convection Heat Losses from a Horizontal Pipe, 448 Example Combined Radiation and Convection, 448 Radiant Energy Transport in Absorbing Media 449 Example Absorption of a Monochromatic Radiant Beam, 451 Macroscopic Balances for Nonisothermal Systems 456 The Macroscopic Energy Balance 456 The Macroscopic l\'lechanical Energy Balance (Bernoulli Equation) 460 Summary of the Macroscopic Balances for Pure Fluids 462 Use of the Macroscopic Balances for Solving Steady-State Problems 463 "Example The Cooling of an Ideal Gas, 463 "Example Parallel- ar Counter-Floui Heat Exchangers, 465 *Example Pouier Requirements for Pumping a Compressible Fluid through. a Long Pipe, 467 Example Mixing of Two Ideal-Gas Streams, 470 *Example Flow of Compressible Fluids througlt liead Meters, 471 Use of the Macroscopic Balances for Solving Unsteady-State Problems 473 Example IIeating of a Liquid in an Agitated Tank, 473 Example Operation of a Simple Temperature Controller, 476 Example Free Batch Expansion of a Compressible Fluid,480

8 PART 11I jmass TRANSPORT / Chapter 16 * 16.1 * 16.2 * Diffusivity and the Mechanisms of Mass Transport Definitions of Concentrations, Velocities, and Mass Fluxes Example Relations among the Molar Fluxes, 501 Fick's Law of Diffusion Temperature and Pressure Dependence of Mass Diffusivity "Examole Estimation of Mass Diffusivity at Low Density, 507 "Example Estimation of Mass Diffusivity at Iligh Density, 507 Theory of Ordinary Diffusion in Gases at Low Density Example Computation of Mass Diffusivity at Low Density, 512 Theories of Ordinary Diffusion in Liquids Example Estimation of Mass Diffusivily for a Binary Liquid Mixture, Chapter 17 * 17.1 * 17.2 * 17.3 * 17.4 * Chapter 18 * 18.1 * Concentration Laminar Flow Distributions in Solids and in Shell Mass Balances: Boundary Conditions Diffusion Through a Stagnant Gas Film *Example Determination of Diffusivity, 526 Example Diffusion Through a Nonisothermal Spherical Film, 527 Diffusion with Heterogeneous Chemical Reaction *ExamPle Diffusion with Slow Heterogeneous Reaction, 531 Diffusion with Homogeneous Chemical Reaction "Example Gas Absorption with Chemical Reaction in an Agitated Tank, 534 Diffusion into a Falling Liquid Film: Forced-Convection Mass Transfer *Example Gas A bsorption from Rising Bubbles, 541 Diffusion and Chemical Reaction Inside a Porous Catalyst: the "Effectiveness Factor" The Equations of Change for Multicomponent The Equations of Continuity for a Binary Mixture Systems The Equation of Continuity of A in Curvilinear Coordinates The Multicomponent Equations of Change in Terms of the Fluxes

9 * 18.6 The Multicomponent Fluxes in Terms of the Transport Properties Use of the Equations of Change to Set Up Diffusion Problems Example Simultaneous lieat and Mass Transfer, 572 Example Thermal Diffusion, 574 Example Pressure Diffusion, 575 Example Forced Dilfusion, 577 Example Three-Component Ordinary Dilfusion with Heterogeneous Chemical Reaction, 578 Dimensional Analysis of the Equations of Change for a Binary Isothermal Fluid Mixture "Example Blending of Miscible Fluids, 582 xix Chapter Concentration Distributions with More lhan Independent Variable One Unsteady Diffusion Example Unsteady-State Evaporàtion, 594 Example Unsteady Diffusion unt]: First-Order Reaction, 598 Example Gas Absorption with Rapid Chemical Reaction, 599 Boundary-Layer Theory: von Kármán Approximate Method Example Unsteady Evaporation in/o a Multicomponent Mixture, 602 Example Diff usion and Chemical Reaction in Isothermal Laminar Flow Along a Soluble Flat Plate, 605 Boundary-Layer Theory: Exact Solutions for Simultaneous Heat, Mass, and Momentum Transfer Example Calculation of Mass-Transjer Rale, Chapter 20 * 20.1 * Concentration Distributions in Turbulent Flow Concentration Fluctuations and the Tirne-Smoothed Concen tra tion Tirne-Smoothing of the Equation of Continuity of A Semiempirical Expressions for the Turbulent Mass Flux Example Concentration Profiles in Turbulent Flow in Smooth Circular Tubes, 630 Example Evaporation of Ammonia in a Wetted Wall Column, The Double Concentration Correlation and I ts Propagation: the Corrsin Equation

10 xx Chapter 21 * 21.1 * 21.2 * 21.3 * Chapter 22 * 22.1 * 22.2 * 22.3 * 22.4 * Interphase Transport in Multicomponent Systems Definition of Binary Mass-Transfer Coefficients in One Phase Correlations of Binary Mass- Transfer Coefficients in One Phase at Low Mass-Transfer Rates *Example Evaporation of a Freely Falling Drop, 648 *Example The Wet-and-Dry-Bulb Psychrometer, 649 Definition of Binary Mass-Transfer Coefficients in Two Phases at Low Mass-Transfer Rates Definition of the Transfer Coefficients for High Mass- Transfer Rates Transfer Coefficients at High Mass-Transfer Rates: Film Theory Example Rapid Evaporation of a Pure Liquid, 666 Example Use of Correction Factors in Droplet Evaporation, 667 Example Wet-Bulb Performance at High Mass- Transfer Rales, 667 Transfer Coefficients at High Mass-Transfer Rates: Penetration Theory Transfer Coefficients at High Mass-Transfer Rates: Boundary-Layer Theory Example Rapid Evaporationfrom a Plane Surface, 676 Transfer Coefficients in Multicomponent Systems Example Mass Transfer in a Fixed-Bed Catalytic Reactor, 678 Macroscopic Balances for Multicomponent Systems The Macroscopic Mass Balances The Macroscopic Momentum Balance The Macroscopic Energy Balance The Macroscopic Mechanical Energy Balance Use of the Macroscopic Balances to Solve Steady-State Problems *Example Energy Balance for a Suljur Dioxide Converter, 690 *Example Ileight of a Packed-Tower Absorber, 692 Example Expansion of a Reactive Gas Mixture througb a Frictionless Adiabatic Nozzle, 697 Use of the Macroscopic Balances for Solving Unsteady- State Problems Example Start-Up of a Chemical Reactor, 700 Example Unsteady Operation of a Packed Column,

11 Postface Appendix A Summary of Vector and Tensor Notation Appendix A.1 Vector Operations Irorn a Geometrical Viewpoint A.2 Vector Operations from an Analytical Viewpoint Example A.2-I. Proof of a Vector Identity, 722 A.3 The Vector Differential Operations A.4 Second Order Tensors Example A.4-I. Proof of a Tensor Identity, 731 A.5 Integral Operations for Vectors and Tensors A.6 Vector and Tensor Components in Curvilinear Coordinates A.7 Differential Operations in Curvilinear Coordinates Example A.7-1. DilferentialOperations in Cylindrical Coordinates, 739 B.1 B.2 B Tables for Prediction of Transport Properties Intermolecular Force Parameters and Critical Properties Functions for Prediction of Transport Properties of Gases at Low Densities xxi Appendix Notation C.1 C.2 C.3 C Constants and Conversion Mathematical Physical Constants Conversion Factors Constants Factors Author Subject Index Index

Chemical and Biological Engineering Department University of Wisconsin-Madison

Transport Phenomena Revised Second Edition R. Byron Bird Warren E. Stewart Edwin N. Lightfoot Chemical and Biological Engineering Department University of Wisconsin-Madison John Wiley & Sons, Inc. New