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Fundamentals of Momentum, Heat, and Mass Transfer
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Table of Contents

1. Introduction to Momentum Transfer 1 1.1 Fluids and the Continuum 1 1.2 Properties at a Point 2 1.3 Point-to-Point Variation of Properties in a Fluid 5 1.4 Units 8 1.5 Compressibility 10 1.6 Surface Tension 11 2. Fluid Statics 16 2.1 Pressure Variation in a Static Fluid 16 2.2 Uniform Rectilinear Acceleration 19 2.3 Forces on Submerged Surfaces 20 2.4 Buoyancy 23 2.5 Closure 25 3. Description of a Fluid in Motion 29 3.1 Fundamental Physical Laws 29 3.2 Fluid-Flow Fields: Lagrangian and Eulerian Representations 29 3.3 Steady and Unsteady Flows 30 3.4 Streamlines 31 3.5 Systems and Control Volumes 32 4. Conservation of Mass: Control-Volume Approach 34 4.1 Integral Relation 34 4.2 Specific Forms of the Integral Expression 35 4.3 Closure 40 5. Newton's Second Law of Motion: Control-Volume Approach 44 5.1 Integral Relation for Linear Momentum 44 5.2 Applications of the Integral Expression for Linear Momentum 47 5.3 Integral Relation for Moment of Momentum 53 5.4 Applications to Pumps and Turbines 55 5.5 Closure 59 6. Conservation of Energy: Control-Volume Approach 65 6.1 Integral Relation for the Conservation of Energy 65 6.2 Applications of the Integral Expression 71 6.3 The Bernoulli Equation 74 6.4 Closure 79 7. Shear Stress in Laminar Flow 85 7.1 Newton's Viscosity Relation 85 7.2 Non-Newtonian Fluids 86 7.3 Viscosity 88 7.4 Shear Stress in Multidimensional Laminar Flows of a Newtonian Fluid 93 7.5 Closure 97 8. Analysis of a Differential Fluid Element in Laminar Flow 99 8.1 Fully Developed Laminar Flow in a Circular Conduit of Constant Cross Section 99 8.2 Laminar Flow of a Newtonian Fluid Down an Inclined-Plane Surface 102 8.3 Closure 104 9. Differential Equations of Fluid Flow 107 9.1 The Differential Continuity Equation 107 9.2 Navier-Stokes Equations 110 9.3 Bernoulli's Equation 118 9.4 Spherical Coordinate Forms of the Navier-Stokes Equations 119 9.5 Closure 121 10. Inviscid Fluid Flow 124 10.1 Fluid Rotation at a Point 124 10.2 The Stream Function 127 10.3 Inviscid, Irrotational Flow about an Infinite Cylinder 129 10.4 Irrotational Flow, the Velocity Potential 131 10.5 Total Head in Irrotational Flow 134 10.6 Utilization of Potential Flow 135 10.7 Potential Flow Analysis-Simple Plane Flow Cases 136 10.8 Potential Flow Analysis-Superposition 137 10.9 Closure 139 11. Dimensional Analysis and Similitude 141 11.1 Dimensions 141 11.2 Dimensional Analysis of Governing Differential Equations 142 11.3 The Buckingham Method 144 11.4 Geometric, Kinematic, and Dynamic Similarity 147 11.5 Model Theory 148 11.6 Closure 150 12. Viscous Flow 154 12.1 Reynolds's Experiment 154 12.2 Drag 155 12.3 The Boundary-Layer Concept 160 12.4 The Boundary-Layer Equations 161 12.5 Blasius's Solution for the Laminar Boundary Layer on a Flat Plate 163 12.6 Flow with a Pressure Gradient 167 12.7 von Karman Momentum Integral Analysis 169 12.8 Description of Turbulence 172 12.9 Turbulent Shearing Stresses 174 12.10 The Mixing-Length Hypothesis 175 12.11 Velocity Distribution from the Mixing-Length Theory 177 12.12 The Universal Velocity Distribution 178 12.13 Further Empirical Relations for Turbulent Flow 179 12.14 The Turbulent Boundary Layer on a Flat Plate 180 12.15 Factors Affecting the Transition from Laminar to Turbulent Flow 182 12.16 Closure 183 13. Flow in Closed Conduits 186 13.1 Dimensional Analysis of Conduit Flow 186 13.2 Friction Factors for Fully Developed Laminar, Turbulent, and Transition Flow in Circular Conduits 188 13.3 Friction Factor and Head-Loss Determination for Pipe Flow 191 13.4 Pipe-Flow Analysis 195 13.5 Friction Factors for Flow in the Entrance to a Circular Conduit 198 13.6 Closure 201 14. Fluid Machinery 204 14.1 Centrifugal Pumps 205 14.2 Scaling Laws for Pumps and Fans 213 14.3 Axial- and Mixed-Flow Pump Configurations 216 14.4 Turbines 216 14.5 Closure 217 15. Fundamentals of Heat Transfer 220 15.1 Conduction 220 15.2 Thermal Conductivity 221 15.3 Convection 226 15.4 Radiation 228 15.5 Combined Mechanisms of Heat Transfer 228 15.6 Closure 232 16. Differential Equations of Heat Transfer 236 16.1 The General Differential Equation for Energy Transfer 236 16.2 Special Forms of the Differential Energy Equation 239 16.3 Commonly Encountered Boundary Conditions 240 16.4 Closure 244 17. Steady-State Conduction 247 17.1 One-Dimensional Conduction 247 17.2 One-Dimensional Conduction with Internal Generation of Energy 253 17.3 Heat Transfer from Extended Surfaces 256 17.4 Two- and Three-Dimensional Systems 263 17.5 Closure 269 18. Unsteady-State Conduction 277 18.1 Analytical Solutions 277 18.2 Temperature-Time Charts for Simple Geometric Shapes 286 18.3 Numerical Methods for Transient Conduction Analysis 288 18.4 An Integral Method for One-Dimensional Unsteady Conduction 291 18.5 Closure 295 19. Convective Heat Transfer 301 19.1 Fundamental Considerations in Convective Heat Transfer 301 19.2 Significant Parameters in Convective Heat Transfer 302 19.3 Dimensional Analysis of Convective Energy Transfer 303 19.4 Exact Analysis of the Laminar Boundary Layer 306 19.5 Approximate Integral Analysis of the Thermal Boundary Layer 310 19.6 Energy- and Momentum-Transfer Analogies 312 19.7 Turbulent Flow Considerations 314 19.8 Closure 320 20. Convective Heat-Transfer Correlations 324 20.1 Natural Convection 324 20.2 Forced Convection for Internal Flow 332 20.3 Forced Convection for External Flow 338 20.4 Closure 345 21. Boiling and Condensation 352 21.1 Boiling 352 21.2 Condensation 357 21.3 Closure 363 22. Heat-Transfer Equipment 365 22.1 Types of Heat Exchangers 365 22.2 Single-Pass Heat-Exchanger Analysis: The Log-Mean Temperature Difference 368 22.3 Crossflow and Shell-and-Tube Heat-Exchanger Analysis 372 22.4 The Number-of-Transfer-Units (NTU) Method of Heat-Exchanger Analysis and Design 376 22.5 Additional Considerations in Heat-Exchanger Design 383 22.6 Closure 385 23. Radiation Heat Transfer 390 23.1 Nature of Radiation 390 23.2 Thermal Radiation 391 23.3 The Intensity of Radiation 393 23.4 Planck's Law of Radiation 394 23.5 Stefan-Boltzmann Law 398 23.6 Emissivity and Absorptivity of Solid Surfaces 400 23.7 Radiant Heat Transfer Between Black Bodies 405 23.8 Radiant Exchange in Black Enclosures 412 23.9 Radiant Exchange with Reradiating Surfaces Present 413 23.10 Radiant Heat Transfer Between Gray Surfaces 414 23.11 Radiation from Gases 421 23.12 The Radiation Heat-Transfer Coefficient 423 23.13 Closure 426 24. Fundamentals of Mass Transfer 431 24.1 Molecular Mass Transfer 432 24.2 The Diffusion Coefficient 441 24.3 Convective Mass Transfer 461 24.4 Closure 462 25. Differential Equations of Mass Transfer 467 25.1 The Differential Equation for Mass Transfer 467 25.2 Special Forms of the Differential Mass-Transfer Equation 470 25.3 Commonly Encountered Boundary Conditions 472 25.4 Steps for Modeling Processes Involving Molecular Diffusion 475 25.5 Closure 484 26. Steady-State Molecular Diffusion 489 26.1 One-Dimensional Mass Transfer Independent of Chemical Reaction 489 26.2 One-Dimensional Systems Associated with Chemical Reaction 500 26.3 Two- and Three-Dimensional Systems 510 26.4 Simultaneous Momentum, Heat, and Mass Transfer 513 26.5 Closure 520 27. Unsteady-State Molecular Diffusion 533 27.1 Unsteady-State Diffusion and Fick's Second Law 533 27.2 Transient Diffusion in a Semi-Infinite Medium 534 27.3 Transient Diffusion in a Finite-Dimensional Medium under Conditions of Negligible Surface Resistance 538 27.4 Concentration-Time Charts for Simple Geometric Shapes 546 27.5 Closure 550 28. Convective Mass Transfer 556 28.1 Fundamental Considerations in Convective Mass Transfer 556 28.2 Significant Parameters in Convective Mass Transfer 559 28.3 Dimensional Analysis of Convective Mass Transfer 562 28.4 Exact Analysis of the Laminar Concentration Boundary Layer 564 28.5 Approximate Analysis of the Concentration Boundary Layer 572 28.6 Mass-, Energy-, and Momentum-Transfer Analogies 577 28.7 Models for Convective Mass-Transfer Coefficients 584 28.8 Closure 586 29. Convective Mass Transfer Between Phases 592 29.1 Equilibrium 592 29.2 Two-Resistance Theory 595 29.3 Closure 610 30. Convective Mass-Transfer Correlations 617 30.1 Mass Transfer to Plates, Spheres, and Cylinders 618 30.2 Mass Transfer Involving Flow Through Pipes 626 30.3 Mass Transfer in Wetted-Wall Columns 627 30.4 Mass Transfer in Packed and Fluidized Beds 630 30.5 Gas-Liquid Mass Transfer in Bubble Columns and Stirred Tanks 631 30.6 Capacity Coefficients for Packed Towers 634 30.7 Steps for Modeling Mass-Transfer Processes Involving Convection 635 30.8 Closure 644 31. Mass-Transfer Equipment 655 31.1 Types of Mass-Transfer Equipment 655 31.2 Gas-Liquid Mass-Transfer Operations in Well-Mixed Tanks 657 31.3 Mass Balances for Continuous-Contact Towers: Operating-Line Equations 662 31.4 Enthalpy Balances for Continuous-Contacts Towers 670 31.5 Mass-Transfer Capacity Coefficients 671 31.6 Continuous-Contact Equipment Analysis 672 31.7 Closure 686 Nomenclature 693 Appendixes A. Transformations of the Operators and 2 to Cylindrical Coordinates 700 B. Summary of Differential Vector Operations in Various Coordinate Systems 703 C. Symmetry of the Stress Tensor 706 D. The Viscous Contribution to the Normal Stress 707 E. The Navier-Stokes Equations for Constant p and in Cartesian, Cylindrical, and Spherical Coordinates 709 F. Charts for Solution of Unsteady Transport Problems 711 G. Properties of the Standard Atmosphere 724 H. Physical Properties of Solids 727 I. Physical Properties of Gases and Liquids 730 J. Mass-Transfer Diffusion Coefficients in Binary Systems 743 K. Lennard-Jones Constants 746 L. The Error Function 749 M. Standard Pipe Sizes 750 N. Standard Tubing Gages 752 Index 754

About the Author

James R. Welty arrived at Oregon State University as a freshman in mechanical engineering in 1950 and has been associated with OSU ever since. He earned his B.S. in 1954, and began teaching at OSU in 1958, receiving his Ph.D. in 1962 and becoming a full professor in 1967. He served as head of the Department of Mechanical Engineering from 1970 to 1985, at which time he returned to full-time teaching until his retirement in 1996.

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