# Fundamentals of momentum heat and mass transfer solutions

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## ABOUT fundamentals of momentum heat and mass transfer solutions

The field’s essential standard for more than three decades, Fundamentals of Momentum, Heat and Mass Transfer offers a systematic introduction to transport phenomena and rate processes. Thorough coverage of central principles helps students build a foundational knowledge base while developing vital analysis and problem solving skills. Momentum, heat, and mass transfer are introduced sequentially for clarity of concept and logical organization of processes, while examples of modern applications illustrate real-world practices and strengthen student comprehension. Designed to keep the focus on concept over content, this text uses accessible language and efficient pedagogy to streamline student mastery and facilitate further exploration.

Abundant examples, practice problems, and illustrations reinforce basic principles, while extensive tables simplify comparisons of the various states of matter. Detailed coverage of topics including dimensional analysis, viscous flow, conduction, convection, and molecular diffusion provide broadly-relevant guidance for undergraduates at the sophomore or junior level, with special significance to students of chemical, mechanical, environmental, and biochemical engineering.

Fundamentals of Momentum, Heat, and Mass Transfer, 7th Edition | Wiley

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 15

2.1 Pressure Variation in a Static Fluid 15

2.2 Uniform Rectilinear Acceleration 18

2.3 Forces on Submerged Surfaces 19

2.4 Buoyancy 22

2.5 Closure 24

3. Description of a Fluid in Motion 25

3.1 Fundamental Physical Laws 25

3.2 Fluid-Flow Fields: Lagrangian and Eulerian Representations 25

3.4 Streamlines 27

3.5 Systems and Control Volumes 28

4. Conservation of Mass: Control-Volume Approach 30

4.1 Integral Relation 30

4.2 Specific Forms of the Integral Expression 31

4.3 Closure 36

5. Newton’s Second Law of Motion: Control-Volume Approach 37

5.1 Integral Relation for Linear Momentum 37

5.2 Applications of the Integral Expression for Linear Momentum 40

5.3 Integral Relation for Moment of Momentum 46

5.4 Applications to Pumps and Turbines 48

5.5 Closure 52

6. Conservation of Energy: Control-Volume Approach 53

6.1 Integral Relation for the Conservation of Energy 53

6.2 Applications of the Integral Expression 59

6.3 The Bernoulli Equation 62

6.4 Closure 67

7. Shear Stress in Laminar Flow 68

7.1 Newton’s Viscosity Relation 68

7.2 Non-Newtonian Fluids 69

7.3 Viscosity 71

7.4 Shear Stress in Multidimensional Laminar Flows of a Newtonian Fluid 76

7.5 Closure 80

8. Analysis of a Differential Fluid Element in Laminar Flow 81

8.1 Fully Developed Laminar Flow in a Circular Conduit of Constant Cross Section 81

8.2 Laminar Flow of a Newtonian Fluid Down an Inclined-Plane Surface 84

8.3 Closure 86

9. Differential Equations of Fluid Flow 87

9.1 The Differential Continuity Equation 87

9.2 Navier–Stokes Equations 90

9.3 Bernoulli’s Equation 98

9.4 Spherical Coordinate Forms of the Navier–Stokes Equations 99

9.5 Closure 101

10. Inviscid Fluid Flow 102

10.1 Fluid Rotation at a Point 102

10.2 The Stream Function 105

10.3 Inviscid, Irrotational Flow about an Infinite Cylinder 107

10.4 Irrotational Flow, the Velocity Potential 109

10.5 Total Head in Irrotational Flow 112

10.6 Utilization of Potential Flow 113

10.7 Potential Flow Analysis—Simple Plane Flow Cases 114

10.8 Potential Flow Analysis—Superposition 115

10.9 Closure 117

11. Dimensional Analysis and Similitude 118

11.1 Dimensions 118

11.2 Dimensional Analysis of Governing Differential Equations 119

11.3 The Buckingham Method 121

11.4 Geometric, Kinematic, and Dynamic Similarity 124

11.5 Model Theory 125

11.6 Closure 127

12. Viscous Flow 129

12.1 Reynolds’s Experiment 129

12.2 Drag 130

12.3 The Boundary-Layer Concept 135

12.4 The Boundary-Layer Equations 136

12.5 Blasius’s Solution for the Laminar Boundary Layer on a Flat Plate 138

12.6 Flow with a Pressure Gradient 142

12.7 von Kármán Momentum Integral Analysis 144

12.8 Description of Turbulence 147

12.9 Turbulent Shearing Stresses 149

12.10 The Mixing-Length Hypothesis 150

12.11 Velocity Distribution from the Mixing-Length Theory 152

12.12 The Universal Velocity Distribution 153

12.13 Further Empirical Relations for Turbulent Flow 154

12.14 The Turbulent Boundary Layer on a Flat Plate 155

12.15 Factors Affecting the Transition from Laminar to Turbulent Flow 157

12.16 Closure 158

13. Flow in Closed Conduits 159

13.1 Dimensional Analysis of Conduit Flow 159

13.2 Friction Factors for Fully Developed Laminar, Turbulent, and Transition Flow in Circular Conduits 161

13.3 Friction Factor and Head-Loss Determination for Pipe Flow 164

13.4 Pipe-Flow Analysis 168

13.5 Friction Factors for Flow in the Entrance to a Circular Conduit 171

13.6 Closure 174

14. Fluid Machinery 175

14.1 Centrifugal Pumps 176

14.2 Scaling Laws for Pumps and Fans 184

14.3 Axial- and Mixed-Flow Pump Configurations 187

14.4 Turbines 187

14.5 Closure 188

15. Fundamentals of Heat Transfer 189

15.1 Conduction 189

15.2 Thermal Conductivity 190

15.3 Convection 195

15.5 Combined Mechanisms of Heat Transfer 197

15.6 Closure 201

16. Differential Equations of Heat Transfer 203

16.1 The General Differential Equation for Energy Transfer 203

16.2 Special Forms of the Differential Energy Equation 206

16.3 Commonly Encountered Boundary Conditions 207

16.4 Closure 211

17.1 One-Dimensional Conduction 212

17.2 One-Dimensional Conduction with Internal Generation of Energy 218

17.3 Heat Transfer from Extended Surfaces 221

17.4 Two- and Three-Dimensional Systems 228

17.5 Closure 234

18.1 Analytical Solutions 235

18.2 Temperature-Time Charts for Simple Geometric Shapes 244

18.3 Numerical Methods for Transient Conduction Analysis 246

18.4 An Integral Method for One-Dimensional Unsteady Conduction 249

18.5 Closure 253

19. Convective Heat Transfer 254

19.1 Fundamental Considerations in Convective Heat Transfer 254

19.2 Significant Parameters in Convective Heat Transfer 255

19.3 Dimensional Analysis of Convective Energy Transfer 256

19.4 Exact Analysis of the Laminar Boundary Layer 259

19.5 Approximate Integral Analysis of the Thermal Boundary Layer 263

19.6 Energy- and Momentum-Transfer Analogies 265

19.7 Turbulent Flow Considerations 267

19.8 Closure 273

20. Convective Heat-Transfer Correlations 274

20.1 Natural Convection 274

20.2 Forced Convection for Internal Flow 282

20.3 Forced Convection for External Flow 288

20.4 Closure 295

21. Boiling and Condensation 297

21.1 Boiling 297

21.2 Condensation 302

21.3 Closure 308

22. Heat-Transfer Equipment 309

22.1 Types of Heat Exchangers 309

22.2 Single-Pass Heat-Exchanger Analysis: The Log-Mean Temperature Difference 312

22.3 Crossflow and Shell-and-Tube Heat-Exchanger Analysis 316

22.4 The Number-of-Transfer-Units (NTU) Method of Heat-Exchanger Analysis and Design 320

22.5 Additional Considerations in Heat-Exchanger Design 327

22.6 Closure 329

23.3 The Intensity of Radiation 333

23.4 Planck’s Law of Radiation 334

23.5 Stefan–Boltzmann Law 338

23.6 Emissivity and Absorptivity of Solid Surfaces 340

23.7 Radiant Heat Transfer Between Black Bodies 345

23.8 Radiant Exchange in Black Enclosures 352

23.10 Radiant Heat Transfer Between Gray Surfaces 354

23.12 The Radiation Heat-Transfer Coefficient 363

23.13 Closure 366

24. Fundamentals of Mass Transfer 367

24.1 Molecular Mass Transfer 368

24.2 The Diffusion Coefficient 377

24.3 Convective Mass Transfer 397

24.4 Closure 398

25. Differential Equations of Mass Transfer 399

25.1 The Differential Equation for Mass Transfer 399

25.2 Special Forms of the Differential Mass-Transfer Equation 402

25.3 Commonly Encountered Boundary Conditions 404

25.4 Steps for Modeling Processes Involving Molecular Diffusion 407

25.5 Closure 416

26.1 One-Dimensional Mass Transfer Independent of Chemical Reaction 417

26.2 One-Dimensional Systems Associated with Chemical Reaction 428

26.3 Two- and Three-Dimensional Systems 438

26.4 Simultaneous Momentum, Heat, and Mass Transfer 441

26.5 Closure 448

27.1 Unsteady-State Diffusion and Fick’s Second Law 449

27.2 Transient Diffusion in a Semi-Infinite Medium 450

27.3 Transient Diffusion in a Finite-Dimensional Medium under Conditions of Negligible Surface Resistance 454

27.4 Concentration-Time Charts for Simple Geometric Shapes 462

27.5 Closure 466

28. Convective Mass Transfer 467

28.1 Fundamental Considerations in Convective Mass Transfer 467

28.2 Significant Parameters in Convective Mass Transfer 470

28.3 Dimensional Analysis of Convective Mass Transfer 473

28.4 Exact Analysis of the Laminar Concentration Boundary Layer 475

28.5 Approximate Analysis of the Concentration Boundary Layer 483

28.6 Mass-, Energy-, and Momentum-Transfer Analogies 488

28.7 Models for Convective Mass-Transfer Coefficients 495

28.8 Closure 497

29. Convective Mass Transfer Between Phases 498

29.1 Equilibrium 498

29.2 Two-Resistance Theory 501

29.3 Closure 516

30. Convective Mass-Transfer Correlations 517

30.1 Mass Transfer to Plates, Spheres, and Cylinders 518

30.2 Mass Transfer Involving Flow Through Pipes 526

30.3 Mass Transfer in Wetted-Wall Columns 527

30.4 Mass Transfer in Packed and Fluidized Beds 530

30.5 Gas–Liquid Mass Transfer in Bubble Columns and Stirred Tanks 531

30.6 Capacity Coefficients for Packed Towers 534

30.7 Steps for Modeling Mass-Transfer Processes Involving Convection 535

30.8 Closure 544

31. Mass-Transfer Equipment 545

31.1 Types of Mass-Transfer Equipment 545

31.2 Gas–Liquid Mass-Transfer Operations in Well-Mixed Tanks 547

31.3 Mass Balances for Continuous-Contact Towers: Operating-Line Equations 552

31.4 Enthalpy Balances for Continuous-Contacts Towers 560

31.5 Mass-Transfer Capacity Coefficients 561

31.6 Continuous-Contact Equipment Analysis 562

31.7 Closure 576

Nomenclature 577

Chapter Homework Problems P-1

Appendices

A. Transformations of the Operators ∇ and ∇2 to Cylindrical Coordinates A-1

B. Summary of Differential Vector Operations in Various Coordinate Systems A-4

C. Symmetry of the Stress Tensor A-7

D. The Viscous Contribution to the Normal Stress A-8

E. The Navier–Stokes Equations for Constant ρ and μ in Cartesian, Cylindrical, and Spherical Coordinates A-10

F. Charts for Solution of Unsteady Transport Problems A-12

G. Properties of the Standard Atmosphere A-25

H. Physical Properties of Solids A-28

I. Physical Properties of Gases and Liquids A-31

J. Mass-Transfer Diffusion Coefficients in Binary Systems A-44

K. Lennard–Jones Constants A-47

L. The Error Function A-50

M. Standard Pipe Sizes A-51

N. Standard Tubing Gages A-53

Index I-1

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