Transport Phenomena: An Introduction to Advanced Topics

TRANSPORT PHENOMENA: An Introduction to Advanced Topics......Page 5
CONTENTS......Page 7
PREFACE......Page 11
1.1 A MESSAGE FOR THE STUDENT......Page 13
1.2 DIFFERENTIAL EQUATIONS......Page 15
1.3 CLASSIFICATION OF PARTIAL DIFFERENTIAL EQUATIONS AND BOUNDARY CONDITIONS......Page 19
1.5 VECTORS, TENSORS, AND THE EQUATION OF MOTION......Page 20
1.6 THE MEN FOR WHOM THE NAVIER–STOKES EQUATIONS ARE NAMED......Page 24
1.7 SIR ISAAC NEWTON......Page 25
REFERENCES......Page 26
2.1 INTRODUCTION......Page 27
2.2 TWO-DIMENSIONAL POTENTIAL FLOW......Page 28
2.3 NUMERICAL SOLUTION OF POTENTIAL FLOW PROBLEMS......Page 32
2.4 CONCLUSION......Page 34
REFERENCES......Page 35
3.2 HAGEN–POISEUILLE FLOW......Page 36
3.3 TRANSIENT HAGEN–POISEUILLE FLOW......Page 37
3.4 POISEUILLE FLOW IN AN ANNULUS......Page 38
3.5 DUCTS WITH OTHER CROSS SECTIONS......Page 39
3.6 COMBINED COUETTE AND POISEUILLE FLOWS......Page 40
3.7 COUETTE FLOWS IN ENCLOSURES......Page 41
3.8 GENERALIZED TWO-DIMENSIONAL FLUID MOTION IN DUCTS......Page 44
3.9 SOME CONCERNS IN COMPUTATIONAL FLUID MECHANICS......Page 47
3.10 FLOW IN THE ENTRANCE OF DUCTS......Page 48
3.12 MICROFLUIDICS: FLOW IN VERY SMALL CHANNELS......Page 50
3.12.1 Electrokinetic Phenomena......Page 51
3.12.2 Gases in Microfluidics......Page 52
3.13 FLOWS IN OPEN CHANNELS......Page 53
3.14 PULSATILE FLOWS IN CYLINDRICAL DUCTS......Page 54
3.15 SOME CONCLUDING REMARKS FOR INCOMPRESSIBLE VISCOUS FLOWS......Page 55
REFERENCES......Page 56
4.1 INTRODUCTION......Page 58
4.2 THE FLAT PLATE......Page 59
4.3 FLOW SEPARATION PHENOMENA ABOUT BLUFF BODIES......Page 62
4.4 BOUNDARY LAYER ON A WEDGE: THE FALKNER–SKAN PROBLEM......Page 64
4.5 THE FREE JET......Page 65
4.6 INTEGRAL MOMENTUM EQUATIONS......Page 66
4.7 HIEMENZ STAGNATION FLOW......Page 67
4.8 FLOW IN THE WAKE OF A FLAT PLATE AT ZERO INCIDENCE......Page 68
4.9 CONCLUSION......Page 69
REFERENCES......Page 70
5.1 INTRODUCTION......Page 71
5.2 LINEARIZED HYDRODYNAMIC STABILITY THEORY......Page 72
5.3 INVISCID STABILITY: THE RAYLEIGH EQUATION......Page 75
5.4 STABILITY OF FLOW BETWEEN CONCENTRIC CYLINDERS......Page 76
5.5.1 Transition in Hagen–Poiseuille Flow......Page 78
5.6 TURBULENCE......Page 79
5.7 HIGHER ORDER CLOSURE SCHEMES......Page 83
5.8 INTRODUCTION TO THE STATISTICAL THEORY OF TURBULENCE......Page 86
5.9 CONCLUSION......Page 91
REFERENCES......Page 93
6.1 INTRODUCTION......Page 95
6.2 STEADY-STATE CONDUCTION PROBLEMS IN RECTANGULAR COORDINATES......Page 96
6.3 TRANSIENT CONDUCTION PROBLEMS IN RECTANGULAR COORDINATES......Page 98
6.4 STEADY-STATE CONDUCTION PROBLEMS IN CYLINDRICAL COORDINATES......Page 100
6.5 TRANSIENT CONDUCTION PROBLEMS IN CYLINDRICAL COORDINATES......Page 101
6.6 STEADY-STATE CONDUCTION PROBLEMS IN SPHERICAL COORDINATES......Page 104
6.7 TRANSIENT CONDUCTION PROBLEMS IN SPHERICAL COORDINATES......Page 105
6.9.1 Conduction in Extended Surface Heat Transfer......Page 107
6.9.2 Anisotropic Materials......Page 109
6.9.3 Composite Spheres......Page 111
REFERENCES......Page 112
7.1 INTRODUCTION......Page 113
7.2 PROBLEMS IN RECTANGULAR COORDINATES......Page 114
7.2.1 Couette Flow with Thermal Energy Production......Page 115
7.2.3 The Thermal Entrance Region in Rectangular Coordinates......Page 116
7.2.4 Heat Transfer to Fluid Moving Past a Flat Plate......Page 118
7.3 PROBLEMS IN CYLINDRICAL COORDINATES......Page 119
7.3.1 Thermal Entrance Length in a Tube: The Graetz Problem......Page 120
7.4.1 Vertical Heated Plate: The Pohlhausen Problem......Page 122
7.4.2 The Heated Horizontal Cylinder......Page 123
7.4.3 Natural Convection in Enclosures......Page 124
7.4.4 Two-Dimensional Rayleigh–Benard Problem......Page 126
7.5 CONCLUSION......Page 127
REFERENCES......Page 128
8.1 INTRODUCTION......Page 129
8.1.1 Diffusivities in Gases......Page 130
8.1.2 Diffusivities in Liquids......Page 131
8.2 UNSTEADY EVAPORATION OF VOLATILE LIQUIDS: THE ARNOLD PROBLEM......Page 132
8.3.1 Diffusion into Quiescent Liquids: Absorption......Page 134
8.3.2 Absorption with Chemical Reaction......Page 135
8.3.3 Concentration-Dependent Diffusivity......Page 136
8.3.5 Diffusion Through a Membrane with Variable D......Page 137
8.4.1 The Porous Cylinder in Solution......Page 138
8.4.2 The Isothermal Cylindrical Catalyst Pellet......Page 139
8.4.4 Diffusion Through a Membrane with Edge Effects......Page 140
8.4.5 Diffusion with Autocatalytic Reaction in a Cylinder......Page 141
8.5 DIFFUSION IN SPHERICAL SYSTEMS......Page 142
8.5.1 The Spherical Catalyst Pellet with Exothermic Reaction......Page 144
8.6.1 Diffusion with Moving Boundaries......Page 145
8.6.3 Diffusion in Biological Systems......Page 147
8.6.4 Controlled Release......Page 148
REFERENCES......Page 149
9.1 INTRODUCTION......Page 151
9.2.1 Thin Film on a Vertical Wall......Page 152
9.2.2 Convective Transport with Reaction at the Wall......Page 153
9.2.3 Mass Transfer Between a Flowing Fluid and a Flat Plate......Page 154
9.3.1 Fully Developed Flow in a Tube......Page 155
9.3.2 Variations for Mass Transfer in a Cylindrical Tube......Page 156
9.3.3 Mass Transfer in an Annulus with Laminar Flow......Page 157
9.4 MASS TRANSFER BETWEEN A SPHERE AND A MOVING FLUID......Page 158
9.5.1 Using Oscillatory Flows to Enhance Interphase Transport......Page 159
9.5.2 Chemical Vapor Deposition in Horizontal Reactors......Page 161
9.5.3 Dispersion Effects in Chemical Reactors......Page 162
9.5.4 Transient Operation of a Tubular Reactor......Page 163
REFERENCES......Page 165
10.1 INTRODUCTION......Page 167
10.2 SOLUTION THROUGH ANALOGY......Page 168
10.3 ELEMENTARY CLOSURE PROCESSES......Page 170
10.4 SCALAR TRANSPORT WITH TWO-EQUATION MODELS OF TURBULENCE......Page 173
10.5 TURBULENT FLOWS WITH CHEMICAL REACTIONS......Page 174
10.5.1 Simple Closure Schemes......Page 176
10.6.1 The Fokker–Planck Equation and pdf Modeling of Turbulent Reactive Flows......Page 177
10.6.2 Transported pdf Modeling......Page 179
10.7 THE LAGRANGIAN VIEW OF TURBULENT TRANSPORT......Page 180
10.8 CONCLUSIONS......Page 183
REFERENCES......Page 184
11.1.1 Gas Bubbles in Liquids......Page 186
11.1.2 Bubble Formation at Orifices......Page 188
11.1.3 Bubble Oscillations and Mass Transfer......Page 189
11.2.1 Droplet Breakage......Page 192
11.3.2 Collision Mechanisms......Page 195
11.3.4 Dynamic Behavior of the Particle Size Distribution......Page 198
11.3.5 Other Aspects of Particle Size Distribution Modeling......Page 199
11.3.6 A Highly Simplified Example......Page 200
11.4.1 The Stefan–Maxwell Equations......Page 201
11.5 CONCLUSION......Page 203
REFERENCES......Page 204
PROBLEMS TO ACCOMPANY TRANSPORT PHENOMENA: AN INTRODUCTION TO ADVANCED TOPICS......Page 207
APPENDIX A FINITE DIFFERENCE APPROXIMATIONS FOR DERIVATIVES......Page 250
APPENDIX B ADDITIONAL NOTES ON BESSEL’S EQUATION AND BESSEL FUNCTIONS......Page 253
APPENDIX C SOLVING LAPLACE AND POISSON (ELLIPTIC) PARTIAL DIFFERENTIAL EQUATIONS......Page 257
APPENDIX D SOLVING ELEMENTARY PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS......Page 261
APPENDIX E ERROR FUNCTION......Page 265
APPENDIX F GAMMA FUNCTION......Page 267
APPENDIX G REGULAR PERTURBATION......Page 269
APPENDIX H SOLUTION OF DIFFERENTIAL EQUATIONS BY COLLOCATION......Page 272
INDEX......Page 277