Scaling Analysis in Modeling Transport and Reaction Processes: A Systematic Approach to Model Building and the Art of Approximation

SCALING ANALYSIS IN MODELING TRANSPORT AND REACTION PROCESSES......Page 3
CONTENTS......Page 9
Preface......Page 13
Acknowledgments......Page 17
1.1 Motivation for Using Scaling Analysis......Page 19
1.2 Organization of the Book......Page 23
2.2 Mathematical Basis for Scaling Analysis......Page 25
2.3 Order-of-One Scaling Analysis......Page 26
2.4 Scaling Alternative for Dimensional Analysis......Page 31
2.5 Summary......Page 36
3.1 Introduction......Page 37
3.2 Fully Developed Laminar Flow......Page 38
3.3 Creeping- and Lubrication-Flow Approximations......Page 44
3.4 Boundary-Layer-Flow Approximation......Page 50
3.5 Quasi-Steady-State-Flow Approximation......Page 56
3.6 Flows with End and Sidewall Effects......Page 61
3.7 Free Surface Flow......Page 63
3.8 Porous Media Flow......Page 70
3.9 Compressible Fluid Flow......Page 74
3.10 Dimensional Analysis Correlation for the Terminal Velocity......Page 80
3.11 Summary......Page 85
3.E Example Problems......Page 88
3.P Practice Problems......Page 128
4.1 Introduction......Page 163
4.2 Steady-State Heat Transfer with End Effects......Page 164
4.3 Film and Penetration Theory Approximations......Page 171
4.4 Small Biot Number Approximation......Page 177
4.5 Small Peclet Number Approximation......Page 181
4.6 Boundary-Layer or Large Peclet Number Approximation......Page 185
4.7 Heat Transfer with Phase Change......Page 191
4.8 Temperature-Dependent Physical Properties......Page 198
4.9 Thermally Driven Free Convection: Boussinesq Approximation......Page 201
4.10 Dimensional Analysis Correlation for Cooking a Turkey......Page 205
4.11 Summary......Page 211
4.E Example Problems......Page 214
4.P Practice Problems......Page 242
5.1 Introduction......Page 270
5.2 Film Theory Approximation......Page 271
5.3 Penetration Theory Approximation......Page 277
5.4 Small Peclet Number Approximation......Page 279
5.5 Small Damköhler Number Approximation......Page 284
5.6 Large Peclet Number Approximation......Page 287
5.7 Quasi-Steady-State Approximation......Page 291
5.8 Membrane Permeation with Nonconstant Diffusivity......Page 295
5.9 Solutally Driven Free Convection Due to Evapotranspiration......Page 299
5.10 Dimensional Analysis for a Membrane-Lung Oxygenator......Page 305
5.11 Summary......Page 311
5.E Example Problems......Page 315
5.P Practice Problems......Page 354
6.1 Introduction......Page 378
6.2 Concept of the Microscale Element......Page 380
6.3 Scaling the Microscale Element......Page 382
6.5 Intermediate Reaction Regime......Page 389
6.6 Fast Reaction Regime......Page 390
6.7 Instantaneous Reaction Regime......Page 391
6.8 Scaling the Macroscale Element......Page 395
6.9 Kinetic Domain of the Slow Reaction Regime......Page 398
6.11 Implications of Scaling Analysis for Reactor Design......Page 399
6.12 Mass-Transfer Coefficients for Reacting Systems......Page 405
6.13 Design of a Continuous Stirred Tank Reactor......Page 408
6.14 Design of a Packed Column Absorber......Page 412
6.15 Summary......Page 415
6.P Practice Problems......Page 417
7.1 Introduction......Page 432
7.2 Design of a Membrane Lung Oxygenator......Page 433
7.3 Pulsed Single-Bed Pressure-Swing Adsorption......Page 442
7.4 Thermally Induced Phase-Separation Process......Page 456
7.5 Fluid-Wall Aerosol Flow Reactor for Hydrogen Production......Page 466
7.6 Summary......Page 482
7.P Practice Problems......Page 485
Appendix A Sign Convention for the Force on a Fluid Particle......Page 498
B.2 Equations of Motion......Page 500
B.4 Thermal Energy Equation......Page 501
B.5 Equation of Continuity for a Binary Mixture......Page 502
C.1 Rectangular Coordinates......Page 504
C.3 Spherical Coordinates......Page 505
D.1 Rectangular Coordinates......Page 507
D.2 Cylindrical Coordinates......Page 508
D.3 Spherical Coordinates......Page 510
E.2 Cylindrical Coordinates......Page 512
E.3 Spherical Coordinates......Page 513
F.1 Rectangular Coordinates......Page 514
F.3 Spherical Coordinates......Page 515
G.1 Rectangular Coordinates......Page 517
G.2 Cylindrical Coordinates......Page 518
G.3 Spherical Coordinates......Page 520
H.2 Gauss Ostrogradskii Divergence Theorem......Page 522
Notation......Page 524
Index......Page 533