Scaling Analysis in Modeling Transport and Reaction Processes

William B. Krantz, PhD, PE, is the Isaac M. Meyer Chair Professor in the Department of Chemical and Biomolecular Engineering at the National University of Singapore, Rieveschl Ohio Eminent Scholar and Professor Emeritus at the University of Cincinnati, and President's Teaching Scholar and Professor Emeritus at the University of Colorado. He is a Fellow of the American Association for the Advancement of Science, American Institute of Chemical Engineers, and the American Society for Engineering Education. He has been the recipient of a Guggenheim and three Fulbright-Hayes fellowships. Dr. Krantz is the editor of three research monographs, the author of over 200 technical papers, and the coinventor on five patents.

• Preface xiAcknowledgments xv1 Introduction 11.1 Motivation for Using Scaling Analysis 11.2 Organization of the Book 52 Systematic Method for Scaling Analysis 72.1 Introduction 72.2 Mathematical Basis for Scaling Analysis 72.3 Order-of-One Scaling Analysis 82.4 Scaling Alternative for Dimensional Analysis 132.5 Summary 183 Applications in Fluid Dynamics 193.1 Introduction 193.2 Fully Developed Laminar Flow 203.3 Creeping- and Lubrication-Flow Approximations 263.4 Boundary-Layer-Flow Approximation 323.5 Quasi-Steady-State-Flow Approximation 383.6 Flows with End and Sidewall Effects 433.7 Free Surface Flow 453.8 Porous Media Flow 523.9 Compressible Fluid Flow 563.10 Dimensional Analysis Correlation for the Terminal Velocity 623.11 Summary 673.e Example Problems 703.p Practice Problems 1104 Applications in Heat Transfer 1454.1 Introduction 1454.2 Steady-State Heat Transfer with End Effects 1464.3 Film and Penetration Theory Approximations 1534.4 Small Biot Number Approximation 1594.5 Small Peclet Number Approximation 1634.6 Boundary-Layer or Large Peclet Number Approximation 1674.7 Heat Transfer with Phase Change 1734.8 Temperature-Dependent Physical Properties 1804.9 Thermally Driven Free Convection: Boussinesq Approximation 1834.10 Dimensional Analysis Correlation for Cooking a Turkey 1874.11 Summary 1934.e Example Problems 1964.p Practice Problems 2245 Applications in Mass Transfer 2525.1 Introduction 2525.2 Film Theory Approximation 2535.3 Penetration Theory Approximation 2595.4 Small Peclet Number Approximation 2615.5 Small Damköhler Number Approximation 2665.6 Large Peclet Number Approximation 2695.7 Quasi-Steady-State Approximation 2735.8 Membrane Permeation with Nonconstant Diffusivity 2775.9 Solutally Driven Free Convection Due to Evapotranspiration 2815.10 Dimensional Analysis for a Membrane-Lung Oxygenator 2875.11 Summary 2935.e Example Problems 2975.p Practice Problems 3366 Applications in Mass Transfer with Chemical Reaction 3606.1 Introduction 3606.2 Concept of the Microscale Element 3626.3 Scaling the Microscale Element 3646.4 Slow Reaction Regime 3716.5 Intermediate Reaction Regime 3716.6 Fast Reaction Regime 3726.7 Instantaneous Reaction Regime 3736.8 Scaling the Macroscale Element 3776.9 Kinetic Domain of the Slow Reaction Regime 3806.10 Diffusional Domain of the Slow Reaction Regime 3816.11 Implications of Scaling Analysis for Reactor Design 3816.12 Mass-Transfer Coefficients for Reacting Systems 3876.13 Design of a Continuous Stirred Tank Reactor 3906.14 Design of a Packed Column Absorber 3946.15 Summary 3976.p Practice Problems 3997 Applications in Process Design 4147.1 Introduction 4147.2 Design of a Membrane Lung Oxygenator 4157.3 Pulsed Single-Bed Pressure-Swing Adsorption 4247.4 Thermally Induced Phase-Separation Process 4387.5 Fluid-Wall Aerosol Flow Reactor for Hydrogen Production 4487.6 Summary 4647.p Practice Problems 467Appendix A Sign Convention for the Force on a Fluid Particle 480Appendix B Generalized Form of the Transport Equations 482B. 1 Continuity Equation 482B. 2 Equations of Motion 482B. 3 Equations of Motion for Porous Media 483B. 4 Thermal Energy Equation 483B. 5 Equation of Continuity for a Binary Mixture 484Appendix c Continuity Equation 486C. 1 Rectangular Coordinates 486C. 2 Cylindrical Coordinates 487C. 3 Spherical Coordinates 487Appendix d Equations of Motion 489D. 1 Rectangular Coordinates 489D. 2 Cylindrical Coordinates 490D. 3 Spherical Coordinates 492Appendix E Equations of Motion for Porous Media 494E. 1 Rectangular Coordinates 494E. 2 Cylindrical Coordinates 494E. 3 Spherical Coordinates 495Appendix F Thermal Energy Equation 496F. 1 Rectangular Coordinates 496F. 2 Cylindrical Coordinates 497F. 3 Spherical Coordinates 497Appendix G Equation of Continuity for a Binary Mixture 499G.1 Rectangular Coordinates 499G. 2 Cylindrical Coordinates 500G. 3 Spherical Coordinates 502Appendix H Integral Relationships 504H.1 Leibnitz Formula for Differentiating an Integral 504H.2 Gauss Ostrogradskii Divergence Theorem 504Notation 506Index 515