Scaling Analysis In Modeling Transport And Reaction Processe

Description:
This book is unique as the first effort to expound on the subject of systematic scaling analysis. Not written for a specific discipline, the book targets any reader interested in transport phenomena and reaction processes. The book is logically divided into chapters on the use of systematic scaling analysis in fluid dynamics, heat transfer, mass transfer, and reaction processes. An integrating chapter is included that considers more complex problems involving combined transport phenomena. Each chapter includes several problems that are explained in considerable detail. These are followed by several worked examples for which the general outline for the scaling is given. Each chapter also includes many practice problems. This book is based on recognizing the value of systematic scaling analysis as a pedagogical method for teaching transport and reaction processes and as a research tool for developing and solving models and in designing experiments. Thus, the book can serve as both a textbook and a reference book.

Table of Contents:
1. Introduction. 1.1 Motivation for Using Scaling Analysis. 1.2 Organization of this Book. 2. Systematic Method for Scaling Analysis. 2.1 Introduction. 2.2 Mathematical Basis for Scaling Analysis. 2.3 Order-of-One Scaling Analysis. 2.4 The Scaling Alternative for Dimensional Analysis. 2.5 Summary. 3. Applications in Fluid Dynamics. 3.1 Introduction. 3.2 Fully Developed Laminar Flow. 3.3 Creeping and Lubrication-Flow Approximations. 3.4 Boundary-Layer Flow Approximation. 3.5 Quasi-Steady-State Flow Approximation. 3.6 Flows with End and Sidewall Effects. 3.7 Free Surface Flow. 3.8 Porous Media Flow. 3.9 Compressible Fluid Flow. 3.10 Dimensional Analysis Correlation for the Terminal Velocity of a Sphere. 3.11 Summary. 3.E Example Problems. 3.E.1 Gravity-Driven Laminar Film Flow down a Vertical Wall. 3.E.2 Flow between Two Approaching Parallel Circular Flat Plates. 3.E.3 Design of a Hydraulic Ram. 3.E.4 Rotating Disk Flow. 3.E.5 Entry Region Flow between Parallel Plates. 3.E.6 Rotating Flow in an Annulus with End Effects. 3.E.7 Impulsively Initiated Pressure-Driven Laminar Tube Flow. 3.E.8 Laminar Cylindrical Jet Flow. 3.E.9 Gravity-Driven Film Flow over Saturated Porous Media. 3.E.10 Flow in a Hollow Fiber Membrane with Permeation. 3.E.11 Falling Head Method for Determining Soil Permeability. 3.P Practice Problems. 3.P.1 Alternate Scales for Laminar Flow between Stationary and Moving Parallel Plates. 3.P.2 Laminar Flow between Stationary and Moving Parallel Plates. 3.P.3 Gravity- and Pressure-Driven Laminar Flow in a Vertical Tube. 3.P.4 Axial Flow in a Rotating Tube. 3.P.5 Laminar Flow between Converging Flat Plates. 3.P.6 Laminar Flow between Diverging Flat Plates. 3.P.7 Laminar Flow in a Diverging Nozzle. 3.P.8 Steady-State Flow between Parallel Circular Disks. 3.P.9 Unsteady-State Flow between Parallel Circular Disks . 3.P.10 Steady-State Flow between Spinning Parallel Circular Disks. 3.P.11 Lubrication-Flow Approximation for a Hydraulic Ram. 3.P.12 Flow in a Rotating Disk Viscometer. 3.P.13 Flow in an Oscillating Disk Viscometer. 3.P.14 Falling Needle Viscometer. 3.P.15 Leading Edge Considerations for Laminar Boundary-Layer Flow. 3.P.16 Laminar Boundary-Layer Flow with Blowing. 3.P.17 Laminar Boundary-Layer Flow with Suction. 3.P.18 Entry Region Laminar Flow in a Cylindrical Tube. 3.P.19 Pressure-Driven Flow in an Oscillating Tube. 3.P.20 Countercurrent Liquid-Gas Flow in a Cylindrical Tube. 3.P.21 Stratified Flow of Two Immiscible Liquid Layers. 3.P.22 Laminar Cylindrical Jet Flow. 3.P.23 Free Surface Flow down a Plane with Condensation. 3.P.24 Free Surface Flow over a Horizontal Filter. 3.P.25 Curtain-Coating Flow. 3.P.26 Flow in a Semi-Infinite Porous Media Bounded by a Flat Plate. 3.P.27 Porous Media Flow between Parallel Flat Plates. 3.P.28 Gravity-Driven Film Flow over a Saturated Porous Media. 3.P.29 Radial Flow from a Porous Cylindrical Tube. 3.P.30 Entry-Region Flow in a Tube with a Porous Annulus . 3.P.31 Steady-State Laminar Flow of a Compressible Gas. 3.P.32 Velocity Profile Distortion Effects Owing to Fluid Injection and Withdrawal . 3.P.33 Flow between Parallel Impermeable and Permeable Flat Plates. 3.P.34 Flow in an Annulus with Fluid Injection and Withdrawal. 3.P.35 Flow in a Closed-End Permeable Hollow Fiber Membrane. 3.P.36 Dimensional Analysis for Flow around a Falling Sphere. 3.P.37 Dimensional Analysis for Impulsively Initiated Laminar Tube Flow. 3.P.38 Dimensional Analysis for Flow in an Oscillating Tube. 3.P.39 Dimensional Analysis for Curtain-Coating Flow. 3.P.40 Dimensional Analysis for Flow between Parallel Membranes. 3.P.41 Dimensional Analysis for Flow in a Hollow Fiber Membrane. 4. Applications in Heat Transfer. 4.1 Introduction. 4.2 Steady-State Heat Transfer with End Effects. 4.3 Film Theory and Penetration Theory Approximations. 4.4 Small Biot Number Approximation. 4.5 Small Peclet number approximation. 4.6 Boundary-Layer or Large Peclet Number Approximation. 4.7 Heat Transfer with Phase Change. 4.8 Temperature-Dependent Physical Properties. 4.9 Thermally Driven Free Convection - the Boussinesq Approximation. 4.10 Dimensional Analysis Correlation for Cooking a Turkey. 4.11 Summary. 4.E Example Problems. 4.E.1 Steady-State Heat Conduction in a Rectangular Fin. 4.E.2 Unsteady-State Resistance Heating in a Wire. 4.E.3 Convective Heat Transfer with Injection through Permeable Walls. 4.E.4 Steady-State Heat Transfer to Falling Film Flow. 4.E.5 Unsteady-State Heat Transfer from a Sphere at Large Biot Numbers. 4.E.6 Evaporative Cooling of a Liquid Film. 4.E.7 Free convection Heat Transfer Adjacent to a Vertical Heated Flat Plate. 4.E.8 Dimensional Analysis Correlation for Electrical Heat Generation in a Wire. 4.P Practice Problems. 4.P.1 Steady-State Heat Conduction in a Slab with Specified Cooling Flux. 4.P.2 Steady-State Conduction in a Slab with Specified Heat Flux. 4.P.3 Steady-State Heat Conduction in a Rectangular Parallelepiped. 4.P.4 Steady-State Conduction in a Cylinder with Specified Temperatures at its Boundaries. 4.P.5 Steady-State Conduction in an Annulus with Specified Temperatures at its Boundaries. 4.P.6 Steady-State Heat Conduction in a Circular Fin. 4.P.7 Unsteady-State Axial Heat Conduction in a Solid Cylinder. 4.P.8 Unsteady-State Radial Heat Conduction in a Solid Cylinder. 4.P.9 Unsteady-State Radial Heat Cconduction in a Spherical Shell. 4.P.10 Steady-State Conduction in a Cylinder with External Phase Convection. 4.P.11 Unsteady-State Heat Transfer to a Sphere at Small Biot Numbers. 4.P.12 Unsteady-State Heat Transfer in a Solid Sphere. 4.P.13 Unsteady-State Convective Heat Transfer to a Plane Wall. 4.P.14 Unsteady-State Convective Heat Transfer to a Solid Cylinder. 4.P.15 Entrance Effect Limitations in Laminar Slit Flow. 4.P.16 Convective Heat Transfer for Fully Developed Laminar Flow between Heated Parallel Flat Plates. 4.P.17 Entrance Effect Limitations in the Thermal Boundary-Layer Approximation for Falling Film Flow. 4.P.18 Thermal Boundary-Layer Heat Transfer for Fully Developed Laminar Flow between Heated Parallel Flat Plates. 4.P.19 Heat Transfer from a Hot Inviscid Gas to Fully Developed Laminar Falling Film Flow. 4.P.20 Thermal Boundary-Layer Development along a Heated Flat Plate. 4.P.21 Thermal Boundary-Layer Development with an Unheated Entry Region. 4.P.22 Thermal Boundary-Layer Development with Flux Condition. 4.P.23 Thermal Boundary-Layer Development with Suction. 4.P.24 Evaporative Cooling of a Liquid Film with Radiative Heat Transfer. 4.P.25 Melting of Frozen Soil Owing to Constant Radiative Heat Flux. 4.P.26 Melting of Frozen Soil Initially at Sub-Freezing Temperature. 4.P.27 Freezing of Water-Saturated Soil Initially above its Freezing Temperature. 4.P.28 Freezing of Water-Saturated Soil Overlaid by Snow. 4.P.29 Heat Conduction in a Cylinder with a Temperature-Dependent Thermal Diffusivity. 4.P.30 Entry Region Effects for Free Convection Heat Transfer adjacent to a Vertical Heated Flat Plate. 4.P.31 Free Convection from a Heated Vertical Plate with Wall Suction. 4.P.32 Correlation for Temperature in a Slab with Heat Generation. 4.P.33 Correlation for Steady-State Heat Transfer from a Sphere. 4.P.34 Correlation for Hot Wire Anemometer Performance. 4.P.35 Correlation for Unsteady-State Heat Transfer to a Sphere having a Temperature-Dependent Thermal Conductivity. 4.P.36 Characterization of Home Freezer Performance. 5. Applications in Mass Transfer. 5.1 Introduction. 5.2 Film Theory Approximation. 5.3 Penetration Theory Approximation. 5.4 Small Peclet Number Approximation for Laminar Flow with Homogeneous Reaction. 5.5 Small Damkohler Number Approximation for Laminar Flow with Heterogeneous Reaction. 5.6 Large Peclet Number Approximation for Mass Transfer in Falling Film Flow. 5.7 Quasi-Steady-State Approximation for Mass Transfer Owing to Evaporation . 5.8 Membrane Permeation with a Non-Constant Diffusivity. 5.9 Solutally Driven Free Convection Owing to Evapotranspiration from a Vertical Cylinder. 5.10 Dimensional Analysis for a Membrane-Lung Oxygenator . 5.11 Summary. 5.E Example Problems. 5.E.1 Evaporative Casting of a Polymer Film . 5.E.2 Taylor Dispersion. 5.E.3 Convective Diffusion in Tapered Pore . 5.E.4 Dissolution of a Spherical Capsule. 5.E.5 Mass Transfer to a Rotating Disk ? a Uniformly Accessible Surface. 5.E.6 Field-Flow Fractionation. 5.E.7 Mass Transfer in a Membrane Permeation Cell. 5.E.8 Large Damkohler Number Approximation for Lami