An Introduction to Mass and Heat Transfer Principles of Analysis and Design

by Middleman, Stanley

• ISBN13: 9780471111764
• ISBN10: 0471111767
• Edition: 1st
• Format: Paperback
• Copyright: 1997-10-30
• Publisher: Wiley

Summary

This highly recommended book on transport phenomena shows readers how to develop mathematical representations (models) of physical phenomena. The key elements in model development involve assumptions about the physics, the application of basic physical principles, the exploration of the implications of the resulting model, and the evaluation of the degree to which the model mimics reality. This book also expose readers to the wide range of technologies where their skills may be applied.

Author Biography

Stanley Middleman is the author of An Introduction to Mass and Heat Transfer: Principles of Analysis and Design, published by Wiley.

Table of Contents

CHAPTER 1 WHAT IS MASS TRANSFER?	3	(5)
1.1 Examples of Mass Transfer	4	(2)
1.1.1 Design of a Sustained Release System for Control of Insects	4	(1)
1.1.2 Design of a Bubbler for Delivering Dopants to a CVD Reactor	4	(1)
1.1.3 Design of a Dryer for a Polymeric Coating	5	(1)
1.1.4 Design of an Artificial Kidney: An Enzyme/Bead Reactor	5	(1)
1.2 Reexamination and Overview	6	(2)
CHAPTER 2 FUNDAMENTALS OF DIFFUSIVE MASS TRANSFER	8	(31)
2.1 Concentrations, Velocities, and Fick's Law of Diffusion	8	(11)
Example 2.1.1 Diffusion of Napthalene in a Narrow Tube	9	(2)
Example 2.1.2 Calculation of Diffusion Velocities in a "Static" System	11	(1)
Example 2.1.3 Mass Flow Without Molar Flow	12	(1)
Example 2.1.4 Diffusion with a Reaction on a Surface	13	(1)
Example 2.1.5 Diffusion across a Thin Barrier Separating Two Fluids	14	(2)
Example 2.1.6 Calculation of b(p) from Solubility Data	16	(1)
Example 2.1.7 Calculation of D(AB) from Solubility b(p) and Permeability K	17	(1)
Example 2.1.8 Effectiveness of a Vapor Barrier	17	(1)
Example 2.1.9 Diffusion of a Diatomic Gas Through a Metal Barrier	18	(1)
2.2 Estimation of Diffusion Coefficients	19	(5)
2.2.1 Binary Diffusion in Gases at Low Pressure	19	(2)
Example 2.2.1 Diffusivity of H(2) in Argon	21	(1)
2.2.2 Diffusion in Liquids	22	(1)
Example 2.2.2 Estimate the Diffusivity of Benzoic Acid in Water at 25degree C	23	(1)
2.3 Application of These Principles to Analysis and Design of a Sustained Release Hollow-Fiber System	24	(5)
2.3.1 Assessment of Some Assumptions of the Model	28	(1)
2.4 The Quasi-Steady Approximation	29	(2)
Summary	31	(1)
Problems	31	(8)
CHAPTER 3 STEADY, AND QUASI-STEADY MASS TRANSFER	39	(70)
3.1 Mass Balance on a Species	39	(3)
3.2 Boundary Conditions	42	(30)
Example 3.2.1 Mass-Transfer Controlled by External Diffusion Resistance	43	(3)
Example 3.2.2 Diffusion Controlled by External Convection	46	(1)
Example 3.2.3 Respiration of a Spherical Cell	47	(2)
Example 3.2.4 Life Support for a Spherical Organism: First-Order Kinetics for Respiration	49	(3)
Example 3.2.5 Control of Organism Growth	52	(1)
Example 3.2.6 A Steady State Convection/Diffusion Problem	53	(3)
Example 3.2.7 Design of an Outlet for a Reactor	56	(7)
Example 3.2.8 Diffusion Through a Film Within Which There is a Homogeneous Reaction	63	(4)
Example 3.2.9 Diffusion with Second-Order Reaction	67	(3)
Example 3.2.10 A Design for Enhanced Oxygen Transfer	70	(2)
3.3 Design of an Artificial Kidney Utilizing Urease in Polymeric Beads	72	(6)
3.4 A Model to Aid the Interpretation of Data on the Dissolution of "Nuclear Waste" Glass	78	(4)
3.5 Analysis of "Barrier Films" for Packaging	82	(6)
Example 3.5.1 Prevention of Water Intrusion into a Food Package	82	(4)
Example 3.5.2 Retention of Carbonation in a Soda Bottle	86	(2)
3.6 Mass Transfer Issues in the Production of Fuel Pellets for a Controlled Fusion Reactor	88	(3)
Example 3.6.1 Leakage from Glass Microspheres in Storage	89	(2)
3.7 The Use of a Simple Mass Transfer Model to Guide a Strategy for a Medical Procedure: The Repair of Retinal Detachment	91	(5)
Summary	96	(1)
Problems	96	(13)
CHAPTER 4 UNSTEADY STATE (TRANSIENT) MASS TRANSFER	109	(95)
4.1 Unsteady State Mass Transfer	109	(4)
4.1.1 Some Examples of Unsteady State Mass Transfer Problems	112	(1)
Example A Unsteady Diffusion Across a Membrane	112	(1)
Example B A Dissolving Particle	112	(1)
Example C Evaporation of a Solvent from a Film	112	(1)
Example D Stroke and Cell Death	112	(1)
Example E Doping of a Semiconductor FIlm	113	(1)
4.2 General Transient Diffusion: No Reaction or Internal Convection	113	(28)
Example 4.2.1 Unsteady Diffusion Across a Membrane Test Cell	118	(5)
Example 4.2.2 A Dissolving Particle (an External Diffusion Problem)	123	(5)
Example 4.2.3 Transient Evaporation of Solvent from a Sheet of Polymer	128	(2)
4.2.1 Transient Diffusion for Very Short Times	130	(6)
Example 4.2.4 A Device for Treatment of Glaucoma	136	(2)
Example 4.2.5 Doping a Semiconductor Film	138	(1)
Example 4.2.6 Comparison of Two Methods for Measurement of Diffusivity of a Species through a Membrane	139	(2)
4.3 Internal Versus External Resistances	141	(8)
Example 4.3.1 Decaffeination of Coffee Beans	143	(2)
Example 4.3.2 Drying of Paper	145	(3)
Example 4.3.3 Evaporation of Solute from a Small Water Droplet	148	(1)
4.4 Negligible Internal Resistance	149	(14)
Example 4.4.1 Kinetics of a Sustained-Release Drug Delivery System	151	(3)
Example 4.4.2 Dissolution of Solid Particles in Liquids	154	(3)
Example 4.4.3 Control of a Toxic Gas Release in a Closed Space	157	(6)
4.5 Diffusion Limitations in the Decontamination of Soil	163	(5)
Example 4.5.1 Desorption of Tetrachlorobenzene from a River Sediment: Intraparticle Diffusion Controlling	165	(3)
4.6 The Dynamics of Transport through Landfill Barriers	168	(8)
Example 4.6.1 Diffusion Across a Clay Liner	171	(1)
Example 4.6.2 Diffusion Across a Clay Liner: Near Steady State	172	(3)
Example 4.6.3 Contamination of an Aquifer by a Landfill	175	(1)
4.7 Transient Diffusion with a Reaction on the Boundaries	176	(2)
Summary	178	(1)
Problems	179	(25)
CHAPTER 5 DIFFUSION WITH LAMINAR CONVECTION	204	(48)
5.1 The Falling Film Evaporator	204	(11)
Example 5.1.1 Design of a Falling Film Absorber for Oxygen	210	(5)
5.2 Dissolution of a Solid Film by a Flowing Solvent	215	(7)
Example 5.2.1 Cleaning a Solid Residue from Inside a Tube	218	(4)
5.3 The Artificial Kidney (Dialysis Analysis)	222	(12)
Example 5.3.1 Determination of the Permeability of a Dialysis Membrane	230	(1)
Example 5.3.2 Required Size of a Dialysis Unit for Removal of a Solute	231	(1)
Example 5.3.3 The Effect of Dialysis on the Concentration of a Toxin in the Body	232	(2)
5.4 Diffusion-Controlled Film Growth by Chemical Vapor Deposition	234	(4)
5.5 Burning of a Coal Particle	238	(8)
Example 5.5.1 A Model for Fuel Particle Burnout	244	(2)
Summary	246	(1)
Problems	246	(6)
CHAPTER 6 CONVECTIVE MASS TRANSFER COEFFICIENTS	252	(54)
6.1 Some Examples of Convective Mass Transfer	252	(3)
Example 6.1.1 Spinning Fibers from Solution	252	(1)
Example 6.1.2 Reaction in a Catalytic Converter	253	(1)
Example 6.1.3 Burning of a Coal Particle in a Fluidized Bed Furnace	253	(1)
Example 6.1.4 Oxygen Transfer from Bubbles to Liquid	254	(1)
6.2 Film Theory	255	(3)
6.3 Boundary Layer Theory for Mass Transfer from a Flat Plate (The Integral Method)	258	(5)
6.3.1 Momentum Boundary Layer Analysis	259	(2)
6.3.2 Concentration Boundary Layer Analysis	261	(2)
6.4 Predictions of Sherwood Number for Transfer to Laminar Films	263	(9)
Example 6.4.1 Mass Transfer in Flow through a Parallel Plate Channel: Definition of a Concentration Driving Force	267	(3)
Example 6.4.2 Evaporation of Naphthalene from Planar Boundaries of a Channel when the Flow is Laminar	270	(1)
Example 6.4.3 Evaporation of Naphthalene from Planar Boundaries of a Channel when the Flow is Turbulent	271	(1)
6.5 Transfer to a Laminar Falling Film with Gas Side Resistance	272	(5)
Example 6.5.1 Conversion of Evaporation Rate Data to Sherwood Number Data	275	(2)
6.6 Mass Transfer into Aerated Vessels	277	(7)
6.6.1 Bubble Dynamics	277	(2)
6.6.2 Capacity Coefficients in Aerated Systems	279	(2)
Example 6.6.1 Gas Flow to Sustain Growth in a Fermentor	281	(2)
Example 6.6.2 Experimental Determination of k(c)a(v)	283	(1)
6.7 Mass Transfer in Parallel Plate Reverse Osmosis System	284	(4)
Example 6.7.1 Effect of Concentration Polarization on Permeate Flow	286	(2)
6.8 Mass Transfer to Particles in a Turbulent Stirred Tank	288	(3)
Example 6.8.1 Particle Dissolution in an Agitated Tank: Mass Transfer Coefficient	290	(1)
Example 6.8.2 Particle Dissolution in an Agitated Tank: Dissolution Time	290	(1)
6.9 Mass Transfer in Fluidized Bed Furnace	291	(2)
Summary	293	(2)
Problems	295	(11)
CHAPTER 7 CONTINUOUS GAS/LIQUID CONTACTORS	306	(29)
7.1 Two-Resistance Film Theory	307	(5)
7.2 Analysis of Continuous Contact Transfer	312	(5)
7.3 The Performance Equation for Dilute Systems	317	(5)
Example 7.3.1 How to Find K(y)a(v) from Performance Data on a Column	318	(2)
Example 7.3.2 Find Tower Height for a Specified Performance	320	(2)
7.4 Minimum Flowrate Ratio (L/G)(min)	322	(1)
7.5 Maximum Vapor Flowrate (Flooding)	323	(2)
Example 7.5.1 Choosing a Tower Diameter	324	(1)
7.6 A Design Procedure for Linear Systems	325	(3)
Example 7.6.1 Find the Required Tower Height	326	(2)
7.7 Correlations for Performance Characteristics of Packed Towers	328	(4)
Example 7.7.1 Use of Empirical Correlations	329	(2)
Example 7.7.2 Effect of Flowrates on the Height of a Gas Phase Transfer Unit (H(G))	331	(1)
Summary	332	(1)
Problems	332	(3)
CHAPTER 8 MEMBRANE TRANSFER AND MEMBRANE SEPARATION SYSTEMS	335	(32)
8.1 Introduction	335	(1)
8.2 Mass Transfer Analyses of Some Membrane Phenomena	336	(3)
Example 8.2.1 Calculation of the Pure Water Permeability	337	(1)
Example 8.2.2 Rejection Coefficient of a Membrane	338	(1)
8.3 A Solution-Diffusion Model of Steady Membrane Transport	339	(9)
Example 8.3.1 Coefficients for the Membrane of Examples 8.2.1 and 8.2.2	343	(1)
Example 8.3.2 Mass Transfer Coefficient for the Membrane	343	(1)
Example 8.3.3 Performance of a Tubular Membrane	344	(4)
8.4 Design Equations for a Tubular Membrane System with Large Fractional Recovery	348	(5)
Example 8.4.1 Performance Analysis of a Tubular Membrane System with No Polarization Effects	350	(3)
8.5 Hollow Fiber Membrane Systems	353	(6)
Example 8.5.1 Performance Characteristics of a Hollow Fiber Membrane	356	(3)
Summary	359	(1)
Problems	359	(8)
CHAPTER 9 INTRODUCTION	367	(4)
9.1 Some Heat Transfer Problems	367	(4)
9.1.1 Production of a Polymeric Film	367	(1)
9.1.2 Desalination by Vaporization/Condensation	367	(1)
9.1.3 A Solar Hot Water Heater	368	(1)
9.1.4 Contaminant Entrainment by Buoyancy	369	(2)
CHAPTER 10 HEAT TRANSFER BY CONDUCTION	371	(30)
10.1 Fourier's Law of Conductive Heat Transfer	371	(6)
10.1.1 A Design Problem, Measurement of k	373	(2)
10.1.2 Conductive Heat Loss Across a Window Pane	375	(2)
10.2 The Composite Solid	377	(6)
10.2.1 The Planar Solid	377	(2)
10.2.2 A Convective Boundary Condition	379	(1)
10.2.3 Heat Transfer Across a Composite Cylindrical Solid	380	(2)
10.2.4 The Use of Additional Material to Reduce Heat Loss	382	(1)
10.3 Finned Heat Exchangers	383	(9)
10.3.1 Analysis of a Simple Finned Surface	383	(4)
Example 10.3.1 Finding XXX and the Heat Loss from a Finned Surface	387	(1)
Example 10.3.2 Calculation of Improved Heat Transfer with Fins	388	(3)
Example 10.3.3 Optimum Fin Length for Fixed Weight	391	(1)
10.4 Conduction with Internal Heat Generation	392	(3)
Example 10.4.1 Convective Cooling of an Insulated Wire	394	(1)
Summary	395	(1)
Problems	395	(6)
CHAPTER 11 TRANSIENT HEAT TRANSFER BY CONDUCTION	401	(32)
11.1 Unsteady Heat Transfer Across the Boundaries of Solids	401	(14)
11.1.1 The Solid with Uniform Internal Temperature	401	(1)
Example 11.1.1 A Design Problem: Measurement of the Convective Transfer Coefficient	402	(3)
11.1.2 Unsteady Heat Conduction Within Bounded Solids	405	(7)
Example 11.1.2 Cooling of a Long Copper Cylinder	412	(1)
Example 11.1.3 Time to Cool a Solid Sphere, at any Biot Number	413	(1)
Example 11.1.4 Dependence of Cooling Rate on Sphere Radius	414	(1)
Example 11.1.5 Temperature Across the Radius of a Sphere	415	(1)
11.2 The Heat Conduction Equation	415	(4)
Example 11.2.1 Cooling of a Long Plastic Cylinder	417	(2)
11.3 Heat Transfer at the Surface of a Semi-Infinite Medium	419	(5)
Example 11.3.1 Surface Temperature of a Cooling Sheet	421	(3)
11.4 Modeling and Dimensional Analysis; Geometrical Similarity	424	(3)
Example 11.4.1 Experimental Design and Analysis of Data	425	(2)
Summary	427	(1)
Problems	428	(5)
CHAPTER 12 CONVECTIVE HEAT TRANSFER	433	(73)
12.1 Some Preliminary Concepts Regarding Convective Heat Transfer	433	(6)
Example 12.1.1 Cooling and Solidification of Carbon Fibers	433	(1)
Example 12.1.2 Temperature Control of an Evaporator	434	(1)
Example 12.1.3 Temperature Control in a Blood Oxygenator	434	(1)
12.1.1 Film Theory	435	(4)
12.2 An Exact Laminar Boundary Layer Theory: Heat Transfer from a Flat Plate	439	(4)
12.3 Correlations of Heat Transfer Data	443	(6)
12.3.1 Turbulent Flow Inside Pipes	443	(1)
12.3.2 Flow Outside and Across Pipes and Cylinders	444	(1)
12.3.3 Flow Past Single Spheres	445	(1)
12.3.4 The Temperature Dependence of Physical Properties Used in the Correlations	445	(1)
12.3.5 A Simple Model of the Effect of a Temperature-Dependent Viscosity	446	(3)
12.4 Heat Transfer Analysis in Pipe Flow	449	(8)
12.4.1 The Basic Heat Balance	449	(3)
Example 12.4.1 Flow Through a Chilled Tube	452	(2)
Example 12.4.2 A Tubular Heater for Air	454	(1)
12.4.2 Constant Heat Flux at the Pipe Surface	455	(1)
Example 12.4.3 A Tubular Heater for Air: Constant Heat Input	456	(1)
12.5 Models of Convection in Laminar Flows	457	(12)
12.5.1 A Parallel Plate Heat Exchanger with Isothermal Surfaces	458	(3)
12.5.2 The Thermal Entry Region of a Parallel Plate Heat Exchanger with Isothermal Surfaces	461	(3)
12.5.3 The Tubular Heat Exchanger	464	(1)
12.5.4 Heat Transfer to a Tube with Constant Surface Flux	465	(1)
Example 12.5.1 Design of a Solar Heater: Constant h	466	(1)
Example 12.5.2 Design of a Parallel Tube Heat Exchanger	467	(2)
12.6 Design and Analysis of a Laminar Flow Heat Exchanger for a Blood Substitute	469	(3)
Example 12.6.1 Required Length for a Compact Laminar Flow Heat Exchanger	469	(2)
Example 12.6.2 Temperature Requirement for the External Heat Transfer Fluid	471	(1)
12.7 Design of a Continuous Sterilizer for a Bioprocess Waste Stream	472	(7)
Example 12.7.1 Estimating Heat Transfer Characteristics in a Pilot Scale Sterilization System	474	(3)
Example 12.7.2 A More Exact Analysis of the Performance of a Pilot Scale Sterilization System	477	(2)
12.8 Convective Heat Transfer from a Cylindrical Fiber in Steady Axial Motion	479	(8)
Example 12.8.1 Temperature Uniformity across the Radius of a Fiber	483	(2)
Example 12.8.2 Evaluation of the Total Cooling of a Fiber	485	(2)
12.9 Optimal Geometry for Convective Cooling	487	(9)
12.9.1 Optimal Design for Multiple Parallel Isothermal Surfaces	487	(4)
Example 12.9.1 Conditions for Optimum Performance	491	(1)
Example 12.9.2 Design of an Optimal Cooling System	492	(1)
12.9.2 Optimal Design and Operation for a Single Heat-Generating Surface	492	(2)
Example 12.9.3 Sensitivity of Performance to Deviations from Optimal Design	494	(2)
Summary	496	(1)
Problems	496	(10)
CHAPTER 13 SIMPLE HEAT EXCHANGERS	506	(44)
13.1 Introduction	506	(1)
13.2 Double-Pipe Heat Exchanger Analysis	506	(11)
Example 13.2.1 Maximum Cooling Capacity of an Exchanger of Fixed Area	508	(2)
Example 13.2.2 Find the Required Length of a Heat Exchanger with Specified Flows: Turbulent Flow in Both Streams	510	(4)
Example 13.2.3 Find the Required Length of a Heat Exchanger with Specified Flows: Laminar Flow on One Side	514	(3)
13.3 Other Heat Exchanger Configurations	517	(5)
Example 13.3.1 The 1 Shell Pass/2 Tube Pass Exchanger	517	(5)
13.4 Effectiveness Concept for Heat Exchangers	522	(11)
Example 13.4.1 Performance of a "Cross-Flow" Heat Exchanger (One Temperature, One Flow Unknown)	525	(1)
Example 13.4.2 Comparison of F(R, P) and NTU(XXX) (Both Flowrates Specified; Two Unknown Temperatures)	526	(2)
Example 13.4.3 Performance of a Heat Exchanger	528	(1)
Example 13.4.4 Heat Exchanger with Condensation	529	(1)
Example 13.4.5 Series/Parallel Exchangers	530	(2)
Example 13.4.6 Exchanger with a Bleed-Off Stream	532	(1)
13.5 Optimum Outlet Temperature	533	(4)
Example 13.5.1 Calculation of the Optimum Outlet Water Temperature	536	(1)
13.6 Analysis and Design of a System for Heating a Gelatin Solution	537	(6)
13.6.1 Transient Analysis of the Batch System	537	(2)
Example 13.6.1 Performance of a Plate Heat Exchanger	539	(1)
13.6.2 Determination of Individual Side Coefficients	540	(2)
Example 13.6.2 Design of a Heating System for Gelatin	542	(1)
Summary	543	(1)
Problems	544	(6)
CHAPTER 14 NATURAL CONVECTION HEAT TRANSFER	550	(34)
14.1 Introduction	550	(3)
14.2 Buoyancy-Induced Flow: Natural Convection in a Confined Region	553	(3)
Example 14.2.1 Analysis of Natural Convection Between Infinite Parallel Plates	553	(2)
Example 14.2.2 Buoyancy-Driven Convective Velocities in Water and Air	555	(1)
14.3 Buoyancy-Induced Flow: Natural Convection in an Unconfined Region	556	(6)
14.4 Correlations of Data for Free Convection Heat Transfer Coefficients	562	(5)
Example 14.4.1 Heat Loss from a Horizontal Pipe	564	(2)
Example 14.4.2 Heat Transfer Across a Horizontal Bounded Air Film	566	(1)
Example 14.4.3 Temperature of a Surface	567	(1)
14.5 Natural Convection in an Enclosed Space	567	(2)
Example 14.5.1 Natural Convection Heat Transfer across an Enclosed Air Space	569	(1)
14.6 Combined Natural and Forced Convection	569	(3)
Example 14.6.1 Effect of Natural Convection on Laminar Flow Heat Transfer in a Horizontal Tube	570	(2)
14.7 An Integral Boundary Layer Analysis of Convection from a Vertical Heated Plane	572	(3)
14.8 Optimum Spacing for Heat Dissipation	575	(4)
Example 14.8.1 Design and Performance of a Convective Heater	578	(1)
Summary	579	(1)
Problems	580	(4)
CHAPTER 15 HEAT TRANSFER BY RADIATION	584	(31)
15.1 Introduction	584	(1)
15.2 Emission and Exchange of Radiation	585	(15)
Example 15.2.1 Heat Losses from a Plate	586	(1)
15.2.1 Radiation Exchange Between Black Bodies	587	(3)
Example 15.2.2 View Factors for Black Body Radiation between a Hemisphere and a Plane	590	(2)
15.2.2 Radiation Exchange Between Black Bodies in an Adiabatic Enclosure	592	(1)
Example 15.2.3 Design of a Solar Heater (Black Bodies: No Convection)	593	(1)
15.2.3 Radiation Exchange Between Gray Bodies	594	(1)
Example 15.2.4 Analysis of the Net Radiation Flux Between Parallel Gray Surfaces	595	(2)
Example 15.2.5 Radiation Effect on Temperature Measurement	597	(1)
Example 15.2.6 Effectiveness of a Radiation Shield	598	(1)
15.2.4 Radiation Flux Plots	599	(1)
15.3 Radiation and Convection	600	(7)
Example 15.3.1 Design of a Solar Heater (Accounting for Convection)	600	(4)
Example 15.3.2 Design of a Solar Heater for Domestic Hot Water	604	(3)
15.4 Radiation and Conduction	607	(3)
Example 15.4.1 Radiative Heat Rise in a Solid Panel	609	(1)
Summary	610	(1)
Problems	610	(5)
CHAPTER 16 SIMULTANEOUS HEAT AND MASS TRANSFER	615	(23)
16.1 Introduction	615	(1)
16.2 Evaporative Cooling of a Liquid Droplet	615	(3)
Example 16.2.1 Temperature of an Evaporating Droplet of Water	617	(1)
16.3 Evaporative Blowing Effect on Heat Transfer	618	(10)
Example 16.3.1 Evaporation of a Droplet Falling through Air	622	(3)
Example 16.3.2 Evaporation of Alkane Fuel Droplets	625	(3)
16.4 Analysis of a Liquid Source Delivery System	628	(5)
Example 16.4.1 Performance of a Vapor Delivery System	631	(2)
16.5 Evaporative Cooling of a Falling Liquid Film	633	(2)
Example 16.5.1 Prediction of Experimental Cooling Data	633	(2)
Summary	635	(1)
Problems	635	(3)
APPENDIX A SOLUTIONS TO THE DIFFUSION EQUATION	638	(8)
A1 Planar Diffusion in One Dimension	638	(4)
A2 Radial Diffusion in a Long Cylinder	642	(2)
A3 Radial Diffusion in a Sphere	644	(2)
APPENDIX B SOME USEFUL FUNCTIONS	646	(6)
B1 Bessel Functions	646	(3)
B2 The Error Function	649	(2)
B3 The Gamma Function	651	(1)
References	651	(1)
APPENDIX C PHYSICAL PROPERTY VALUES	652	(13)
C1 Vapor Pressure of Pure Compounds	652	(1)
C2 Vapor/Liquid Equilibrium and Solubility (Henry's Law)	653	(2)
C3 Mass Density	655	(1)
C3.1 Gases	655	(1)
C3.2 Liquids	655	(1)
C3.3 Solids	655	(1)
Example Calculate the Mass Density of Solid Benzoic Acid, C(7)H(6)O(2)	656	(1)
C4 Molar Heat of Vaporization of Liquids	656	(1)
C5 Molar Heat Capacities	657	(1)
C5.1 Gases	657	(1)
C5.2 Liquids	657	(1)
C5.3 Solids	657	(1)
C6 Viscosity of Gases and Liquids	657	(3)
C6.1 Gases	657	(1)
C6.2 Liquids	658	(2)
C7 Thermal Conductivities of Gases and Liquids	660	(2)
C7.1 Monatomic Gases	660	(1)
C7.2 Polyatomic Gases	660	(1)
C7.3 Liquids	660	(1)
C7.4 Solids	661	(1)
C8 Diffusion Coefficients in Gases and Liquids	662	(1)
C9 Interfacial Tension	662	(1)
C10 Properties of Water and Air	663	(1)
References	664	(1)
APPENDIX D UNIT CONVERSIONS	665	(4)
INDEX	669