Introduction to chemical engineering computing / Bruce A. Finlayson.

By: Finlayson, Bruce A
Language: English Publisher: Hoboken, N.J. : Wiley-Interscience, [2006]Copyright date: 2006Description: xv, 339 pages : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 0471740624 (cloth)Subject(s): Chemical engineering -- Data processingGenre/Form: Electronic books.DDC classification: 660.0285 LOC classification: TP184 | .F56 2006Online resources: Full text is available at Wiley Online Library Click here to view
Contents:
Table of Contents Preface xv 1 Introduction 1 Organization, 2 Algebraic Equations, 3 Process Simulation, 3 Differential Equations, 3 Appendices, 4 2 Equations of State 7 Equations of State—Mathematical Formulation, 8 Solving Equations of State Using Excel (Single Equation in One Unknown), 12 Solution Using “Goal Seek”, 12 Solution Using “Solver”, 13 Example of a Chemical Engineering Problem Solved Using “Goal Seek”, 13 Solving Equations of State Using MATLAB (Single Equation in One Unknown), 15 Example of a Chemical Engineering Problem Solved Using MATLAB, 16 Another Example of a Chemical Engineering Problem Solved Using MATLAB, 18 Equations of State With Aspen Plus, 20 Example Using Aspen Plus, 20 Specific Volume of a Mixture, 21 Chapter Summary, 26 Problems, 26 Numerical Problems, 28 3 Vapor–Liquid Equilibria 29 Flash and Phase Separation, 30 Isothermal Flash—Development of Equations, 30 Example Using Excel, 32 Thermodynamic Parameters, 33 Example Using MATLAB, 34 Example Using Aspen Plus, 35 Nonideal Liquids—Test of Thermodynamic Model, 39 NIST Thermo Data Engine in Aspen Plus, 41 Chapter Summary, 44 Problems, 44 Numerical Problems, 48 4 Chemical Reaction Equilibria 49 Chemical Equilibrium Expression, 50 Example of Hydrogen for Fuel Cells, 51 Solution Using Excel, 52 Solution Using MATLAB, 53 Chemical Reaction Equilibria with Two or More Equations, 56 Multiple Equations, Few Unknowns Using MATLAB, 56 Chemical Reaction Equilibria Using Aspen Plus, 59 Chapter Summary, 59 Problems, 60 Numerical Problems, 63 5 Mass Balances with Recycle Streams 65 Mathematical Formulation, 66 Example Without Recycle, 68 Example with Recycle; Comparison of Sequential and Simultaneous Solution Methods, 70 Example of Process Simulation Using Excel for Simple Mass Balances, 72 Example of Process Simulation Using Aspen Plus for Simple Mass Balances, 73 Example of Process Simulation with Excel Including Chemical Reaction Equilibria, 74 Did the Iterations Converge?, 75 Extensions, 76 Chapter Summary, 76 Class Exercises, 76 Class Discussion (After Viewing Problem 5.10 on the Book Website), 76 Problems, 77 6 Thermodynamics and Simulation of Mass Transfer Equipment 85 Thermodynamics, 86 Guidelines for Choosing, 89 Properties Environment | Home | Methods Selection Assistant, 89 Thermodynamic Models, 90 Example: Multicomponent Distillation with Shortcut Methods, 91 Multicomponent Distillation with Rigorous Plate-to-Plate Methods, 95 Example: Packed Bed Absorption, 97 Example: Gas Plant Product Separation, 100 Example: Water Gas Shift Equilibrium Reactor with Sensitivity Block and Design Specification Block, 102 Chapter Summary, 106 Class Exercise, 106 Problems (using Aspen Plus), 106 7 Process Simulation 109 Model Library, 110 Example: Ammonia Process, 110 Development of the Model, 112 Solution of the Model, 115 Examination of Results, 115 Testing the Thermodynamic Model, 118 Utility Costs, 118 Greenhouse Gas Emissions, 120 Convergence Hints, 120 Optimization, 122 Integrated Gasification Combined Cycle, 125 Cellulose to Ethanol, 126 Chapter Summary, 128 Class Exercise, 128 Problems, 128 Problems Involving Corn Stover and Ethanol, 131 8 Chemical Reactors 137 Mathematical Formulation of Reactor Problems, 138 Example: Plug Flow Reactor and Batch Reactor, 138 Example: Continuous Stirred Tank Reactor, 140 Using MATLAB to Solve Ordinary Differential Equations, 140 Simple Example, 140 Use of the “Global” Command, 142 Passing Parameters, 143 Example: Isothermal Plug Flow Reactor, 144 Example: Nonisothermal Plug Flow Reactor, 146 Using Comsol Multiphysics to Solve Ordinary Differential Equations, 148 Simple Example, 148 Example: Isothermal Plug Flow Reactor, 150 Example: Nonisothermal Plug Flow Reactor, 151 Reactor Problems with Mole Changes and Variable Density, 153 Chemical Reactors with Mass Transfer Limitations, 155 Plug Flow Chemical Reactors in Aspen Plus, 158 Continuous Stirred Tank Reactors, 161 Solution Using Excel, 162 Solution Using MATLAB, 163 CSTR with Multiple Solutions, 163 Transient Continuous Stirred Tank Reactors, 164 Chapter Summary, 168 Problems, 169 Numerical Problems (See Appendix E), 174 9 Transport Processes in One Dimension 175 Applications in Chemical Engineering—Mathematical Formulations, 176 Heat Transfer, 176 Diffusion and Reaction, 177 Fluid Flow, 178 Unsteady Heat Transfer, 180 Introduction to Comsol Multiphysics, 180 Example: Heat Transfer in a Slab, 181 Solution Using Comsol Multiphysics, 181 Solution Using MATLAB, 184 Example: Reaction and Diffusion, 185 Parametric Solution, 186 Example: Flow of a Newtonian Fluid in a Pipe, 188 Example: Flow of a Non-Newtonian Fluid in a Pipe, 190 Example: Transient Heat Transfer, 193 Solution Using Comsol Multiphysics, 193 Solution Using MATLAB, 195 Example: Linear Adsorption, 196 Example: Chromatography, 199 Pressure Swing Adsorption, 203 Chapter Summary, 204 Problems, 204 Chemical Reaction, 204 Chemical Reaction and Heat Transfer, 205 Mass Transfer, 207 Heat Transfer, 207 Electrical Fields, 207 Fluid Flow, 208 Numerical Problems (See Appendix E), 213 10 Fluid Flow in Two and Three Dimensions 215 Mathematical Foundation of Fluid Flow, 217 Navier–Stokes Equation, 217 Non-Newtonian Fluid, 218 Nondimensionalization, 219 Option One: Slow Flows, 219 Option Two: High-Speed Flows, 220 Example: Entry Flow in a Pipe, 221 Example: Entry Flow of a Non-Newtonian Fluid, 226 Example: Flow in Microfluidic Devices, 227 Example: Turbulent Flow in a Pipe, 230 Example: Start-Up Flow in a Pipe, 233 Example: Flow Through an Orifice, 235 Example: Flow in a Serpentine Mixer, 239 Microfluidics, 240 Mechanical Energy Balance for Laminar Flow, 243 Pressure Drop for Contractions and Expansions, 245 Generation of Two-Dimensional Inlet Velocity Profiles for Three-Dimensional Simulations, 246 Chapter Summary, 249 Problems, 249 11 Heat and Mass Transfer in Two and Three Dimensions 259 Convective Diffusion Equation, 260 Nondimensional Equations, 261 Example: Heat Transfer in Two Dimensions, 262 Example: Heat Conduction with a Hole, 264 Example: Convective Diffusion in Microfluidic Devices, 265 Example: Concentration-Dependent Viscosity, 268 Example: Viscous Dissipation, 269 Example: Chemical Reaction, 270 Example: Wall Reactions, 272 Example: Mixing in a Serpentine Mixer, 272 Microfluidics, 274 Characterization of Mixing, 276 Average Concentration along an Optical Path, 276 Peclet Number, 276 Example: Convection and Diffusion in a Three-Dimensional T-Sensor, 278 Chapter Summary, 280 Problems, 280 Steady, Two-Dimensional Problems, 280 Heat Transfer with Flow, 283 Reaction with Known Flow, 284 Reaction with No Flow, 285 Solve for Concentration and Flow, 286 Numerical Problems, 289 Appendix A HintsWhen Using Excel® 291 Introduction, 291 Calculation, 292 Plotting, 293 Import and Export, 294 Presentation, 294 Appendix B HintsWhen Using MATLAB® 297 General Features, 298 Screen Format, 298 Stop/Closing the Program, 299 m-files and Scripts, 299 Workspaces and Transfer of Information, 300 “Global” Command, 300 Display Tools, 301 Classes of Data, 301 Programming Options: Input/Output, Loops, Conditional Statements, Timing, and Matrices, 302 Input/Output, 302 Loops, 303 Conditional Statements, 303 Timing Information, 304 Matrices, 304 Matrix Multiplication, 304 Element by Element Calculations, 305 More Information, 306 Finding and Fixing Errors, 306 Eigenvalues of a Matrix, 307 Evaluate an Integral, 307 Spline Interpolation, 307 Interpolate Data, Evaluate the Polynomial, and Plot the Result, 308 Solve Algebraic Equations, 309 Using “fsolve”, 309 Solve Algebraic Equations Using “fzero” or “fminsearch” (Both in Standard MATLAB), 309 Integrate Ordinary Differential Equations that are Initial Value Problems, 309 Differential-Algebraic Equations, 311 Checklist for Using “ode45” and Other Integration Packages, 311 Plotting, 312 Simple Plots, 312 Add Data to an Existing Plot, 312 Dress Up Your Plot, 312 Multiple Plots, 313 3D Plots, 313 More Complicated Plots, 314 Use Greek Letters and Symbols in the Text, 314 Bold, Italics, and Subscripts, 314 Other Applications, 315 Plotting Results from Integration of Partial Differential Equations Using Method of Lines, 315 Import/Export Data, 315 Import/Export with Comsol Multiphysics, 318 Programming Graphical User Interfaces, 318 MATLAB Help, 318 Applications of MATLAB, 319 Appendix C Hints When Using Aspen Plus® 321 Introduction, 321 Flowsheet, 323 Model Library, 323 Place Units on Flowsheet, 324 Connect the Units with Streams, 324 Data, 324 Setup, 324 Data Entry, 325 Specify Components, 325 Specify Properties, 325 Specify Input Streams, 326 Specify Block Parameters, 326 Run the Problem, 326 Scrutinize the Stream Table, 327 Checking Your Results, 328 Change Conditions, 328 Report, 329 Transfer the Flowsheet and Mass and Energy Balance to a Word Processing Program, 329 Prepare Your Report, 329 Save Your Results, 330 Getting Help, 330 Advanced Features, 330 Flowsheet Sections, 330 Mass Balance Only Simulations and Inclusion of Solids, 331 Transfer Between Excel and Aspen, 331 Block Summary, 331 Calculator Blocks, 332 Aspen Examples, 334 Molecule Draw, 334 Applications of Aspen Plus, 334 Appendix D HintsWhen Using Comsol Multiphysics® 335 Basic Comsol Multiphysics Techniques, 336 Opening Screens, 336 Equations, 337 Specify the Problem and Parameters, 337 Physics, 339 Definitions, 339 Geometry, 339 Materials, 340 Discretization, 341 Boundary Conditions, 341 Mesh, 342 Solve and Examine the Solution, 342 Solve, 342 Plot, 342 Publication Quality Figures, 343 Results, 343 Probes, 344 Data Sets, 344 Advanced Features, 345 Mesh, 345 Transfer to Excel, 346 LiveLink with MATLAB, 347 Variables, 348 Animation, 349 Studies, 349 Help with Convergence, 349 Help with Time-Dependent Problems, 350 Jump Discontinuity, 350 Help, 351 Applications of Comsol Multiphysics, 351 Appendix E Mathematical Methods 353 Algebraic Equations, 354 Successive Substitution, 354 Newton–Raphson, 354 Ordinary Differential Equations as Initial Value Problems, 356 Euler’s Method, 356 Runge–Kutta Methods, 357 MATLAB and ode45 and ode15s, 357 Ordinary Differential Equations as Boundary Value Problems, 358 Finite Difference Method, 359 Finite Difference Method in Excel, 360 Finite Element Method in One Space Dimension, 361 Initial Value Methods, 363 Partial Differential Equations in time and One Space Dimension, 365 Problems with Strong Convection, 366 Partial Differential Equations in Two Space Dimensions, 367 Finite-Difference Method for Elliptic Equations in Excel, 367 Finite Element Method for Two-Dimensional Problems, 368 Summary, 370 Problems, 370 References 373 Index 379
Summary: About the Author BRUCE A. FINLAYSON, PhD, is Rehnberg Professor Emeritus of Chemical Engineering in the Department of Chemical Engineering of the University of Washington. He is also a former president of the American Institute of Chemical Engineers (AIChE). Among his many accolades and honors, Dr. Finlayson is a recipient of the AIChE’s prestigious William H. Walker Award and an elected member of the National Academy of Engineering.
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Includes bibliographical references (p. 323-325) and indexes.

Table of Contents
Preface xv
1 Introduction 1

Organization, 2

Algebraic Equations, 3

Process Simulation, 3

Differential Equations, 3

Appendices, 4

2 Equations of State 7

Equations of State—Mathematical Formulation, 8

Solving Equations of State Using Excel (Single Equation in One Unknown), 12

Solution Using “Goal Seek”, 12

Solution Using “Solver”, 13

Example of a Chemical Engineering Problem Solved Using “Goal Seek”, 13

Solving Equations of State Using MATLAB (Single Equation in

One Unknown), 15

Example of a Chemical Engineering Problem Solved Using MATLAB, 16

Another Example of a Chemical Engineering Problem Solved Using

MATLAB, 18

Equations of State With Aspen Plus, 20

Example Using Aspen Plus, 20

Specific Volume of a Mixture, 21

Chapter Summary, 26

Problems, 26

Numerical Problems, 28

3 Vapor–Liquid Equilibria 29

Flash and Phase Separation, 30

Isothermal Flash—Development of Equations, 30

Example Using Excel, 32

Thermodynamic Parameters, 33

Example Using MATLAB, 34

Example Using Aspen Plus, 35

Nonideal Liquids—Test of Thermodynamic Model, 39

NIST Thermo Data Engine in Aspen Plus, 41

Chapter Summary, 44

Problems, 44

Numerical Problems, 48

4 Chemical Reaction Equilibria 49

Chemical Equilibrium Expression, 50

Example of Hydrogen for Fuel Cells, 51

Solution Using Excel, 52

Solution Using MATLAB, 53

Chemical Reaction Equilibria with Two or More Equations, 56

Multiple Equations, Few Unknowns Using MATLAB, 56

Chemical Reaction Equilibria Using Aspen Plus, 59

Chapter Summary, 59

Problems, 60

Numerical Problems, 63

5 Mass Balances with Recycle Streams 65

Mathematical Formulation, 66

Example Without Recycle, 68

Example with Recycle; Comparison of Sequential and Simultaneous

Solution Methods, 70

Example of Process Simulation Using Excel for Simple Mass Balances, 72

Example of Process Simulation Using Aspen Plus for Simple

Mass Balances, 73

Example of Process Simulation with Excel Including Chemical Reaction

Equilibria, 74

Did the Iterations Converge?, 75

Extensions, 76

Chapter Summary, 76

Class Exercises, 76

Class Discussion (After Viewing Problem 5.10 on the Book Website), 76

Problems, 77

6 Thermodynamics and Simulation of Mass Transfer Equipment 85

Thermodynamics, 86

Guidelines for Choosing, 89

Properties Environment | Home | Methods Selection Assistant, 89

Thermodynamic Models, 90

Example: Multicomponent Distillation with Shortcut Methods, 91

Multicomponent Distillation with Rigorous Plate-to-Plate Methods, 95

Example: Packed Bed Absorption, 97

Example: Gas Plant Product Separation, 100

Example: Water Gas Shift Equilibrium Reactor with Sensitivity Block and

Design Specification Block, 102

Chapter Summary, 106

Class Exercise, 106

Problems (using Aspen Plus), 106

7 Process Simulation 109

Model Library, 110

Example: Ammonia Process, 110

Development of the Model, 112

Solution of the Model, 115

Examination of Results, 115

Testing the Thermodynamic Model, 118

Utility Costs, 118

Greenhouse Gas Emissions, 120

Convergence Hints, 120

Optimization, 122

Integrated Gasification Combined Cycle, 125

Cellulose to Ethanol, 126

Chapter Summary, 128

Class Exercise, 128

Problems, 128

Problems Involving Corn Stover and Ethanol, 131

8 Chemical Reactors 137

Mathematical Formulation of Reactor Problems, 138

Example: Plug Flow Reactor and Batch Reactor, 138

Example: Continuous Stirred Tank Reactor, 140

Using MATLAB to Solve Ordinary Differential Equations, 140

Simple Example, 140

Use of the “Global” Command, 142

Passing Parameters, 143

Example: Isothermal Plug Flow Reactor, 144

Example: Nonisothermal Plug Flow Reactor, 146

Using Comsol Multiphysics to Solve Ordinary Differential Equations, 148

Simple Example, 148

Example: Isothermal Plug Flow Reactor, 150

Example: Nonisothermal Plug Flow Reactor, 151

Reactor Problems with Mole Changes and Variable Density, 153

Chemical Reactors with Mass Transfer Limitations, 155

Plug Flow Chemical Reactors in Aspen Plus, 158

Continuous Stirred Tank Reactors, 161

Solution Using Excel, 162

Solution Using MATLAB, 163

CSTR with Multiple Solutions, 163

Transient Continuous Stirred Tank Reactors, 164

Chapter Summary, 168

Problems, 169

Numerical Problems (See Appendix E), 174

9 Transport Processes in One Dimension 175

Applications in Chemical Engineering—Mathematical Formulations, 176

Heat Transfer, 176

Diffusion and Reaction, 177

Fluid Flow, 178

Unsteady Heat Transfer, 180

Introduction to Comsol Multiphysics, 180

Example: Heat Transfer in a Slab, 181

Solution Using Comsol Multiphysics, 181

Solution Using MATLAB, 184

Example: Reaction and Diffusion, 185

Parametric Solution, 186

Example: Flow of a Newtonian Fluid in a Pipe, 188

Example: Flow of a Non-Newtonian Fluid in a Pipe, 190

Example: Transient Heat Transfer, 193

Solution Using Comsol Multiphysics, 193

Solution Using MATLAB, 195

Example: Linear Adsorption, 196

Example: Chromatography, 199

Pressure Swing Adsorption, 203

Chapter Summary, 204

Problems, 204

Chemical Reaction, 204

Chemical Reaction and Heat Transfer, 205

Mass Transfer, 207

Heat Transfer, 207

Electrical Fields, 207

Fluid Flow, 208

Numerical Problems (See Appendix E), 213

10 Fluid Flow in Two and Three Dimensions 215

Mathematical Foundation of Fluid Flow, 217

Navier–Stokes Equation, 217

Non-Newtonian Fluid, 218

Nondimensionalization, 219

Option One: Slow Flows, 219

Option Two: High-Speed Flows, 220

Example: Entry Flow in a Pipe, 221

Example: Entry Flow of a Non-Newtonian Fluid, 226

Example: Flow in Microfluidic Devices, 227

Example: Turbulent Flow in a Pipe, 230

Example: Start-Up Flow in a Pipe, 233

Example: Flow Through an Orifice, 235

Example: Flow in a Serpentine Mixer, 239

Microfluidics, 240

Mechanical Energy Balance for Laminar Flow, 243

Pressure Drop for Contractions and Expansions, 245

Generation of Two-Dimensional Inlet Velocity Profiles for

Three-Dimensional Simulations, 246

Chapter Summary, 249

Problems, 249

11 Heat and Mass Transfer in Two and Three Dimensions 259

Convective Diffusion Equation, 260

Nondimensional Equations, 261

Example: Heat Transfer in Two Dimensions, 262

Example: Heat Conduction with a Hole, 264

Example: Convective Diffusion in Microfluidic Devices, 265

Example: Concentration-Dependent Viscosity, 268

Example: Viscous Dissipation, 269

Example: Chemical Reaction, 270

Example: Wall Reactions, 272

Example: Mixing in a Serpentine Mixer, 272

Microfluidics, 274

Characterization of Mixing, 276

Average Concentration along an Optical Path, 276

Peclet Number, 276

Example: Convection and Diffusion in a Three-Dimensional T-Sensor, 278

Chapter Summary, 280

Problems, 280

Steady, Two-Dimensional Problems, 280

Heat Transfer with Flow, 283

Reaction with Known Flow, 284

Reaction with No Flow, 285

Solve for Concentration and Flow, 286

Numerical Problems, 289

Appendix A HintsWhen Using Excel® 291

Introduction, 291

Calculation, 292

Plotting, 293

Import and Export, 294

Presentation, 294

Appendix B HintsWhen Using MATLAB® 297

General Features, 298

Screen Format, 298

Stop/Closing the Program, 299

m-files and Scripts, 299

Workspaces and Transfer of Information, 300

“Global” Command, 300

Display Tools, 301

Classes of Data, 301

Programming Options: Input/Output, Loops, Conditional Statements, Timing, and Matrices, 302

Input/Output, 302

Loops, 303

Conditional Statements, 303

Timing Information, 304

Matrices, 304

Matrix Multiplication, 304

Element by Element Calculations, 305

More Information, 306

Finding and Fixing Errors, 306

Eigenvalues of a Matrix, 307

Evaluate an Integral, 307

Spline Interpolation, 307

Interpolate Data, Evaluate the Polynomial, and Plot the Result, 308

Solve Algebraic Equations, 309

Using “fsolve”, 309

Solve Algebraic Equations Using “fzero” or “fminsearch” (Both in Standard MATLAB), 309

Integrate Ordinary Differential Equations that are Initial Value Problems, 309

Differential-Algebraic Equations, 311

Checklist for Using “ode45” and Other Integration Packages, 311

Plotting, 312

Simple Plots, 312

Add Data to an Existing Plot, 312

Dress Up Your Plot, 312

Multiple Plots, 313

3D Plots, 313

More Complicated Plots, 314

Use Greek Letters and Symbols in the Text, 314

Bold, Italics, and Subscripts, 314

Other Applications, 315

Plotting Results from Integration of Partial Differential Equations Using Method of Lines, 315

Import/Export Data, 315

Import/Export with Comsol Multiphysics, 318

Programming Graphical User Interfaces, 318

MATLAB Help, 318

Applications of MATLAB, 319

Appendix C Hints When Using Aspen Plus® 321

Introduction, 321

Flowsheet, 323

Model Library, 323

Place Units on Flowsheet, 324

Connect the Units with Streams, 324

Data, 324

Setup, 324

Data Entry, 325

Specify Components, 325

Specify Properties, 325

Specify Input Streams, 326

Specify Block Parameters, 326

Run the Problem, 326

Scrutinize the Stream Table, 327

Checking Your Results, 328

Change Conditions, 328

Report, 329

Transfer the Flowsheet and Mass and Energy Balance to a Word Processing Program, 329

Prepare Your Report, 329

Save Your Results, 330

Getting Help, 330

Advanced Features, 330

Flowsheet Sections, 330

Mass Balance Only Simulations and Inclusion of Solids, 331

Transfer Between Excel and Aspen, 331

Block Summary, 331

Calculator Blocks, 332

Aspen Examples, 334

Molecule Draw, 334

Applications of Aspen Plus, 334

Appendix D HintsWhen Using Comsol Multiphysics® 335

Basic Comsol Multiphysics Techniques, 336

Opening Screens, 336

Equations, 337

Specify the Problem and Parameters, 337

Physics, 339

Definitions, 339

Geometry, 339

Materials, 340

Discretization, 341

Boundary Conditions, 341

Mesh, 342

Solve and Examine the Solution, 342

Solve, 342

Plot, 342

Publication Quality Figures, 343

Results, 343

Probes, 344

Data Sets, 344

Advanced Features, 345

Mesh, 345

Transfer to Excel, 346

LiveLink with MATLAB, 347

Variables, 348

Animation, 349

Studies, 349

Help with Convergence, 349

Help with Time-Dependent Problems, 350

Jump Discontinuity, 350

Help, 351

Applications of Comsol Multiphysics, 351

Appendix E Mathematical Methods 353

Algebraic Equations, 354

Successive Substitution, 354

Newton–Raphson, 354

Ordinary Differential Equations as Initial Value Problems, 356

Euler’s Method, 356

Runge–Kutta Methods, 357

MATLAB and ode45 and ode15s, 357

Ordinary Differential Equations as Boundary Value Problems, 358

Finite Difference Method, 359

Finite Difference Method in Excel, 360

Finite Element Method in One Space Dimension, 361

Initial Value Methods, 363

Partial Differential Equations in time and One Space Dimension, 365

Problems with Strong Convection, 366

Partial Differential Equations in Two Space Dimensions, 367

Finite-Difference Method for Elliptic Equations in Excel, 367

Finite Element Method for Two-Dimensional Problems, 368

Summary, 370

Problems, 370

References 373

Index 379

About the Author
BRUCE A. FINLAYSON, PhD, is Rehnberg Professor Emeritus of Chemical Engineering in the Department of Chemical Engineering of the University of Washington. He is also a former president of the American Institute of Chemical Engineers (AIChE). Among his many accolades and honors, Dr. Finlayson is a recipient of the AIChE’s prestigious William H. Walker Award and an elected member of the National Academy of Engineering.

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