Mathematical Modeling: A Chemical Engineer's Perspective
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Table of contents
- Cover
- CONTENTSvii
- PREFACExvii
- PART I: METHOD AND MANNER1
- Chapter 1. What is Mathematical Modeling?3
- A Very Simple Example3
- Review of the Simplest Example8
- The Simplest Distributed Model9
- The General Balance Equations for Distributed Systems10
- Respecting Uniformity15
- Extensive and Intensive Quantities18
- General Observations on Forming the Model20
- Chapter 2. Manipulation of Models25
- Getting Rid of Unnecessary Equations26
- The Reduction of the Equations to Dimensionless Form28
- An Alternative Method of Reduction30
- Scaling33
- Shape Factors36
- A Priori Estimates39
- Scaling and Partial Solution in Linear Systems40
- Chapter 3. Solving the Equations45
- Getting a Feel for the Solution45
- Special Forms49
- Getting the Most from Calculations51
- Asymptotics and Perturbations59
- Moments and Generating Functions64
- Observing Conditions67
- Chapter 4. Presenting the Model and Its Behavior75
- The Phase Plane76
- Oscillations in Three Dimensions87
- Forced Oscillations and the Stroboscopic Phase Plane88
- Chapter 5. Maxims for Modelers93
- Chapter 6. Style95
- Literary Style96
- Genre98
- Plagiarism and Attribution101
- Publish or Perish102
- PART II: MATTER105
- Chapter 7. Dispersion in Flow107
- A. On the Dispersion of a Solute in a Fluid Flowing through a Tube109
- 1. Introduction109
- 2. The General Equations of Diffusion and Flow in a Straight Tube110
- 3. The Tube of Circular Cross-Section111
- 4. Some Special Initial Distributions of Solute115
- 5. The General Case116
- 6. Turbulent Flow in a Tube of Circular Cross-Section118
- 7. Viscous Flow in a Tube of Arbitrary Cross-Section118
- References120
- B. On the Dispersion of a Solute by Diffusion, Convection, and Exchange between Phases121
- 1. Introduction121
- 2. Dispersion in Coaxial Cylindrical Annuli122
- 3. Certain Special Cases128
- 4. Dispersion in Coaxial Streams of Arbitrary Cross-Section129
- 5. Application to the Theory of Chromatography133
- 6. Application to a Simplified Theory of Distillation133
- References135
- C. On the Dispersion of Linear Kinematic Waves136
- 1. Introduction136
- 2. The Dispersion of a Flood Wave137
- 3. General Theorems140
- 4. A Kinematic Temperature Wave140
- 5. The Ultimate Form of a Kinematic Wave144
- References146
- Chapter 8. Formal Kinetics147
- D. Prolegomena to the Rational Analysis of Systems of Chemical Reactions149
- 1. Introduction149
- 2. The Representation of Molecular Species and Reactions between Them150
- 3. The Representation and Calculus of Composition Changes154
- 4. Equilibrium in Systems of Reactions157
- 5. Kinetics of Reactions159
- 6. Reaction Mechanisms161
- 7. Entropy Production165
- 8. Discussion166
- Nomenclature167
- References168
- E. Prolegomena to the Rational Analysis of Systems of Chemical Reactions II. Some Addenda170
- 1. Introduction170
- 2. The Uniqueness of Equilibrium under Adiabatic Conditions171
- 3. The Consistency of Certain Kinetic and Equilibrium Expressions172
- 4. Reaction Mechanisms and Exact Sequences174
- 5. Of Chemical Kinetics in General177
- References179
- F. Modelling Cubic Autocatalysis by Successive Bimolecular Steps180
- 1. Introduction180
- 2. Kinetic Schemes and Mass-Balance Equations181
- 3. Behaviour of First-Order Correction to Autocatalator: Stationary-States and Limit Cycles183
- 4. Comparison of First-Order Equations with Full, Three-Variable Model186
- Conclusions187
- References188
- G. Reactions in Continuous Mixtures189
- Introduction189
- General Formulation for a Single Index191
- Parallel Reaction in a Doubly Distributed Continuum194
- Examples195
- Generalized Background Kinetics199
- Discrete Distributions201
- Distributions of k(x)202
- Asymptotic Behavior204
- Sequential Parallel Reactions205
- Mechanisms207
- Literature Cited209
- H. Reaction of a Continuous Mixture in a Bubbling Fluidized Bed211
- Introduction211
- Gamma Distributions213
- Application of the Gamma Distribution214
- A General Theorem for Simple, Linear Reactor Models215
- Application to a Model of the Bubbling Fluidized Bed215
- The Damköhler Number218
- The Fluid Bed with Astarita's Uniform Kinetics220
- Nomenclature221
- References223
- Chapter 9. Statics and Dynamics of Chemical Reactors225
- I. Some Common Features of Periodically Forced Reacting Systems227
- Introduction227
- Numerical Methods229
- Forced Dynamic Phenomena240
- Conclusions248
- References249
- J. *Yet Who Would Have Thought the Old Man to Have Had So Much Blood in Him?"„Reflections on the M252
- Introduction252
- The System254
- Discussion I: Butterfly Points261
- Discussion II: Maximum Multiplicity270
- Conclusions278
- Notation280
- References280
- K. Autonomous Bifurcations of a Simple Biomolecular Surface-Reaction Model282
- 1. Introduction282
- 2. Surface Reaction Model283
- 3. Bifurcation Analysis286
- 4. The Stability of the Steady States294
- 5. Hopf Bifurcations298
- 6. Homoclinic Bifurcations302
- 7. Discussion303
- References305
- L. Forced Oscillations of a Self-Oscillating Bimolecular Surface Reaction Model307
- 1. Introduction307
- 2. Surface Reaction Model309
- 3. Mathematical and Numerical Framework311
- 4. Excitation Diagram314
- 5. Discussion327
- References331
- Chapter 10. Mass and Heat Transfer335
- M. An Example of the Relation between Discrete and Continuous Models337
- The Geometry of the Hexaga337
- Heat Transfer339
- The Discrete Model341
- The Continuous Model342
- Two Lemmas343
- Equivalence of the Models in the Limit ε→0344
- N. A General Theory of Anisotropic Membranes345
- Introduction345
- Exponential Dependence346
- Designing for Maximum Anisotropy350
- Application353
- Other Configurations355
- Nomenclature357
- References358
- Chapter 11. Modeling in General359
- O. Of Chemical Engineering and the Liberal Arts: An Inaugural for the Olaf Hougen Visiting Professor361
- P. Two Eyes Are Better Than One: Some Refledons on the Importance of Having More Than One Viewpoint374
- References399
- Q. Reflections on Keats' Equation400
- Keats' Equation400
- A Model of Algal Growth408
- Notation413
- References414
- R. Chemical Engineering Greetings415
- PART III: MISCELLANEA417
- Acknowledgments: An Autobiographical Appendix with Asides419
- Early Education, 1935–1943420
- Canford, 1943–1946421
- Billingham, 1946–1948422
- Edinburgh, 1948–1950423
- Billingham, 1950–1955426
- Minnesota, 1955–1956430
- Edinburgh, 1956–1958432
- Minneapolis, 1958–1964433
- Cambridge, 1964–1965436
- Aside on Formal Chemical Kinetics, 1963–1995438
- Minneapolis, 1965–1971442
- Cambridge, 1971–1972443
- Minneapolis, 1972–1974444
- Minneapolis, 1974–1996447
- Minnesota and Sabbaticals, 1978–1996448
- BIBLIOGRAPHY455
- Books455
- Edited Books456
- Chapters in Books Edited by Others456
- Journal Papers456
- INDEX OF GRADUATE STUDENTS AND CO-AUTHORS467
- SUBJECT INDEX TO THE PAPERS IN THE BIBLIOGRAPHY469
- INDEX473
Mathematical modeling is the art and craft of building a system of equations that is both sufficiently complex to do justice to physical reality and sufficiently simple to give real insight into the situation. Mathematical Modeling: A Chemical Engineer's Perspective provides an elementary introduction to the craft by one of the century's most distinguished practitioners.
Though the book is written from a chemical engineering viewpoint, the principles and pitfalls are common to all mathematical modeling of physical systems. Seventeen of the author's frequently cited papers are reprinted to illustrate applications to convective diffusion, formal chemical kinetics, heat and mass transfer, and the philosophy of modeling. An essay of acknowledgments, asides, and footnotes captures personal reflections on academic life and personalities.
* Describes pitfalls as well as principles of mathematical modeling
* Presents twenty examples of engineering problems
* Features seventeen reprinted papers
* Presents personal reflections on some of the great natural philosophers
* Emphasizes modeling procedures that precede extensive calculations
Though the book is written from a chemical engineering viewpoint, the principles and pitfalls are common to all mathematical modeling of physical systems. Seventeen of the author's frequently cited papers are reprinted to illustrate applications to convective diffusion, formal chemical kinetics, heat and mass transfer, and the philosophy of modeling. An essay of acknowledgments, asides, and footnotes captures personal reflections on academic life and personalities.
* Describes pitfalls as well as principles of mathematical modeling
* Presents twenty examples of engineering problems
* Features seventeen reprinted papers
* Presents personal reflections on some of the great natural philosophers
* Emphasizes modeling procedures that precede extensive calculations