Preface ........................................................ xi
Acknowledgements .............................................. xix
Chapter 1: Brief review of static optimization methods ......... 1
1.1 Introduction: Significance of Mathematical Models .......... 1
1.2 Unconstrained Problems ..................................... 4
1.3 Equality Constraints and Lagrange Multipliers .............. 7
1.4 Methods of Mathematical Programming ....................... 11
1.5 Iterative Search Methods .................................. 13
1.6 On Some Stochastic Optimization Techniques ................ 17
Chapter 2: Dynamic optimization problems ...................... 45
2.1 Discrete Representations and Dynamic Programming
Algorithms ................................................ 45
2.2 Recurrence Equations ...................................... 47
2.3 Discrete Processes Linear with Respect to the Time
Interval .................................................. 51
2.4 Discrete Algorithm of the Pontryagin's Type for
Processes Linear in θN .................................... 55
2.5 Hamilton-Jacobi-Bellman Equations for Continuous
Systems ................................................... 58
2.6 Continuous Maximum Principle .............................. 70
2.7 Calculus of Variations .................................... 73
2.8 Viscosity Solutions and Non-smooth Analyses ............... 76
2.9 Stochastic Control and Stochastic Maximum Principle ....... 84
Chapter 3: Energy limits for thermal engines and heat-pumps
at steady states ................................... 85
3.1 Introduction: Role of Optimization in Determining
Thermodynamic Limits ...................................... 85
3.2 Classical Problem of Thermal Engine Driven by Heat Flux ... 90
3.3 Toward Work Limits in Sequential Systems ................. 109
3.4 Energy Utilization and Heat-pumps ........................ 112
3.5 Thermal Separation Processes ............................. 116
3.6 Steady Chemical, Electrochemical and Other Systems ....... 117
3.7 Limits in Living Systems ................................. 123
3.8 Final Remarks ............................................ 124
Chapter 4: Hamiltonian optimization of imperfect
cascades .......................................... 127
4.1 Basic Properties of Irreversible Cascade Operations
with a Work Flux ......................................... 127
4.2 Description of Imperfect Units in Terms of Carnot
Temperature Control ...................................... 132
4.3 Single-stage Formulae in a Model of Cascade Operation .... 138
4.4 Work Optimization in Cascade by Discrete Maximum
Principle ................................................ 141
4.5 Example .................................................. 155
4.6 Continuous Imperfect System with Two Finite Reservoirs ... 157
4.7 Final Remarks ............................................ 164
Chapter 5: Maximum power from solar energy ................... 167
5.1 Introducing Carnot Controls for Modeling Solar-assisted
Operations ............................................... 167
5.2 Thermodynamics of Radiation .............................. 175
5.3 Classical Exergy of Radiation ............................ 180
5.4 Flux of Classical Exergy ................................. 184
5.5 Efficiencies of Energy Conversion ........................ 186
5.6 Towards a Dissipative Exergy of Radiation at Flow ........ 187
5.7 Basic Analytical Formulae of Steady Pseudo-Newtonian
Model .................................................... 190
5.8 Steady Non-Linear Models applying Stefan-Boltzmann
Equation ................................................. 192
5.9 Dynamical Theory for Pseudo-Newtonian Models ............. 195
5.10 Dynamical Models using the Stefan-Boltzmann Equation ..... 204
5.11 Towards the Hamilton-Jacobi-Bellman Approaches ........... 211
5.12 Final Remarks ............................................ 212
Chapter 6: Hamilton-Jacobi-Bellman theory of energy systems ... 215
6.1 Introduction ............................................. 215
6.2 Dynamic Optimization of Power in a Finite-resource
Process .................................................. 216
6.3 Two Different Works and Finite-Rate Exergies ............. 219
6.4 Some Aspects of Classical Analytical HJB Theory for
Continuous Systems ....................................... 223
6.5 HJB Equations for Non-Linear Power Generation Systems .... 225
6.6 Analytical Solutions in Systems with Linear Kinetics ..... 227
6.7 Extensions for Systems with Non-Linear Kinetics and
Internal Dissipation ..................................... 230
6.8 Generalized Exergies for Non-Linear Systems with
Minimum Dissipation ...................................... 232
6.9 Final Remarks ............................................ 235
Chapter 7: Numerical optimization in allocation, storage
and recovery of thermal energy and resources ...... 237
7.1 Introduction ............................................. 237
7.2 A Discrete Model for a Non-Linear Problem of Maximum
Power from Radiation ..................................... 239
7.3 Non-Constant Hamiltonians and Convergence of Discrete
DP Algorithms to Viscosity Solutions of HJB Equations .... 240
7.4 Dynamic Programming Equation for Maximum Power From
Radiation ................................................ 249
7.5 Discrete Approximations and Time Adjoint as a Lagrange
Multiplier ............................................... 250
7.6 Mean and Local Intensities in Discrete Processes ......... 257
7.7 Legendre Transform and Original Work Function ............ 259
7.8 Numerical Approaches Applying Dynamic Programming ........ 261
7.9 Dimensionality Reduction in Dynamic Programming
Algorithms ............................................... 265
7.10 Concluding Remarks ....................................... 267
Chapter 8: Optimal control of separation processes ........... 271
8.1 General Thermokinetic Issues ............................. 271
8.2 Thermodynamic Balances toward Minimum Heat or Work ....... 273
8.3 Results for Irreversible Separations Driven by Work or
Heat ..................................................... 279
8.4 Thermoeconomic Optimization of Thermal Drying with
Fluidizing Solids ........................................ 282
8.5 Solar Energy Application to Work-Assisted Drying ......... 312
8.6 Concluding Remarks ....................................... 320
Chapter 9: Optimal decisions for chemical and
electrochemical reactors .......................... 321
9.1 Introduction ............................................. 321
9.2 Driving Forces in Transport Processes and Chemical
Reactions ................................................ 321
9.3 General Non-Linear Equations of Macrokinetics ............ 324
9.4 Classical Chemical and Electrochemical Kinetics .......... 325
9.5 Inclusion of Non-Linear Transport Phenomena .............. 327
9.6 Continuous Description of Chemical (Electrochemical)
Kinetics and Transport Phenomena ......................... 329
9.7 Towards Power Production in Chemical Systems ............. 331
9.8 Thermodynamics of Power Generation in Non-Isothermal
Chemical Engines ......................................... 334
9.9 Non-Isothermal Engines in Terms of Carnot Variables ...... 338
9.10 Entropy Production in Steady Systems ..................... 340
9.11 Dissipative Availabilities in Dynamical Systems .......... 341
9.12 Characteristics of Steady Isothermal Engines ............. 343
9.13 Sequential Models for Dynamic Power Generators ........... 351
9.14 A Computational Algorithm for Dynamical Process with
Power Maximization ....................................... 355
9.15 Results of Computations .................................. 358
9.16 Some Additional Comments ................................. 359
9.17 Comparison of Chemical and Thermal Operations of Power
Production ............................................... 360
9.18 Fuel Cell Application .................................... 361
9.19 Final Remarks ............................................ 365
Chapter 10: Energy limits and evolution in biological
systems ........................................... 367
10.1 Introduction ............................................ 367
10.2 Energy and Size Limits .................................. 368
10.3 Toward a Quantitative Description of Development
and Evolution of Species ................................ 375
10.4 Significance of Complexity and Entropy .................. 378
10.5 Evolutions of Multiple Organs without Mutations ......... 381
10.6 Organisms with Mutations or Specializations of Organs ... 383
10.7 A Variational Approach to the Dynamics of Evolution ..... 384
10.8 Concluding Remarks ...................................... 388
Chapter 11: Systems theory in thermal & chemical
engineering ....................................... 391
11.1 Introduction ............................................. 391
11.2 System Energy Analyses ................................... 392
11.3 Mathematical Modeling of Industrial Energy Management .... 392
11.4 Linear Model of the Energy Balance for an Industrial
Plant and its Applications ............................... 395
11.5 Non-Linear Mathematical Model of a Short-Term Balance
of Industrial Energy System .............................. 399
11.6 Mathematical Optimization Model for the Preliminary
Design of Industrial Energy Systems ...................... 401
11.7 Remarks on Diverse Methodologies and Link with
Ecological Criteria ...................................... 406
11.8 Control Thermodynamics for Explicitly Dynamical
Systems .................................................. 412
11.9 Interface of Energy Limits, Structure Design,
Thermoeconomics and Ecology .............................. 414
11.10 Towards the Thermoeconomics and Integration of
Heat Energy .............................................. 425
Chapter 12: Heat integration within process integration ....... 427
Chapter 13: Maximum heat recovery and its consequences for
process system design ............................. 437
13.1 Introduction and Problem Formulation ..................... 437
13.2 Composite Curve (CC) Plot ................................ 439
13.3 Problem Table (PR-T) Method .............................. 446
13.4 Grand Composite Curve (GCC) Plot ......................... 450
13.5 Special Topics in MER/MUC Calculations ................... 454
13.6 Summary and Further Reading .............................. 458
Chapter 14: Targeting and supertargeting in heat exchanger
network design .................................... 461
14.1 Targeting Stage in Overall Design Process ................ 461
14.2 Basis of Sequential Approaches for HEN Targeting.......... 462
14.3 Basis of Simultaneous Approaches for HEN Targeting ....... 467
Chapter 15: Minimum utility cost (MUC) target by
optimization approaches ........................... 469
15.1 Introduction and MER Problem Solution by Mathematical
Programming .............................................. 469
15.2 MUC Problem Solution Methods ............................. 472
15.3 Dual Matches ............................................. 485
15.4 Minimum Utility Cost under Disturbances .................. 488
Chapter 16: Minimum number of units (MNU) and minimum
total surface area (MTA) targets .................. 495
16.1 Introduction ............................................. 495
16.2 Minimum Number of Matches (MNM) Target ................... 496
16.3 Minimum Total Area for Matches (MTA-M) Target ............ 515
16.4 Minimum Number of Shells (MNS) Target .................... 521
16.5 Minimum Total Area for Shells (MTA-S) Target ............. 525
Chapter 17: Simultaneous HEN targeting for total annual
cost .............................................. 533
Chapter 18: Heat exchanger network synthesis .................. 547
18.1 Introduction ............................................. 547
18.2 Sequential Approaches .................................... 548
18.3 Simultaneous Approaches to HEN Synthesis ................. 566
Chapter 19: Heat exchanger network retrofit ................... 583
19.1 Introduction ............................................. 583
19.2 Network Pinch Method ..................................... 586
19.3 Simultaneous Approaches for HEN Retrofit ................. 596
Chapter 20: Approaches to water network design ................ 613
20.1 Introduction ............................................. 613
20.2 Mathematical Models and Data for Water Network
Problem .................................................. 617
20.3 Overview of Approaches in the Literature ................. 621
References ............................................... 659
Glossary of symbols ...................................... 725
Index .................................................... 735
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