Design and Optimizatian ef Thermal Systems

Second Edition

Yogesh Jaluria

CRC Press Taylor &. Francis Group Boca Raton London New York

CRC Press is an imprint of the Taylor & Francis Croup, an informa business

Contents

Chapter 1 Introduction 1

1.1 Engineering Design 2 1.1.1 Design Versus Analysis 2 1.1.2 Synthesis for Design 6 1.1.3 Selection Versus Design 7

1.2 Design as Part of Engineering Enterprise 9 1.2.1 Need or Opportunity 9 1.2.2 Evaluation and Market Analysis 10 1.2.3 Feasibility and Chances of Success 12 1.2.4 Engineering Design 14 1.2.5 Research and Development 15 1.2.6 Need for Optimization 16 1.2.7 Fabrication, Testing, and Production 18

1.3 Thermal Systems 19 1.3.1 Basic Characteristics 19 1.3.2 Analysis 22 1.3.3 Types and Examples 25

1.4 Outline and Scope of the Book 40 1.5 Summary 43 References 44

Chapter 2 Basic Considerations in Design 47

2.1 Formulation of the Design Problem 47 2.1.1 Requirements and Specifications 47 2.1.2 Given Quantities 50 2.1.3 Design Variables 51 2.1.4 Constraints or Limitations 53 2.1.5 Additional Considerations 55

2.2 Conceptual Design 58 2.2.1 Innovative Conceptual Design 58 2.2.2 Selection from Available Concepts 62 2.2.3 Modifications in the Design of Existing Systems 64

2.3 Steps in the Design Process 70 2.3.1 Physical System 72 2.3.2 Modeling 75

2.3.3 Simulation 76 2.3.4 Evaluation: Acceptable Design 81 2.3.5 Optimal Design 83 2.3.6 Safety Features, Automation, and Control 86 2.3.7 Communicating the Design 90 2.3.8 Patents and Copyrights 92

2.4 Computer-Aided Design 97 2.4.1 Main Features 97 2.4.2 Computer-Aided Design of Thermal Systems 98

2.5 Material Selection 104 2.5.1 Different Materials 104 2.5.2 Material Properties and Characteristics

for Thermal Systems 108 2.5.3 Selection and Substitution of Materials 110

2.6 Summary 113 References 115 Problems 116

Chapter3 Modeling of Thermal Systems 125

3.1 Introduction 125 3.1.1 Importance of Modeling in Design 125 3.1.2 Basic Features of Modeling 125

3.2 Typesof Models 128 3.2.1 Analog Models 129 3.2.2 Mathematical Models 130 3.2.3 Physical Models 130 3.2.4 Numerical Models 131 3.2.5 Interaction Between Models 133 3.2.6 Other Classifications 133

3.3 Mathematical Modeling 134 3.3.1 General Procedure 134 3.3.2 Final Model and Validation 160

3.4 Physical Modeling and Dimensionai Analysis 165 3.4.1 Dimensionai Analysis 166 3.4.2 Modeling and Similitude 176 3.4.3 Overall Physical Model 180

3.5 Curve Fitting 180 3.5.1 ExactFit 181 3.5.2 Best Fit 183

3.6 Summary 194 References 196 Problems 197

Chapter 4 Numerical Modeling and Simulation 207

4.1 Numerical Modeling 208 4.1.1 General Features 208 4.1.2 Development ofa Numerical Model 210 4.1.3 Available Software 211

4.2 Solution Procedures 212 4.2.1 Linear Algebraic Systems 213 4.2.2 Nonlinear Algebraic Systems 220 4.2.3 Ordinary Differential Equations 227 4.2.4 Partial Differential Equations 238

4.3 Numerical Model for a System 247 4.3.1 Modeling of Individual Components 248 4.3.2 Merging of Different Models 251 4.3.3 Accuracy and Validation 252

4.4 System Simulation 253 4.4.1 Importance of Simulation 254 4.4.2 Different Classes 256 4.4.3 Flow of Information 259

4.5 Methods for Numerical Simulation 264 4.5.1 Steady Lumped Systems 264 4.5.2 Dynamic Simulation of Lumped Systems 272 4.5.3 Distributed Systems 278 4.5.4 Simulation of Large Systems 282 4.5.5 Numerical Simulation Versus Real System 283

4.6 Summary 284 References 285 Problems 286

Chapter 5 Acceptable Design of a Thermal System: A Synthesis of Different Design Steps 299

5.1 Introduction 299 5.2 Initial Design 300 5.3 Design Strategies 309

5.3.1 Commonly Used Design Approach 309 5.3.2 Other Strategies 309 5.3.3 Iterative Redesign Procedure 317

5.4 Design of Systems from Different Application Areas 322 5.4.1 Manufacturing Processes 323 5.4.2 Cooling of Electronic Equipment 329 5.4.3 Environmental Systems 336 5.4.4 Heat Transfer Equipment 342 5.4.5 Fluid Flow Systems 350

5.4.6 Other Areas 361 5.4.7 Design of Components Versus Design of Systems 361

5.5 Additionai Considerations for Large Practical Systems 362 5.6 Summary 373 References 374 Problems 375

Chapter 6 Economic Considerations 383

6.1 Introduction 383 6.2 Calculation of Interest 385

6.2.1 Simple Interest 385 6.2.2 Compound Interest 385 6.2.3 Continuous Compounding 387 6.2.4 Effective Interest Rate 388

6.3 Worth of Money as a Function of Time 390 6.3.1 Present Worth 390 6.3.2 Future Worth 391 6.3.3 Inflation 393

6.4 Series of Payments 396 6.4.1 Future Worth of Uniform Series of Amounts 396 6.4.2 Present Worth of Uniform Series of Amounts 397 6.4.3 Continuous Compounding in a Series of Amounts 399 6.4.4 Changing Amount in Series of Payments 400 6.4.5 ShiftinTime 402 6.4.6 Different Frequencies 403 6.4.7 Changes in Schedule 403

6.5 Raising Capital 405 6.5.1 Bonds 406 6.5.2 Stocks 408

6.6 Taxes 408 6.6.1 Inclusion of Taxes 409 6.6.2 Depreciation 410

6.7 Economic Factor in Design 413 6.7.1 Cost Comparison 413 6.7.2 Rate of Return 417

6.8 Application to Thermal Systems 419 6.9 Summary 421 References 421 Problems 422

Chapter 7 Problem Formulation for Optimization 429

7.1 Introduction 429 7.1.1 Optimization in Design 429 7.1.2 Final Optimized Design 431

7.2 Basic Concepts 432 7.2.1 Objective Function 432 7.2.2 Constraints 434 7.2.3 Operating Conditions Versus Hardware 437 7.2.4 Mathematical Formulation 438

7.3 Optimization Methods 440 7.3.1 Calculus Methods 440 7.3.2 Search Methods 441 7.3.3 Linear and Dynamic Programming 442 7.3.4 Geometrie Programming 444 7.3.5 Other Methods 444

7.4 Optimization of Thermal Systems 447 7.4.1 Important Considerations 447 7.4.2 Different Approaches 448 7.4.3 Different Types of Thermal Systems 449 7.4.4 Examples 451 7.4.5 Consideration of the Second Law of Thermodynamics 455

7.5 Practical Aspects in Optimal Design 457 7.5.1 Choice of Variables for Optimization 457 7.5.2 Sensitivity Analysis 459 7.5.3 Dependence on Objective Function: Trade-Offs 461 7.5.4 Multi-Objective Optimization 462 7.5.5 Part of Overall Design Strategy 464 7.5.6 Change of Concept or Model 465

7.6 Summary 466 References 467 Problems 468

Chapter 8 Lagrange Multipliers 473

8.1 Introduction to Calculus Methods 473 8.2 The Lagrange Multiplier Method 475

8.2.1 Basic Approach 475 8.2.2 Physical Interpretation 477 8.2.3 Significance of the Multipliers 485

8.3 Optimization of Unconstrained Problems 486 8.3.1 Use of Gradients for Optimization 487 8.3.2 Determination of Minimum or Maximum 487 8.3.3 Conversion of Constrained to Unconstrained

Problem 489 8.4 Optimization of Constrained Problems 491 8.5 Applicability to Thermal Systems 494

8.5.1 UseofCurveFitting 494 8.5.2 Examples 495 8.5.3 Inequality Constraints 499

8.5.4 Some Practical Considerations 500 8.5.5 Computational Approach 501

8.6 Summary 503 References 504 Problems 505

Chapter 9 Search Methods 511

9.1 Basic Considerations 511 9.1.1 Importance of Search Methods 512 9.1.2 Types of Approaches 513 9.1.3 Application to Thermal Systems 514

9.2 Single-Variable Problem 515 9.2.1 Uniform Exhaustive Search 517 9.2.2 Dichotomous Search 519 9.2.3 Fibonacci Search 521 9.2.4 Golden Section and Other Search Methods 523 9.2.5 Comparison of Different Elimination Methods 524

9.3 Unconstrained Search with Multiple Variables 527 9.3.1 Lattice Search 529 9.3.2 Univariate Search 530 9.3.3 Steepest Ascent/Descent Method 532

9.4 Multivariable Constrained Optimization 537 9.4.1 Penalty Function Method 537 9.4.2 Search Along a Constraint 542

9.5 Examples of Thermal Systems 547 9.6 Summary 551 References 553 Problems 554

Chapter 10 Geometrie, Linear, and Dynamic Programming and Other Methods for Optimization 559

10.1 Geometrie Programming 559 10.1.1 Applicability 560 10.1.2 Unconstrained Optimization 561 10.1.3 Mathematical Proof 570 10.1.4 Constrained Optimization 573 10.1.5 Nonzero Degree of Difficulty 578

10.2 Linear Programming 579 10.3 Dynamic Programming 588 10.4 Other Methods 590 10.5 Summary 591 References 592 Problems 593

Chapter 11 Knowledge-Based Design and Additional Considerations 599

11.1 Knowledge-Based Systems 599 11.1.1 Introduction 600 11.1.2 Basie Components 602 11.1.3 Expert Knowledge 607 11.1.4 Design Methodology 609 11.1.5 Application to Thermal Systems 610

11.2 Additional Constraints 621 11.3 Professional Ethics 623 11.4 Sources of Information 625 11.5 An Overview of Design of Thermal Systems 628 11.6 Summary 631 References 632 Problems 633 Design Projects 635

Appendix A Computer Programs 639

Appendix B Material Properties 659

Appendix C Interest Tables 679

Appendix D Heat Transfer Correlations 687

Index 697