The late JOHN A. DUFFIE was Professor Emeritus of Chemical-Engineering and past Director of the Solar Energy Laboratory at the University of Wisconsin-Madison.

WILLIAM A. BECKMAN is the Ouweneel-Bascom Professor Emeritus of Mechanical Engineering and Director Emeritus of the Solar Energy Laboratory at the University of Wisconsin-Madison.

NATHAN BLAIR manages the Distributed Systems and Storage Group in the Strategic Energy Analysis center at the National Renewable Energy Laboratory.

Preface xi

Preface to the Fourth Edition xiii

Preface to the Third Edition xv

Preface to the Second Edition xvii

Preface to the First Edition xix

Part I Fundamentals 1

1 Solar Radiation 3

1.1 The Sun 3

1.2 The Solar Constant 5

1.3 Spectral Distribution of Extraterrestrial Radiation 6

1.4 Variation of Extraterrestrial Radiation 8

1.5 Definitions 9

1.6 Direction of Beam Radiation 12

1.7 Angles for Tracking Surfaces 20

1.8 Ratio of Beam Radiation on Tilted Surface to That on Horizontal Surface 24

1.9 Shading 30

1.10 Extraterrestrial Radiation on a Horizontal Surface 37

1.11 Summary 41

References 43

2 Available Solar Radiation 45

2.1 Definitions 45

2.2 Pyrheliometers and Pyrheliometric Scales 46

2.3 Pyranometers 50

2.4 Measurement of Duration of Sunshine 55

2.5 Solar Radiation Data 56

2.6 Atmospheric Attenuation of Solar Radiation 61

2.7 Estimation of Average Solar Radiation 66

2.8 Estimation of Clear-Sky Radiation 70

2.9 Distribution of Clear and Cloudy Days and Hours 73

2.10 Beam and Diffuse Components of Hourly Radiation 76

2.11 Beam and Diffuse Components of Daily Radiation 79

2.12 Beam and Diffuse Components of Monthly Radiation 81

2.13 Estimation of Hourly Radiation from Daily Data 83

2.14 Radiation on Sloped Surfaces 86

2.15 Radiation on Sloped Surfaces: Isotropic Sky 91

2.16 Radiation on Sloped Surfaces: Anisotropic Sky 92

2.17 Radiation Augmentation 98

2.18 Beam Radiation on Moving Surfaces 103

2.19 Average Radiation on Sloped Surfaces: Isotropic Sky 104

2.20 Average Radiation on Sloped Surfaces: KT Method 108

2.21 Effects of Receiving Surface Orientation on H_T 114

2.22 Utilizability 116

2.23 Generalized Utilizability 120

2.24 Daily Utilizability 128

2.25 Summary 134

References 136

3 Selected Heat Transfer Topics 141

3.1 The Electromagnetic Spectrum 141

3.2 Photon Radiation 142

3.3 The Blackbody: Perfect Absorber and Emitter 142

3.4 Planck’s Law and Wien’s Displacement Law 143

3.5 Stefan-Boltzmann Equation 144

3.6 Radiation Tables 145

3.7 Radiation Intensity and Flux 147

3.8 Infrared Radiation Exchange Between Gray Surfaces 149

3.9 Sky Radiation 150

3.10 Radiation Heat Transfer Coefficient 151

3.11 Natural Convection Between Flat Parallel Plates and Between Concentric Cylinders 152

3.12 Convection Suppression 157

3.13 Vee-Corrugated Enclosures 161

3.14 Heat Transfer Relations for Internal Flow 162

3.15 Wind Convection Coefficients 166

3.16 Heat Transfer and Pressure Drop in Packed Beds and Perforated Plates 168

3.17 Effectiveness-NTU Calculations for Heat Exchangers 171

3.18 Summary 173

References 174

4 Radiation Characteristics of Opaque Materials 177

4.1 Absorptance and Emittance 178

4.2 Kirchhoff’s Law 180

4.3 Reflectance of Surfaces 181

4.4 Relationships Among Absorptance, Emittance, and Reflectance 185

4.5 Broadband Emittance and Absorptance 186

4.6 Calculation of Emittance and Absorptance 187

4.7 Measurement of Surface Radiation Properties 190

4.8 Selective Surfaces 192

4.9 Mechanisms of Selectivity 196

4.10 Optimum Properties 199

4.11 Angular Dependence of Solar Absorptance 200

4.12 Absorptance of Cavity Receivers 201

4.13 Specularly Reflecting Surfaces 202

4.14 Advanced Radiation Heat Transfer Analysis 203

4.15 Summary 205

References 206

5 Radiation Transmission through Glazing: Absorbed Radiation 209

5.1 Reflection of Radiation 209

5.2 Absorption by Glazing 213

5.3 Optical Properties of Cover Systems 213

5.4 Transmittance for Diffuse Radiation 218

5.5 Transmittance-Absorptance Product 220

5.6 Angular Dependence of (𝜏𝛼) 221

5.7 Spectral Dependence of Transmittance 222

5.8 Effects of Surface Layers on Transmittance 225

5.9 Absorbed Solar Radiation 226

5.10 Monthly Average Absorbed Radiation 230

5.11 Absorptance of Rooms 236

5.12 Absorptance of Photovoltaic Cells 238

5.13 Summary 241

References 243

6 Flat-Plate Collectors 244

6.1 Description of Flat-Plate Collectors 244

6.2 Basic Flat-Plate Energy Balance Equation 245

6.3 Temperature Distributions in Flat-Plate Collectors 246

6.4 Collector Overall Heat Loss Coefficient 248

6.5 Temperature Distribution Between Tubes and the Collector Efficiency Factor 262

6.6 Temperature Distribution in Flow Direction 269

6.7 Collector Heat Removal Factor and Flow Factor 270

6.8 Critical Radiation Level 274

6.9 Mean Fluid and Plate Temperatures 275

6.10 Effective Transmittance-Absorptance Product 276

6.11 Effects of Dust and Shading 279

6.12 Heat Capacity Effects in Flat-Plate Collectors 280

6.13 Liquid Heater Plate Geometries 283

6.14 Air Heaters 288

6.15 Measurements of Collector Performance 295

6.16 Collector Characterizations 296

6.17 Collector Tests: Efficiency, Incidence Angle Modifier, and Time Constant 297

6.18 Test Data 307

6.19 Thermal Test Data Conversion 310

6.20 Flow Rate Corrections to F_R (𝜏𝛼)_n and F_RU_L 313

6.21 Flow Distribution in Collectors 316

6.22 In Situ Collector Performance 317

6.23 Practical Considerations for Flat-Plate Collectors 318

6.24 Putting It All Together 321

6.25 Summary 326

References 327

7 Concentrating Collectors 331

7.1 Collector Configurations 332

7.2 Concentration Ratio 334

7.3 Thermal Performance of Concentrating Collectors 336

7.4 Optical Performance of Concentrating Collectors 343

7.5 Cylindrical Absorber Arrays 344

7.6 Optical Characteristics of Nonimaging Concentrators 346

7.7 Orientation and Absorbed Energy for CPC Collectors 354

7.8 Performance of CPC Collectors 358

7.9 Linear Imaging Concentrators: Geometry 360

7.10 Images Formed by Perfect Linear Concentrators 363

7.11 Images from Imperfect Linear Concentrators 368

7.12 Ray-Trace Methods for Evaluating Concentrators 370

7.13 Incidence Angle Modifiers and Energy Balances 370

7.14 Paraboloidal Concentrators 376

7.15 Central-Receiver Collectors 377

7.16 Practical Considerations 378

7.17 Summary 379

References 380

8 Energy Storage 382

8.1 Process Loads and Solar Collector Outputs 382

8.2 Energy Storage in Solar Thermal Systems 384

8.3 Water Storage 385

8.4 Stratification in Storage Tanks 388

8.5 Packed-Bed Storage 393

8.6 Storage Walls 401

8.7 Seasonal Storage 403

8.8 Phase Change Energy Storage 405

8.9 Chemical Energy Storage 410

8.10 Battery Storage 411

8.11 Hydroelectric and Compressed Air Storage 415

8.12 Summary 418

References 419

9 Solar Process Loads 422

9.1 Examples of Time-Dependent Loads 423

9.2 Hot-Water Loads 424

9.3 Space Heating Loads, Degree-Days, and Balance Temperature 425

9.4 Building Loss Coefficients 428

9.5 Building Energy Storage Capacity 430

9.6 Cooling Loads 430

9.7 Swimming Pool Heating Loads 431

9.8 Summary 433

References 434

10 System Thermal Calculations 436

10.1 Component Models 437

10.2 Collector Heat Exchanger Factor 438

10.3 Duct and Pipe Loss Factors 440

10.4 Controls 443

10.5 Collector Arrays: Series Connections 445

10.6 Performance of Partially Shaded Collectors 447

10.7 Series Arrays with Sections Having Different Orientations 449

10.8 Use of Modified Collector Equations 451

10.9 System Models 455

10.10 Solar Fraction and Solar Savings Fraction 458

10.11 Summary 459

References 461

11 Solar Process Economics 462

11.1 Costs of Solar Process Systems 462

11.2 Design Variables 465

11.3 Economic Figures of Merit 467

11.4 Discounting and Inflation 469

11.5 Present-Worth Factor 471

11.6 Life-Cycle Savings Method 474

11.7 Evaluation of Other Economic Indicators 479

11.8 The P₁, P₂ Method 482

11.9 Uncertainties in Economic Analyses 487

11.10 Economic Analysis Using Solar Savings Fraction 490

11.11 Summary 491

References 491

Part II Applications 493

12 Solar Water Heating: Active and Passive 495

12.1 Water Heating Systems 495

12.2 Freezing, Boiling, and Scaling 499

12.3 Auxiliary Energy 502

12.4 Forced-Circulation Systems 504

12.5 Low-Flow Pumped Systems 505

12.6 Natural-Circulation Systems 507

12.7 Integral Collector Storage Systems 510

12.8 Retrofit Water Heaters 512

12.9 Water Heating in Space Heating and Cooling Systems 512

12.10 Testing and Rating of Solar Water Heaters 513

12.11 Economics of Solar Water Heating 514

12.12 Swimming Pool Heating 517

12.13 Summary 518

References 519

13 Building Heating: Active 521

13.1 Historical Notes 522

13.2 Solar Heating Systems 523

13.3 CSU House III Flat-Plate Liquid System 528

13.4 CSU House II Air System 531

13.5 Heating System Parametric Study 533

13.6 Solar Energy–Heat Pump Systems 537

13.7 Phase Change Storage Systems 542

13.8 Seasonal Energy Storage Systems 545

13.9 Solar and Off-Peak Electric Systems 549

13.10 Solar System Overheating 550

13.11 Solar Heating Economics 551

13.12 Architectural Considerations 554

References 556

14 Building Heating: Passive and Hybrid Methods 559

14.1 Concepts of Passive Heating 560

14.2 Comfort Criteria and Heating Loads 561

14.3 Movable Insulation and Controls 561

14.4 Shading: Overhangs and Wingwalls 562

14.5 Direct-Gain Systems 566

14.6 Collector-Storage Walls and Roofs 571

14.7 Sunspaces 575

14.8 Active Collection–Passive Storage Hybrid Systems 577

14.9 Other Hybrid Systems 578

14.10 Passive Applications 579

14.11 Heat Distribution in Passive Buildings 584

14.12 Costs and Economics of Passive Heating 585

14.13 Summary 587

References 588

15 Solar Cooling 590

15.1 Solar Absorption Cooling 591

15.2 Theory of Absorption Cooling 593

15.3 Combined Solar Heating and Cooling 599

15.4 Simulation Study of Solar Air Conditioning 600

15.5 Operating Experience with Solar Cooling 603

15.6 Applications of Solar Absorption Air Conditioning 606

15.7 Solar Desiccant Cooling 606

15.8 Ventilation and Recirculation Desiccant Cycles 609

15.9 Solar-Mechanical Cooling 611

15.10 Solar-Related Air Conditioning 614

15.11 Passive Cooling 615

References 616

16 Solar Industrial Process Heat 619

16.1 Integration with Industrial Processes 619

16.2 Mechanical Design Considerations 620

16.3 Economics of Industrial Process Heat 621

16.4 Open-Circuit Air Heating Applications 622

16.5 Recirculating Air System Applications 626

16.6 Once-Through Industrial Water Heating 628

16.7 Recirculating Industrial Water Heating 630

16.8 Shallow-Pond Water Heaters 632

16.9 Summary 634

References 634

17 Solar Thermal Power Systems 636

17.1 Thermal Conversion Systems 636

17.2 Gila Bend Pumping System 637

17.3 Luz Systems 639

17.4 Central-Receiver Systems 643

17.5 Solar One and Solar Two Power Plants 645

17.6 Summary 648

References 648

18 Solar Ponds: Evaporative Processes 650

18.1 Salt-Gradient Solar Ponds 650

18.2 Pond Theory 652

18.3 Applications of Ponds 654

18.4 Solar Distillation 655

18.5 Evaporation 661

18.6 Direct Solar Drying 662

18.7 Summary 662

References 663

Part III Design Methods 665

19 Simulations in Solar Process Design 667

19.1 Simulation Programs 668

19.2 Utility of Simulations 668

19.3 Information from Simulations 669

19.4 TRNSYS: Thermal Process Simulation Program 671

19.5 Simulations and Experiments 677

19.6 Meteorological Data 678

19.7 Limitations of Simulations 681

References 681

20 Design of Active Systems: f-Chart 683

20.1 Review of Design Methods 683

20.2 The f-Chart Method 684

20.3 The f-Chart for Liquid Systems 688

20.4 The f-Chart for Air Systems 694

20.5 Service Water Heating Systems 698

20.6 The f-Chart Results 700

20.7 Parallel Solar Energy-Heat Pump Systems 701

20.8 Summary 705

References 705

21 Design of Active Systems by Utilizability Methods 707

21.1 Hourly Utilizability 708

21.2 Daily Utilizability 711

21.3 The 𝜙, f-Chart Method 714

21.4 Summary 724

References 725

22 Design of Passive and Hybrid Heating Systems 726

22.1 Approaches to Passive Design 726

22.2 Solar-Load Ratio Method 727

22.3 Unutilizability Design Method: Direct Gain 736

22.4 Unutilizability Design Method: Collector-Storage Walls 742

22.5 Hybrid Systems: Active Collection with Passive Storage 750

22.6 Other Hybrid Systems 757

22.7 Summary 758

References 758

23 Design of Photovoltaic Systems 760

23.1 Photovoltaic Converters 761

23.2 PV Generator Characteristics and Models 762

23.3 Cell Temperature 773

23.4 Load Characteristics and Direct-Coupled Systems 775

23.5 Controls and Maximum Power Point Trackers 778

23.6 Applications 779

23.7 Design Procedures 780

23.8 High-Flux PV Generators 786

23.9 Summary 786

References 787

24 Wind Energy 789

24.1 Introduction 789

24.2 Wind Resource 793

24.3 One-Dimensional Wind Turbine Model 801

24.4 Estimating Wind Turbine Average Power and Energy Production 806

24.5 Summary 810

References 810

Appendixes 811

A Problems 811

B Nomenclature 870

C International System of Units 875

D Meteorological Data 877

Index 885

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