EBOOK : Fundamentals of Heat Exchanger Design - Ramesh K. Shah and Dušan P. Sekulic


2.2 Interactions Among Design Considerations 93
Summary 94
References 94
Review Questions 95
Problems 95
3 Basic Thermal Design Theory for Recuperators 97
3.1 Formal Analogy between Thermal and Electrical Entities 98
3.2 Heat Exchanger Variables and Thermal Circuit 100
3.2.1 Assumptions for Heat Transfer Analysis 100
3.2.2 Problem Formulation 102
3.2.3 Basic Definitions 104
3.2.4 Thermal Circuit andUA 107
3.3 The"-NTU Method 114
3.3.1 Heat Exchanger Effectiveness" 114
3.3.2 Heat Capacity Rate RatioC* 118
3.3.3 Number of Transfer Units NTU 119

3.4 Effectiveness – Number of Transfer Unit Relationships 121
3.4.1 Single-Pass Exchangers 122
3.5 TheP-NTU Method 139
3.5.1 Temperature EffectivenessP 140
3.5.2 Number of Transfer Units, NTU 140
3.5.3 Heat Capacity Rate RatioR 141
3.5.4 GeneralP–NTU Functional Relationship 141
3.6 P–NTU Relationships 142
3.6.1 Parallel Counterflow Exchanger, Shell Fluid Mixed, 1–2
TEMA E Shell 142
3.6.2 Multipass Exchangers 164
3.7 The Mean Temperature Difference Method 186
3.7.1 Log-Mean Temperature Difference, LMTD 186
3.7.2 Log-Mean Temperature Difference Correction Factor F 187
3.8 FFactors for Various Flow Arrangements 190
3.8.1 Counterflow Exchanger 190
3.8.2 Parallelflow Exchanger 191
3.8.3 Other Basic Flow Arrangements 192
3.8.4 Heat Exchanger Arrays and Multipassing 201
3.9 Comparison of the"-NTU,P–NTU, and MTD Methods 207
3.9.1 Solutions to the Sizing and Rating Problems 207
3.9.2 The"-NTU Method 208
3.9.3 TheP-NTU Method 209
3.9.4 The MTD Method 209
3.10 The -PandP1 P2
Methods 210
3.10.1 The -PMethod 210
3.10.2 TheP1 P2 Method 211
vi CONTENTS
3.11 Solution Methods for Determining Exchanger Effectiveness 212
3.11.1 Exact Analytical Methods 213
3.11.2 Approximate Methods 213
3.11.3 Numerical Methods 213
3.11.4 Matrix Formalism 214
3.11.5 Chain Rule Methodology 214
3.11.6 Flow-Reversal Symmetry 215
3.11.7 Rules for the Determination of Exchanger Effectiveness
with One Fluid Mixed 216
3.12 Heat Exchanger Design Problems 216
Summary 219
References 219
Review Questions 220
Problems 227
4 Additional Considerations for Thermal Design of Recuperators 232
4.1 Longitudinal Wall Heat Conduction Effects 232
4.1.1 Exchangers withC*¼0 236
4.1.2 Single-Pass Counterflow Exchanger 236
4.1.3 Single-Pass Parallelflow Exchanger 239
4.1.4 Single-Pass Unmixed–Unmixed Crossflow Exchanger 239
4.1.5 Other Single-Pass Exchangers 239
4.1.6 Multipass Exchangers 239
4.2 Nonuniform Overall Heat Transfer Coefficients 244
4.2.1 Temperature Effect 248
4.2.2 Length Effect 249
4.2.3 Combined Effect 251
4.3 Additional Considerations for Extended Surface Exchangers 258
4.3.1 Thin Fin Analysis 259
4.3.2 Fin Efficiency 272
4.3.3 Fin Effectiveness 288
4.3.4 Extended Surface Efficiency 289
4.4 Additional Considerations for Shell-and-Tube Exchangers 291
4.4.1 Shell Fluid Bypassing and Leakage 291
4.4.2 Unequal Heat Transfer Area in Individual Exchanger Passes 296
4.4.3 Finite Number of Baffles 297
Summary 298
References 298
Review Questions 299
Problems 302
5 Thermal Design Theory for Regenerators 308
5.1 Heat Transfer Analysis 308
5.1.1 Assumptions for Regenerator Heat Transfer Analysis 308
5.1.2 Definitions and Description of Important Parameters 310
5.1.3 Governing Equations 312
CONTENTS vii
5.2 The"-NTU
o Method 316
5.2.1 Dimensionless Groups 316
5.2.2 Influence of Core Rotation and Valve Switching Frequency 320
5.2.3 Convection Conductance Ratio (hA)* 320
5.2.4 "-NTU
o
Results for a Counterflow Regenerator 321
5.2.5 "-NTU
o
Results for a Parallelflow Regenerator 326
5.3 The – Method 337
5.3.1 Comparison of the"-NTU
o and – Methods 341
5.3.2 Solutions for a Counterflow Regenerator 344
5.3.3 Solution for a Parallelflow Regenerator 345
5.4 Influence of Longitudinal Wall Heat Conduction 348
5.5 Influence of Transverse Wall Heat Conduction 355
5.5.1 Simplified Theory 355
5.6 Influence of Pressure and Carryover Leakages 360
5.6.1 Modeling of Pressure and Carryover Leakages for a Rotary
Regenerator 360
5.7 Influence of Matrix Material, Size, and Arrangement 366
Summary 371
References 372
Review Questions 373
Problems 376
6 Heat Exchanger Pressure Drop Analysis 378
6.1 Introduction 378
6.1.1 Importance of Pressure Drop 378
6.1.2 Fluid Pumping Devices 380
6.1.3 Major Contributions to the Heat Exchanger Pressure Drop 380
6.1.4 Assumptions for Pressure Drop Analysis 381
6.2 Extended Surface Heat Exchanger Pressure Drop 381
6.2.1 Plate-Fin Heat Exchangers 382
6.2.2 Tube-Fin Heat Exchangers 391
6.3 Regenerator Pressure Drop 392
6.4 Tubular Heat Exchanger Pressure Drop 393
6.4.1 Tube Banks 393
6.4.2 Shell-and-Tube Exchangers 393
6.5 Plate Heat Exchanger Pressure Drop 397
6.6 Pressure Drop Associated with Fluid Distribution Elements 399
6.6.1 Pipe Losses 399
6.6.2 Sudden Expansion and Contraction Losses 399
6.6.3 Bend Losses 403
6.7 Pressure Drop Presentation 412
6.7.1 Nondimensional Presentation of Pressure Drop Data 413
6.7.2 Dimensional Presentation of Pressure Drop Data 414
viii CONTENTS
6.8 Pressure Drop Dependence on Geometry and Fluid Properties 418
Summary 419
References 420
Review Questions 420
Problems 422
7 Surface Basic Heat Transfer and Flow Friction Characteristics 425
7.1 Basic Concepts 426
7.1.1 Boundary Layers 426
7.1.2 Types of Flows 429
7.1.3 Free and Forced Convection 438
7.1.4 Basic Definitions 439
7.2 Dimensionless Groups 441
7.2.1 Fluid Flow 443
7.2.2 Heat Transfer 446
7.2.3 Dimensionless Surface Characteristics as a Function of the
Reynolds Number 449
7.3 Experimental Techniques for Determining Surface Characteristics 450
7.3.1 Steady-State Kays and London Technique 451
7.3.2 Wilson Plot Technique 460
7.3.3 Transient Test Techniques 467
7.3.4 Friction Factor Determination 471
7.4 Analytical and Semiempirical Heat Transfer and Friction Factor
Correlations for Simple Geometries 473
7.4.1 Fully Developed Flows 475
7.4.2 Hydrodynamically Developing Flows 499
7.4.3 Thermally Developing Flows 502
7.4.4 Simultaneously Developing Flows 507
7.4.5 Extended Reynolds Analogy 508
7.4.6 Limitations ofj vs. Re Plot 510
7.5 Experimental Heat Transfer and Friction Factor Correlations for
Complex Geometries 511
7.5.1 Tube Bundles 512
7.5.2 Plate Heat Exchanger Surfaces 514
7.5.3 Plate-Fin Extended Surfaces 515
7.5.4 Tube-Fin Extended Surfaces 519
7.5.5 Regenerator Surfaces 523
7.6 Influence of Temperature-Dependent Fluid Properties 529
7.6.1 Correction Schemes for Temperature-Dependent Fluid
Properties 530
7.7 Influence of Superimposed Free Convection 532
7.7.1 Horizontal Circular Tubes 533
7.7.2 Vertical Circular Tubes 535
7.8 Influence of Superimposed Radiation 537
7.8.1 Liquids as Participating Media 538
CONTENTS ix
7.8.2 Gases as Participating Media 538
Summary 542
References 544
Review Questions 548
Problems 553
8 Heat Exchanger Surface Geometrical Characteristics 563
8.1 Tubular Heat Exchangers 563
8.1.1 Inline Arrangement 563
8.1.2 Staggered Arrangement 566
8.2 Tube-Fin Heat Exchangers 569
8.2.1 Circular Fins on Circular Tubes 569
8.2.2 Plain Flat Fins on Circular Tubes 572
8.2.3 General Geometric Relationships for Tube-Fin Exchangers 574
8.3 Plate-Fin Heat Exchangers 574
8.3.1 Offset Strip Fin Exchanger 574
8.3.2 Corrugated Louver Fin Exchanger 580
8.3.3 General Geometric Relationships for Plate-Fin Surfaces 584
8.4 Regenerators with Continuous Cylindrical Passages 585
8.4.1 Triangular Passage Regenerator 585
8.5 Shell-and-Tube Exchangers with Segmental Baffles 587
8.5.1 Tube Count 587
8.5.2 Window and Crossflow Section Geometry 589
8.5.3 Bypass and Leakage Flow Areas 592
8.6 Gasketed Plate Heat Exchangers 597
Summary 598
References 598
Review Questions 599
9 Heat Exchanger Design Procedures 601
9.1 Fluid Mean Temperatures 601
9.1.1 Heat Exchangers withC* 0 603
9.1.2 Counterflow and Crossflow Heat Exchangers 604
9.1.3 Multipass Heat Exchangers 604
9.2 Plate-Fin Heat Exchangers 605
9.2.1 Rating Problem 605
9.2.2 Sizing Problem 617
9.3 Tube-Fin Heat Exchangers 631
9.3.1 Surface Geometries 631
9.3.2 Heat Transfer Calculations 631
9.3.3 Pressure Drop Calculations 632
9.3.4 Core Mass Velocity Equation 632
9.4 Plate Heat Exchangers 632
9.4.1 Limiting Cases for the Design 633
9.4.2 Uniqueness of a PHE for Rating and Sizing 635
x CONTENTS
9.4.3 Rating a PHE 637
9.4.4 Sizing a PHE 645
9.5 Shell-and-Tube Heat Exchangers 646
9.5.1 Heat Transfer and Pressure Drop Calculations 646
9.5.2 Rating Procedure 650
9.5.3 Approximate Design Method 658
9.5.4 More Rigorous Thermal Design Method 663
9.6 Heat Exchanger Optimization 664
Summary 667
References 667
Review Questions 668
Problems 669
10 Selection of Heat Exchangers and Their Components 673
10.1 Selection Criteria Based on Operating Parameters 674
10.1.1 Operating Pressures and Temperatures 674
10.1.2 Cost 675
10.1.3 Fouling and Cleanability 675
10.1.4 Fluid Leakage and Contamination 678
10.1.5 Fluids and Material Compatibility 678
10.1.6 Fluid Type 678
10.2 General Selection Guidelines for Major Exchanger Types 680
10.2.1 Shell-and-Tube Exchangers 680
10.2.2 Plate Heat Exchangers 693
10.2.3 Extended-Surface Exchangers 694
10.2.4 Regenerator Surfaces 699
10.3 Some Quantitative Considerations 699
10.3.1 Screening Methods 700
10.3.2 Performance Evaluation Criteria 713
10.3.3 Evaluation Criteria Based on the Second Law of
Thermodynamics 723
10.3.4 Selection Criterion Based on Cost Evaluation 724
Summary 726
References 726
Review Questions 727
Problems 732
11 Thermodynamic Modeling and Analysis 735
11.1 Introduction 735
11.1.1 Heat Exchanger as a Part of a System 737
11.1.2 Heat Exchanger as a Component 738
11.2 Modeling a Heat Exchanger Based on the First Law of
Thermodynamics 738
11.2.1 Temperature Distributions in Counterflow and Parallelflow
Exchangers 739
11.2.2 True Meaning of the Heat Exchanger Effectiveness 745
CONTENTS xi
11.2.3 Temperature Difference Distributions for Parallelflow and
Counterflow Exchangers 748
11.2.4 Temperature Distributions in Crossflow Exchangers 749
11.3 Irreversibilities in Heat Exchangers 755
11.3.1 Entropy Generation Caused by Finite Temperature Differences 756
11.3.2 Entropy Generation Associated with Fluid Mixing 759
11.3.3 Entropy Generation Caused by Fluid Friction 762
11.4 Thermodynamic Irreversibility and Temperature Cross Phenomena 763
11.4.1 Maximum Entropy Generation 763
11.4.2 External Temperature Cross and Fluid Mixing Analogy 765
11.4.3 Thermodynamic Analysis for 1–2 TEMA J Shell-and-Tube
Heat Exchanger 766
11.5 A Heuristic Approach to an Assessment of Heat Exchanger
Effectiveness 771
11.6 Energy, Exergy, and Cost Balances in the Analysis and Optimization
of Heat Exchangers 775
11.6.1 Temperature–Enthalpy Rate Change Diagram 776
11.6.2 Analysis Based on an Energy Rate Balance 779
11.6.3 Analysis Based on Energy/Enthalpy and Cost Rate Balancing 783
11.6.4 Analysis Based on an Exergy Rate Balance 786
11.6.5 Thermodynamic Figure of Merit for Assessing Heat
Exchanger Performance 787
11.6.6 Accounting for the Costs of Exergy Losses in a Heat
Exchanger 791
11.7 Performance Evaluation Criteria Based on the Second Law of
Thermodynamics 796
Summary 800
References 801
Review Questions 802
Problems 804
12 Flow Maldistribution and Header Design 809
12.1 Geometry-Induced Flow Maldistribution 809
12.1.1 Gross Flow Maldistribution 810
12.1.2 Passage-to-Passage Flow Maldistribution 821
12.1.3 Manifold-Induced Flow Maldistribution 834
12.2 Operating Condition–Induced Flow Maldistribution 837
12.2.1 Viscosity-Induced Flow Maldistribution 837
12.3 Mitigation of Flow Maldistribution 844
12.4 Header and Manifold Design 845
12.4.1 Oblique-Flow Headers 848
12.4.2 Normal-Flow Headers 852
12.4.3 Manifolds 852
Summary 853
References 853
xii CONTENTS
Review Questions 855
Problems 859
13 Fouling and Corrosion 863
13.1 Fouling and its Effect on Exchanger Heat Transfer and Pressure Drop 863
13.2 Phenomenological Considerations of Fouling 866
13.2.1 Fouling Mechanisms 867
13.2.2 Single-Phase Liquid-Side Fouling 870
13.2.3 Single-Phase Gas-Side Fouling 871
13.2.4 Fouling in Compact Exchangers 871
13.2.5 Sequential Events in Fouling 872
13.2.6 Modeling of a Fouling Process 875
13.3 Fouling Resistance Design Approach 881
13.3.1 Fouling Resistance and Overall Heat Transfer Coefficient
Calculation 881
13.3.2 Impact of Fouling on Exchanger Heat Transfer Performance 882
13.3.3 Empirical Data for Fouling Resistances 886
13.4 Prevention and Mitigation of Fouling 890
13.4.1 Prevention and Control of Liquid-Side Fouling 890
13.4.2 Prevention and Reduction of Gas-Side Fouling 891
13.4.3 Cleaning Strategies 892
13.5 Corrosion in Heat Exchangers 893
13.5.1 Corrosion Types 895
13.5.2 Corrosion Locations in Heat Exchangers 895
13.5.3 Corrosion Control 897
Summary 898
References 898
Review Questions 899
Problems 903
Appendix A: Thermophysical Properties 906
Appendix B:"-NTU Relationships for Liquid-Coupled Exchangers 911
Appendix C: Two-Phase Heat Transfer and Pressure Drop Correlations 913
C.1 Two-Phase Pressure Drop Correlations 913
C.2 Heat Transfer Correlations for Condensation 916
C.3 Heat Transfer Correlations for Boiling 917
Appendix D:UandCUAValues for Various Heat Exchangers 92

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2.2 Interactions Among Design Considerations 93
Summary 94
References 94
Review Questions 95
Problems 95
3 Basic Thermal Design Theory for Recuperators 97
3.1 Formal Analogy between Thermal and Electrical Entities 98
3.2 Heat Exchanger Variables and Thermal Circuit 100
3.2.1 Assumptions for Heat Transfer Analysis 100
3.2.2 Problem Formulation 102
3.2.3 Basic Definitions 104
3.2.4 Thermal Circuit andUA 107
3.3 The"-NTU Method 114
3.3.1 Heat Exchanger Effectiveness" 114
3.3.2 Heat Capacity Rate RatioC* 118
3.3.3 Number of Transfer Units NTU 119

3.4 Effectiveness – Number of Transfer Unit Relationships 121
3.4.1 Single-Pass Exchangers 122
3.5 TheP-NTU Method 139
3.5.1 Temperature EffectivenessP 140
3.5.2 Number of Transfer Units, NTU 140
3.5.3 Heat Capacity Rate RatioR 141
3.5.4 GeneralP–NTU Functional Relationship 141
3.6 P–NTU Relationships 142
3.6.1 Parallel Counterflow Exchanger, Shell Fluid Mixed, 1–2
TEMA E Shell 142
3.6.2 Multipass Exchangers 164
3.7 The Mean Temperature Difference Method 186
3.7.1 Log-Mean Temperature Difference, LMTD 186
3.7.2 Log-Mean Temperature Difference Correction Factor F 187
3.8 FFactors for Various Flow Arrangements 190
3.8.1 Counterflow Exchanger 190
3.8.2 Parallelflow Exchanger 191
3.8.3 Other Basic Flow Arrangements 192
3.8.4 Heat Exchanger Arrays and Multipassing 201
3.9 Comparison of the"-NTU,P–NTU, and MTD Methods 207
3.9.1 Solutions to the Sizing and Rating Problems 207
3.9.2 The"-NTU Method 208
3.9.3 TheP-NTU Method 209
3.9.4 The MTD Method 209
3.10 The -PandP1 P2
Methods 210
3.10.1 The -PMethod 210
3.10.2 TheP1 P2 Method 211
vi CONTENTS
3.11 Solution Methods for Determining Exchanger Effectiveness 212
3.11.1 Exact Analytical Methods 213
3.11.2 Approximate Methods 213
3.11.3 Numerical Methods 213
3.11.4 Matrix Formalism 214
3.11.5 Chain Rule Methodology 214
3.11.6 Flow-Reversal Symmetry 215
3.11.7 Rules for the Determination of Exchanger Effectiveness
with One Fluid Mixed 216
3.12 Heat Exchanger Design Problems 216
Summary 219
References 219
Review Questions 220
Problems 227
4 Additional Considerations for Thermal Design of Recuperators 232
4.1 Longitudinal Wall Heat Conduction Effects 232
4.1.1 Exchangers withC*¼0 236
4.1.2 Single-Pass Counterflow Exchanger 236
4.1.3 Single-Pass Parallelflow Exchanger 239
4.1.4 Single-Pass Unmixed–Unmixed Crossflow Exchanger 239
4.1.5 Other Single-Pass Exchangers 239
4.1.6 Multipass Exchangers 239
4.2 Nonuniform Overall Heat Transfer Coefficients 244
4.2.1 Temperature Effect 248
4.2.2 Length Effect 249
4.2.3 Combined Effect 251
4.3 Additional Considerations for Extended Surface Exchangers 258
4.3.1 Thin Fin Analysis 259
4.3.2 Fin Efficiency 272
4.3.3 Fin Effectiveness 288
4.3.4 Extended Surface Efficiency 289
4.4 Additional Considerations for Shell-and-Tube Exchangers 291
4.4.1 Shell Fluid Bypassing and Leakage 291
4.4.2 Unequal Heat Transfer Area in Individual Exchanger Passes 296
4.4.3 Finite Number of Baffles 297
Summary 298
References 298
Review Questions 299
Problems 302
5 Thermal Design Theory for Regenerators 308
5.1 Heat Transfer Analysis 308
5.1.1 Assumptions for Regenerator Heat Transfer Analysis 308
5.1.2 Definitions and Description of Important Parameters 310
5.1.3 Governing Equations 312
CONTENTS vii
5.2 The"-NTU
o Method 316
5.2.1 Dimensionless Groups 316
5.2.2 Influence of Core Rotation and Valve Switching Frequency 320
5.2.3 Convection Conductance Ratio (hA)* 320
5.2.4 "-NTU
o
Results for a Counterflow Regenerator 321
5.2.5 "-NTU
o
Results for a Parallelflow Regenerator 326
5.3 The – Method 337
5.3.1 Comparison of the"-NTU
o and – Methods 341
5.3.2 Solutions for a Counterflow Regenerator 344
5.3.3 Solution for a Parallelflow Regenerator 345
5.4 Influence of Longitudinal Wall Heat Conduction 348
5.5 Influence of Transverse Wall Heat Conduction 355
5.5.1 Simplified Theory 355
5.6 Influence of Pressure and Carryover Leakages 360
5.6.1 Modeling of Pressure and Carryover Leakages for a Rotary
Regenerator 360
5.7 Influence of Matrix Material, Size, and Arrangement 366
Summary 371
References 372
Review Questions 373
Problems 376
6 Heat Exchanger Pressure Drop Analysis 378
6.1 Introduction 378
6.1.1 Importance of Pressure Drop 378
6.1.2 Fluid Pumping Devices 380
6.1.3 Major Contributions to the Heat Exchanger Pressure Drop 380
6.1.4 Assumptions for Pressure Drop Analysis 381
6.2 Extended Surface Heat Exchanger Pressure Drop 381
6.2.1 Plate-Fin Heat Exchangers 382
6.2.2 Tube-Fin Heat Exchangers 391
6.3 Regenerator Pressure Drop 392
6.4 Tubular Heat Exchanger Pressure Drop 393
6.4.1 Tube Banks 393
6.4.2 Shell-and-Tube Exchangers 393
6.5 Plate Heat Exchanger Pressure Drop 397
6.6 Pressure Drop Associated with Fluid Distribution Elements 399
6.6.1 Pipe Losses 399
6.6.2 Sudden Expansion and Contraction Losses 399
6.6.3 Bend Losses 403
6.7 Pressure Drop Presentation 412
6.7.1 Nondimensional Presentation of Pressure Drop Data 413
6.7.2 Dimensional Presentation of Pressure Drop Data 414
viii CONTENTS
6.8 Pressure Drop Dependence on Geometry and Fluid Properties 418
Summary 419
References 420
Review Questions 420
Problems 422
7 Surface Basic Heat Transfer and Flow Friction Characteristics 425
7.1 Basic Concepts 426
7.1.1 Boundary Layers 426
7.1.2 Types of Flows 429
7.1.3 Free and Forced Convection 438
7.1.4 Basic Definitions 439
7.2 Dimensionless Groups 441
7.2.1 Fluid Flow 443
7.2.2 Heat Transfer 446
7.2.3 Dimensionless Surface Characteristics as a Function of the
Reynolds Number 449
7.3 Experimental Techniques for Determining Surface Characteristics 450
7.3.1 Steady-State Kays and London Technique 451
7.3.2 Wilson Plot Technique 460
7.3.3 Transient Test Techniques 467
7.3.4 Friction Factor Determination 471
7.4 Analytical and Semiempirical Heat Transfer and Friction Factor
Correlations for Simple Geometries 473
7.4.1 Fully Developed Flows 475
7.4.2 Hydrodynamically Developing Flows 499
7.4.3 Thermally Developing Flows 502
7.4.4 Simultaneously Developing Flows 507
7.4.5 Extended Reynolds Analogy 508
7.4.6 Limitations ofj vs. Re Plot 510
7.5 Experimental Heat Transfer and Friction Factor Correlations for
Complex Geometries 511
7.5.1 Tube Bundles 512
7.5.2 Plate Heat Exchanger Surfaces 514
7.5.3 Plate-Fin Extended Surfaces 515
7.5.4 Tube-Fin Extended Surfaces 519
7.5.5 Regenerator Surfaces 523
7.6 Influence of Temperature-Dependent Fluid Properties 529
7.6.1 Correction Schemes for Temperature-Dependent Fluid
Properties 530
7.7 Influence of Superimposed Free Convection 532
7.7.1 Horizontal Circular Tubes 533
7.7.2 Vertical Circular Tubes 535
7.8 Influence of Superimposed Radiation 537
7.8.1 Liquids as Participating Media 538
CONTENTS ix
7.8.2 Gases as Participating Media 538
Summary 542
References 544
Review Questions 548
Problems 553
8 Heat Exchanger Surface Geometrical Characteristics 563
8.1 Tubular Heat Exchangers 563
8.1.1 Inline Arrangement 563
8.1.2 Staggered Arrangement 566
8.2 Tube-Fin Heat Exchangers 569
8.2.1 Circular Fins on Circular Tubes 569
8.2.2 Plain Flat Fins on Circular Tubes 572
8.2.3 General Geometric Relationships for Tube-Fin Exchangers 574
8.3 Plate-Fin Heat Exchangers 574
8.3.1 Offset Strip Fin Exchanger 574
8.3.2 Corrugated Louver Fin Exchanger 580
8.3.3 General Geometric Relationships for Plate-Fin Surfaces 584
8.4 Regenerators with Continuous Cylindrical Passages 585
8.4.1 Triangular Passage Regenerator 585
8.5 Shell-and-Tube Exchangers with Segmental Baffles 587
8.5.1 Tube Count 587
8.5.2 Window and Crossflow Section Geometry 589
8.5.3 Bypass and Leakage Flow Areas 592
8.6 Gasketed Plate Heat Exchangers 597
Summary 598
References 598
Review Questions 599
9 Heat Exchanger Design Procedures 601
9.1 Fluid Mean Temperatures 601
9.1.1 Heat Exchangers withC* 0 603
9.1.2 Counterflow and Crossflow Heat Exchangers 604
9.1.3 Multipass Heat Exchangers 604
9.2 Plate-Fin Heat Exchangers 605
9.2.1 Rating Problem 605
9.2.2 Sizing Problem 617
9.3 Tube-Fin Heat Exchangers 631
9.3.1 Surface Geometries 631
9.3.2 Heat Transfer Calculations 631
9.3.3 Pressure Drop Calculations 632
9.3.4 Core Mass Velocity Equation 632
9.4 Plate Heat Exchangers 632
9.4.1 Limiting Cases for the Design 633
9.4.2 Uniqueness of a PHE for Rating and Sizing 635
x CONTENTS
9.4.3 Rating a PHE 637
9.4.4 Sizing a PHE 645
9.5 Shell-and-Tube Heat Exchangers 646
9.5.1 Heat Transfer and Pressure Drop Calculations 646
9.5.2 Rating Procedure 650
9.5.3 Approximate Design Method 658
9.5.4 More Rigorous Thermal Design Method 663
9.6 Heat Exchanger Optimization 664
Summary 667
References 667
Review Questions 668
Problems 669
10 Selection of Heat Exchangers and Their Components 673
10.1 Selection Criteria Based on Operating Parameters 674
10.1.1 Operating Pressures and Temperatures 674
10.1.2 Cost 675
10.1.3 Fouling and Cleanability 675
10.1.4 Fluid Leakage and Contamination 678
10.1.5 Fluids and Material Compatibility 678
10.1.6 Fluid Type 678
10.2 General Selection Guidelines for Major Exchanger Types 680
10.2.1 Shell-and-Tube Exchangers 680
10.2.2 Plate Heat Exchangers 693
10.2.3 Extended-Surface Exchangers 694
10.2.4 Regenerator Surfaces 699
10.3 Some Quantitative Considerations 699
10.3.1 Screening Methods 700
10.3.2 Performance Evaluation Criteria 713
10.3.3 Evaluation Criteria Based on the Second Law of
Thermodynamics 723
10.3.4 Selection Criterion Based on Cost Evaluation 724
Summary 726
References 726
Review Questions 727
Problems 732
11 Thermodynamic Modeling and Analysis 735
11.1 Introduction 735
11.1.1 Heat Exchanger as a Part of a System 737
11.1.2 Heat Exchanger as a Component 738
11.2 Modeling a Heat Exchanger Based on the First Law of
Thermodynamics 738
11.2.1 Temperature Distributions in Counterflow and Parallelflow
Exchangers 739
11.2.2 True Meaning of the Heat Exchanger Effectiveness 745
CONTENTS xi
11.2.3 Temperature Difference Distributions for Parallelflow and
Counterflow Exchangers 748
11.2.4 Temperature Distributions in Crossflow Exchangers 749
11.3 Irreversibilities in Heat Exchangers 755
11.3.1 Entropy Generation Caused by Finite Temperature Differences 756
11.3.2 Entropy Generation Associated with Fluid Mixing 759
11.3.3 Entropy Generation Caused by Fluid Friction 762
11.4 Thermodynamic Irreversibility and Temperature Cross Phenomena 763
11.4.1 Maximum Entropy Generation 763
11.4.2 External Temperature Cross and Fluid Mixing Analogy 765
11.4.3 Thermodynamic Analysis for 1–2 TEMA J Shell-and-Tube
Heat Exchanger 766
11.5 A Heuristic Approach to an Assessment of Heat Exchanger
Effectiveness 771
11.6 Energy, Exergy, and Cost Balances in the Analysis and Optimization
of Heat Exchangers 775
11.6.1 Temperature–Enthalpy Rate Change Diagram 776
11.6.2 Analysis Based on an Energy Rate Balance 779
11.6.3 Analysis Based on Energy/Enthalpy and Cost Rate Balancing 783
11.6.4 Analysis Based on an Exergy Rate Balance 786
11.6.5 Thermodynamic Figure of Merit for Assessing Heat
Exchanger Performance 787
11.6.6 Accounting for the Costs of Exergy Losses in a Heat
Exchanger 791
11.7 Performance Evaluation Criteria Based on the Second Law of
Thermodynamics 796
Summary 800
References 801
Review Questions 802
Problems 804
12 Flow Maldistribution and Header Design 809
12.1 Geometry-Induced Flow Maldistribution 809
12.1.1 Gross Flow Maldistribution 810
12.1.2 Passage-to-Passage Flow Maldistribution 821
12.1.3 Manifold-Induced Flow Maldistribution 834
12.2 Operating Condition–Induced Flow Maldistribution 837
12.2.1 Viscosity-Induced Flow Maldistribution 837
12.3 Mitigation of Flow Maldistribution 844
12.4 Header and Manifold Design 845
12.4.1 Oblique-Flow Headers 848
12.4.2 Normal-Flow Headers 852
12.4.3 Manifolds 852
Summary 853
References 853
xii CONTENTS
Review Questions 855
Problems 859
13 Fouling and Corrosion 863
13.1 Fouling and its Effect on Exchanger Heat Transfer and Pressure Drop 863
13.2 Phenomenological Considerations of Fouling 866
13.2.1 Fouling Mechanisms 867
13.2.2 Single-Phase Liquid-Side Fouling 870
13.2.3 Single-Phase Gas-Side Fouling 871
13.2.4 Fouling in Compact Exchangers 871
13.2.5 Sequential Events in Fouling 872
13.2.6 Modeling of a Fouling Process 875
13.3 Fouling Resistance Design Approach 881
13.3.1 Fouling Resistance and Overall Heat Transfer Coefficient
Calculation 881
13.3.2 Impact of Fouling on Exchanger Heat Transfer Performance 882
13.3.3 Empirical Data for Fouling Resistances 886
13.4 Prevention and Mitigation of Fouling 890
13.4.1 Prevention and Control of Liquid-Side Fouling 890
13.4.2 Prevention and Reduction of Gas-Side Fouling 891
13.4.3 Cleaning Strategies 892
13.5 Corrosion in Heat Exchangers 893
13.5.1 Corrosion Types 895
13.5.2 Corrosion Locations in Heat Exchangers 895
13.5.3 Corrosion Control 897
Summary 898
References 898
Review Questions 899
Problems 903
Appendix A: Thermophysical Properties 906
Appendix B:"-NTU Relationships for Liquid-Coupled Exchangers 911
Appendix C: Two-Phase Heat Transfer and Pressure Drop Correlations 913
C.1 Two-Phase Pressure Drop Correlations 913
C.2 Heat Transfer Correlations for Condensation 916
C.3 Heat Transfer Correlations for Boiling 917
Appendix D:UandCUAValues for Various Heat Exchangers 92

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