FUNDAMENTALS OF HEAT EXCHANGER DESIGN
FUNDAMENTALS OF HEAT
EXCHANGER DESIGN
FUNDAMENTALS OF
HEAT EXCHANGER DESIGN Ramesh K. ShahRochester Institute of Technology, Rochester, New York Formerly at Delphi Harrison Thermal Systems, Lockport, New York
Dusˇan P. Sekulic´
University of Kentucky, Lexington, Kentucky This book is printed on acid-free paper. 1
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site at www.wiley.com Library of Congress Cataloging-in-Publication Data: Shah, R. K.Fundamentals of heat exchanger design / Ramesh K. Shah, Dusˇan P. Sekulic´. p. cm. Includes index.
ISBN 0-471-32171-0 1. Heat exchangers–Design and construction.
I. Sekulic´, Dusˇan P. II. Title. TJ263 .S42 2003 621.402 5–dc21
2002010161 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 Contents
Preface xv
78
56
1.6.1 Single-Pass Exchangers
57
1.6.2 Multipass Exchangers
64
1.7 Classification According to Heat Transfer Mechanisms
73 Summary
73 References
73 Review Questions
74
2 Overview of Heat Exchanger Design Methodology
2.1 Heat Exchanger Design Methodology
47
78
2.1.1 Process and Design Specifications
79
2.1.2 Thermal and Hydraulic Design
83
2.1.3 Mechanical Design
87
2.1.4 Manufacturing Considerations and Cost Estimates
90
2.1.5 Trade-off Factors
92
2.1.6 Optimum Design
1.6 Classification According to Flow Arrangements
1.5.4 Regenerators
Nomenclature xix
8
1 Classification of Heat Exchangers
1
1.1 Introduction
1
1.2 Classification According to Transfer Processes
3
1.2.1 Indirect-Contact Heat Exchangers
3
1.2.2 Direct-Contact Heat Exchangers
7
1.3 Classification According to Number of Fluids
1.4 Classification According to Surface Compactness
36
8
1.4.1 Gas-to-Fluid Exchangers
11
1.4.2 Liquid-to-Liquid and Phase-Change Exchangers
12
1.5 Classification According to Construction Features
12
1.5.1 Tubular Heat Exchangers
13
1.5.2 Plate-Type Heat Exchangers
22
1.5.3 Extended Surface Heat Exchangers
93
2.2 Interactions Among Design Considerations
3.8.3 Other Basic Flow Arrangements 192
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 F Factors for Various Flow Arrangements 190
3.8.1 Counterflow Exchanger 190
3.8.2 Parallelflow Exchanger 191
3.8.4 Heat Exchanger Arrays and Multipassing 201
3.5.3 Heat Capacity Rate Ratio R 141
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 The P-NTU Method 209
3.9.4 The MTD Method 209
3.10 The -P and P
1 P
2 Methods 210
3.10.1 The -P Method 210
3.5.4 General P–NTU Functional Relationship 141
3.5.2 Number of Transfer Units, NTU 140
93 Summary
3.2.2 Problem Formulation 102
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
3.2.3 Basic Definitions 104
3.5.1 Temperature Effectiveness P 140
3.2.4 Thermal Circuit and UA 107
3.3 The "-NTU Method
114
3.3.1 Heat Exchanger Effectiveness "
114
3.3.2 Heat Capacity Rate Ratio C* 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 The P-NTU Method 139
vi CONTENTS
3.11 Solution Methods for Determining Exchanger Effectiveness 212
4.4.2 Unequal Heat Transfer Area in Individual Exchanger Passes 296
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
4.4.3 Finite Number of Baffles 297 Summary
4.2.1 Temperature Effect 248
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
4.2.2 Length Effect 249
4.2 Nonuniform Overall Heat Transfer Coefficients 244
3.11.1 Exact Analytical Methods 213
219 Review Questions
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
220 Problems
4.1.6 Multipass Exchangers 239
227
4 Additional Considerations for Thermal Design of Recuperators 232
4.1 Longitudinal Wall Heat Conduction Effects 232
4.1.1 Exchangers with C* ¼ 0
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
CONTENTS vii
5.2 The "-NTU
6.2.2 Tube-Fin Heat Exchangers 391
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
6.3 Regenerator Pressure Drop 392
372 Review Questions
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
373 Problems
371 References
o
5.3 The – Method 337
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
5.3.1 Comparison of the "-NTU
5.7 Influence of Matrix Material, Size, and Arrangement 366 Summary
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
viii CONTENTS
6.8 Pressure Drop Dependence on Geometry and Fluid Properties 418 Summary
7.5.3 Plate-Fin Extended Surfaces 515
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 of j 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
7.5.4 Tube-Fin Extended Surfaces 519
7.4.1 Fully Developed Flows 475
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
7.4.2 Hydrodynamically Developing Flows 499
7.4 Analytical and Semiempirical Heat Transfer and Friction Factor Correlations for Simple Geometries 473
419 References
7.1.3 Free and Forced Convection 438
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
7.1.4 Basic Definitions 439
7.3.4 Friction Factor Determination 471
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
CONTENTS ix
7.8.2 Gases as Participating Media 538 Summary
9.2 Plate-Fin Heat Exchangers 605
598 References
598 Review Questions
599
9 Heat Exchanger Design Procedures 601
9.1 Fluid Mean Temperatures 601
9.1.1 Heat Exchangers with C* 603
9.1.2 Counterflow and Crossflow Heat Exchangers 604
9.1.3 Multipass Heat Exchangers 604
9.2.1 Rating Problem 605
8.5.3 Bypass and Leakage Flow Areas 592
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
8.6 Gasketed Plate Heat Exchangers 597 Summary
8.5.2 Window and Crossflow Section Geometry 589
542 References
8.2.1 Circular Fins on Circular Tubes 569
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
8.2.2 Plain Flat Fins on Circular Tubes 572
8.5.1 Tube Count 587
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
x CONTENTS
9.4.3 Rating a PHE 637
727 Problems
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
732
10.2.2 Plate Heat Exchangers 693
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
10.2.3 Extended-Surface Exchangers 694
10.2.1 Shell-and-Tube Exchangers 680
9.4.4 Sizing a PHE 645
668 Problems
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
669
10.2 General Selection Guidelines for Major Exchanger Types 680
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
CONTENTS xi
11.2.3 Temperature Difference Distributions for Parallelflow and Counterflow Exchangers 748
12.1.3 Manifold-Induced Flow Maldistribution 834
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
12.2 Operating Condition–Induced Flow Maldistribution 837
796 Summary
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
800 References
11.7 Performance Evaluation Criteria Based on the Second Law of Thermodynamics
11.2.4 Temperature Distributions in Crossflow Exchangers 749
11.4.3 Thermodynamic Analysis for 1–2 TEMA J Shell-and-Tube Heat Exchanger 766
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
11.5 A Heuristic Approach to an Assessment of Heat Exchanger Effectiveness
791
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
xii CONTENTS
Review Questions 855
899 Problems
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
903 Appendix A: Thermophysical Properties 906 Appendix B:
13.4.2 Prevention and Reduction of Gas-Side Fouling 891
"-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: U and C
UA
Values for Various Heat Exchangers 920 General References on or Related to Heat Exchangers 926 Index
931
13.4.3 Cleaning Strategies 892
13.4.1 Prevention and Control of Liquid-Side Fouling 890
Problems 859
13.2.4 Fouling in Compact Exchangers 871
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
13.2.5 Sequential Events in Fouling 872
13.4 Prevention and Mitigation of Fouling 890
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
CONTENTS xiii Preface
Over the past quarter century, the importance of heat exchangers has increased immen- sely from the viewpoint of energy conservation, conversion, recovery, and successful implementation of new energy sources. Its importance is also increasing from the stand- point of environmental concerns such as thermal pollution, air pollution, water pollu- tion, and waste disposal. Heat exchangers are used in the process, power, transportation, air-conditioning and refrigeration, cryogenic, heat recovery, alternate fuels, and manufacturing industries, as well as being key components of many industrial products available in the marketplace. From an educational point of view, heat exchangers illustrate in one way or another most of the fundamental principles of the thermal sciences, thus serving as an excellent vehicle for review and application, meeting the guidelines for university studies in the United States and oversees. Significant advances have taken place in the development of heat exchanger manufacturing technology as well as design theory. Many books have been published on the subject, as summarized in the General References at the end of the book. However, our assessment is that none of the books available seems to provide an in-depth coverage of the intricacies of heat exchanger design and theory so as to fully support both a student and a practicing engineer in the quest for creative mastering of both theory and design. Our book was motivated by this consideration. Coverage includes the theory and design of exchangers for many industries (not restricted to, say, the process industry) for a broader, in-depth foundation.
The objective of this book is to provide in-depth thermal and hydraulic design theory of two-fluid single-phase heat exchangers for steady-state operation. Three important goals were borne in mind during the preparation of this book:
1. To introduce and apply concepts learned in first courses in heat transfer, fluid mechanics, thermodynamics, and calculus, to develop heat exchanger design theory. Thus, the book will serve as a link between fundamental subjects men- tioned and thermal engineering design practice in industry.
2. To introduce and apply basic heat exchanger design concepts to the solution of industrial heat exchanger problems. Primary emphasis is placed on fundamental concepts and applications. Also, more emphasis is placed on analysis and less on empiricism.
3. The book is also intended for practicing engineers in addition to students.
Hence, at a number of places in the text, some redundancy is added to make the concepts clearer, early theory is developed using constant and mean overall heat transfer coefficients, and more data are added in the text and tables for industrial xvi PREFACE
To provide comprehensive information for heat exchanger design and analysis in a book of reasonable length, we have opted not to include detailed theoretical derivations of many results, as they can be found in advanced convection heat transfer textbooks. Instead, we have presented some basic derivations and then presented comprehensive information through text and concise tables. system design considerations to ensure proper functioning. Accordingly, a good design engineer must be familiar with both system and component design aspects. Based on industrial experience of over three decades in designing compact heat exchangers for automobiles and other industrial applications and more than twenty years of teaching, we have endeavored to demonstrate interrelationships between the component and sys- tem design aspects, as well as between the needs of industrial and learning environments. Some of the details of component design presented are also based on our own system design experience.
Considering the fact that heat exchangers constitute a multibillion-dollar industry in the United States alone, and there are over 300 companies engaged in the manufacture of a wide array of heat exchangers, it is difficult to select appropriate material for an introductory course. We have included more material than is necessary for a one- semester course, placing equal emphasis on four basic heat exchanger types: shell-and- tube, plate, extended surface, and regenerator. The choice of the teaching material to cover in one semester is up to the instructor, depending on his or her desire to focus on specific exchanger types and specific topics in each chapter. The prerequisites for this course are first undergraduate courses in fluid mechanics, thermodynamics, and heat transfer. It is expected that the student is familiar with the basics of forced convection and the basic concepts of the heat transfer coefficient, heat exchanger effectiveness, and mean temperature difference.
Starting with a detailed classification of a variety of heat exchangers in Chapter 1, an overview of heat exchanger design methodology is provided in Chapter 2. The basic thermal design theory for recuperators is presented in Chapter 3, advanced design theory for recuperators in Chapter 4, and thermal design theory for regenerators in Chapter 5. Pressure drop analysis is presented in Chapter 6. The methods and sources for obtaining heat transfer and flow friction characteristics of exchanger surfaces are presented in Chapter 7. Surface geometrical properties needed for heat exchanger design are covered in Chapter 8. The thermal and hydraulic designs of extended-surface (compact and noncompact plate-fin and tube-fin), plate, and shell-and-tube exchangers are out- lined in Chapter 9. Guidelines for selecting the exchanger core construction and surface geometry are presented in Chapter 10. Chapter 11 is devoted to thermodynamic analysis for heat exchanger design and includes basic studies of temperature distributions in heat exchangers, a heuristic approach to an assessment of heat exchanger effectiveness, and advanced topics important for modeling, analysis, and optimization of heat exchangers as components. All topics covered up to this point are related to thermal–hydraulic design of heat exchangers in steady-state or periodic-flow operation. Operational problems for compact and other heat exchangers are covered in Chapters 12 and 13. They include the problems caused by flow maldistribution and by fouling and corrosion. Solved examples from industrial experience and classroom practice are presented throughout the book to illustrate important concepts and applications. Numerous review questions and problems are also provided at the end of each chapter. If students can answer the review questions and solve the problems correctly, they can be sure of their grasp of the basic concepts and material presented in the text. It is hoped that readers will
PREFACE xvii
develop good understanding of the intricacies of heat exchanger design after going through this material and prior to embarking on specialized work in their areas of greatest interest.
For the thermal design of a heat exchanger for an application, considerable intellec- tual effort is needed in selecting heat exchanger type and determining the appropriate needed for executing sizing and optimizing the exchanger because of the computer- based calculations. Thus, Chapters 7, 9, and 10 are very important, in addition to
Chapter 3, for basic understanding of theory, design, analysis, and selection of heat exchangers. Material presented in Chapters 11 through 13 is significantly more interdisciplinary than the rest of the book and is presented here in a modified methodological approach. In Chapter 11 in particular, analytical modeling is used extensively. Readers will participate actively through a set of examples and problems that extend the breadth and depth of the material given in the main body of the text. A number of examples and problems in
Chapter 11 require analytical derivations and more elaborate analysis, instead of illus- trating the topics with examples that favor only utilization of the formulas and comput- ing numerical values for a problem. The complexity of topics requires a more diverse approach to terminology, less routine treatment of established conventions, and a more creative approach to some unresolved dilemmas.
Because of the breadth of the subject, the coverage includes various design aspects and problems for indirect-contact two-fluid heat exchangers with primarily single-phase fluids on each side. Heat exchangers with condensing and evaporating fluids on one side can also be analyzed using the design methods presented as long as the thermal resistance on the condensing or evaporating side is small or the heat transfer coefficient on that side can be treated as a constant. Design theory for the following exchangers is not covered in this book, due to their complexity and space limitations: two-phase and multiphase heat exchangers (such as condensers and vaporizers), direct-contact heat exchangers (such as humidifiers, dehumidifiers, cooling towers), and multifluid and multistream heat exchangers. Coverage of mechanical design, exchanger fabrication methods, and manufacturing techniques is also deemed beyond the scope of the book.
Books by M. Jakob, D. Q. Kern, and W. M. Kays and A. L. London were considered to be the best and most comprehensive texts on heat exchanger design and analysis following World War II. In the last thirty or so years, a significant number of books have been published on heat exchangers. These are summarized in the General References at the end of the book.
This text is an outgrowth of lecture notes prepared by the authors in teaching courses on heat exchanger design, heat transfer, and design and optimization of thermal systems to senior and graduate students. These courses were taught at the State University of New York at Buffalo and the University of Novi Sad, Yugoslavia. Over the past fifteen years or more, the notes of the first author have been used for teaching purposes at a number of institutions, including the University of Miami by Professor S. Kakac¸, Rensselaer Polytechnic Institute by Professors A. E. Bergles and R. N. Smith, Rochester Institute of Technology by Professor S. G. Kandlikar, Rice University by Professor Y. Bayazitogˇlu, University of Tennessee Space Center by Dr. R. Schultz, University of Texas at Arlington by Professor A. Haji-Sheikh, University of Cincinnati by Professor R. M. Manglik, Northeastern University by Professor Yaman Yener, North Carolina A&T State University by Professor Lonnie Sharpe, Auburn xviii PREFACE
University by Dr. Peter Jones, Southern Methodist University by Dr. Donald Price, University of Tennessee by Professor Edward Keshock, and Gonzaga University by Professor A. Aziz. In addition, these course notes have been used occasionally at a number of other U.S. and foreign institutions. The notes of the second author have also been used for a number of undergraduate and graduate courses at Marquette
The first author would like to express his sincere appreciation to the management of Harrison Thermal Systems, Delphi Corporation (formerly General Motors Corporation), for their varied support activities over an extended period of time. The second author acknowledges with appreciation many years of support by his colleagues and friends on the faculty of the School of Engineering, University of Novi Sad, and more recently at Marquette University and the University of Kentucky. We are also thankful for the support provided by the College of Engineering, University of Kentucky, for preparation of the first five and final three chapters of the book. A special word of appreciation is in order for the diligence and care exercised by Messrs. Dale Hall and Mack Mosley in preparing the manuscript and drawings through Chapter 5.
The first author is grateful to Professor A. L. London of Stanford University for teaching him the ABCs of heat exchangers and for providing constant inspiration and encouragement throughout his professional career and particularly during the course of preparation of this book. The first author would also like to thank Professors Sadik Kakac¸ of the University of Miami and Ralph Webb of the Pennsylvania State University for their support, encouragement, and involvement in many professional activities related to heat exchangers. The second author is grateful to his colleague and friend Professor B. S. Bacˇlic´, University of Novi Sad, for many years of joint work and teaching in the fields of heat exchanger design theory. Numerous discussions the second author have had with Dr. R. Gregory of the University of Kentucky regarding not only what one has to say about a technical topic, but in particular how to formulate it for a reader, were of a great help in resolving some dilemmas. Also, the continuous support and encouragement of Dr. Frederick Edeskuty of Los Alamos National Laboratory, and Professor Richard Gaggioli of Marquette University were immensely important to the second author in an effort to exercise his academic experience on both sides of the Atlantic Ocean. We appreciate Professor P. V. Kadaba of the Georgia Institute of Technology and James Seebald of ABB Alstom Air Preheater for reviewing the complete manuscript and providing constructive suggestions, and Dr. M. S. Bhatti of Delphi Harrison Thermal Systems for reviewing Chapters 1 through 6 and Dr. T. Skiepko of Bialystok Technical University for reviewing Chapter 5 and providing constructive suggestions. The constructive feedback over a period of time provided by many students (too numerous to mention by name) merits a special word of appreciation.
Finally, we must acknowledge the roles played by our wives, Rekha and Gorana, and our children, Nilay and Nirav Shah and Visˇnja and Aleksandar Sekulic´, during the course of preparation of this book. Their loving care, emotional support, assistance, and understanding provided continuing motivation to compete the book.
We welcome suggestions and comments from readers.
Ramesh K. Shah Dusˇan P. Sekulic´ NOMENCLATURE The dimensions for each symbol are represented in both the SI and English systems of units, where applicable. Note that both the hour and second are commonly used as units for time in the English system of units; hence a conversion factor of 3600 should be A total heat transfer surface area (both primary and secondary, if any) on one side of a direct transfer type exchanger (recuperator), total heat transfer surface area of all matrices of a regenerator,
{
, ft
, ft
2
flow area at or near the shell centerline for one crossflow section in a shell-and- tube exchanger, m
2 A o ;cr
, ft
2
flow bypass area of one baffle, m
2 A o ;bp
2
shell-to-baffle leakage flow area, m
minimum free-flow (or open) area on one fluid side of an exchanger, heat transfer surface area on tube outside in a tubular exchanger in Chapter 13 only, m
o
side [see Eq. (5.117)], dimensionless A
max
side to that on the C
min
on the C
k
2 A o ;sb
2
2 A* k
primary surface area on one side of an exchanger, m
a short side (unless specified) of a rectangular cross section, m, ft a amplitude of chevron plate corrugation (see Fig. 7.28), m, ft
2
, ft
2
total wall area for heat conduction from the hot fluid to the cold fluid, or total wall area for transverse heat conduction (in the matrix wall thickness direc- tion), m
2 A w
, ft
2
2 A p
, ft
, ft
2
flow area through window zone, m
2 A o ;w
, ft
2
tube-to-baffle leakage flow area, m
2 A o ;tb
ratio of A
, ft
m
, ft
, ft
2
frontal or face area on one side of an exchanger, m
2 A fr
, ft
2
fin or extended surface area on one side of the exchanger, m
2 A f
2
window area occupied by tubes, m
effective surface area on one side of an extended surface exchanger [defined by Eq. (4.167)], m
2 A eff
, ft
2
total heat transfer area (both primary and secondary, if any) on the cold side of an exchanger, m
2 A c
, ft
2
2 A fr ;t
2
2
fin cross-sectional area for heat conduction in Section 4.3 (A
total wall cross-sectional area for longitudinal conduction [additional subscripts c, h, and t, if present, denote cold side, hot side, and total (hot þ cold) for a regenerator] in Section 5.4, m
2 A k
, ft
2
at the fin base), m
k
is A
k ;o
2 A k
, ft
, ft
2
total heat transfer surface area (both primary and secondary, if any) on the hot fluid side of an exchanger, m
2
A h, ft
2
gross (total) window area, m
2 A fr ;w
NOMENCLATURE xix {
Unless clearly specified, a regenerator in the nomenclature means either a rotary or a fixed-matrix regenerator.
2
us
r
to C C
min
, dimensionless C
UA
cost per unit thermal size (see Fig. 10.13 and Appendix D), c/W/K C
heat capacity rate of the uniform stream, W/K, Btu/hr-8F C
r
w
matrix heat capacity rate; same as C
r
, W/K, Btu/hr-8F C C
w
total wall heat capacitance for a recuperator, M
ratio of C C
], W s=K, Btu/8F C C*
c
w
r ;c ¼ C r ;c =C c
, dimensionless C C
r
total matrix wall heat capacitance, M
w
c
or C
r ;c
r
P
t
[see Eq. (5.6) for hot- and cold-side matrix heat capacitances C C
r ;h
and C C
w
w
r ;h ¼ C r ;h =C h
h
otl
d
o
, m, ft D
h
hydraulic diameter of flow passages, 4r
, 4A
ctl
o
=P, 4A
o
L =A, or 4 = , m, ft
xx NOMENCLATURE {
J
diameter of the circle through the centers of the outermost tubes, D
baffle diameter, m, ft D
, W s=K, Btu/8F C C
=U
w
w
to C C
min
, dimensionless CF cleanliness factor, U
f
c
baffle
, dimensionless c specific heat of solid, J =kg K,
{
Btu/lbm-8F c annual cost of operation percentile, dimensionless c
p
specific heat of fluid at constant pressure, J =kg K, Btu/lbm-8F c
w
specific heat of wall material, J =kg K, Btu/lbm-8F d exergy destruction rate, W, Btu/hr D
, C*
, C*
B parameter for a thin fin with end leakage allowed, h
, C
) C annual cost, c/yr C * heat capacity rate ratio, C
min
=C
max
, dimensionless C C flow stream heat capacitance, Mc
p
d
(c/ft
, W s=K, Btu/8F C
D
drag coefficient, p = ð u
2
1
=2g
2
2
Þ, dimensionless C
for the fin analysis; Bi ¼ hð =2Þ=k
e
=mk
f
, dimensionless Bi Biot number, Bi
¼ hð =2Þ=k
f
w
C correction factor when used with a subscript different from c, h, min, or max, dimensionless C unit cost, c/J(c/Btu), c/kg (c/lbm), c/kW [c/(Btu/hr)], c/kW yr(c/Btu on yearly basis), c/m
for the regenerator analysis, dimensionless b distance between two plates in a plate-fin heat exchanger [see Fig. 8.7 for b
1
or b
2
(b on fluid 1 or 2 side)], m, ft b long side (unless specified) of a rectangular cross section, m, ft c some arbitrary monetary unit (instead of $, £, etc.), money C flow stream heat capacity rate with a subscript c or h, _ m mc
p
, W =K, Btu/hr-8F
c
max
min
r ;h
w
c
w
=P
t
[see Eq. (5.7) for the hot- and cold-side matrix heat capacity rates C
and C
w
r ;c
], W/K, Btu/hr-8F C*
r
total matrix heat capacity rate ratio, C
r
=C
N or M
c
maximum of C
minimum of C
c
and C
h
, W =K, Btu/hr-8F
C
min
c
w
and C
h
, W/K, Btu/hr-8F C
ms
heat capacity rate of the maldistributed stream, W/K, Btu/hr-8F C
r
heat capacity rate of a regenerator, M
- ratio of C C
=2g
= ð u
D
c
Þ, p g
c
D
2 m
w
= ð2LG
Fanning friction factor,
F log-mean temperature difference correction factor [defined by Eq. (3.183)], dimensionless f
roughness Reynolds number, eu* = , dimensionless
þ
Þ, dimensionless e surface roughness size, m, ft e
c
h
2
2 N r
Þ, Eu/4, dimensionless G fluid mass velocity based on the minimum free area, _ m m =A
for the crossflow section of a tube bundle in a shell-and-tube heat exchan- ger), kg =m
o ;c
by A
o
(replace A
o