Heat Elements of Transfer by Ethirajan Rathakrishnan

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Heat Elements of Transfer by Ethirajan Rathakrishnan

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Contents

Preface xiii
The Author xv
1 Basic Concepts and Definitions 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Driving Potential . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Dimensions and Units . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 Dimensional Homogeneity . . . . . . . . . . . . . . . . . 4
1.3 Closed and Open Systems . . . . . . . . . . . . . . . . . . . . . 6
1.3.1 Closed System (ControlMass) . . . . . . . . . . . . . . 6
1.3.2 Isolated System . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.3 Open System (ControlVolume) . . . . . . . . . . . . . . 8
1.4 Forms of Energy . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4.1 Internal Energy . . . . . . . . . . . . . . . . . . . . . . . 11
1.5 Properties of a System . . . . . . . . . . . . . . . . . . . . . . . 13
1.5.1 Intensive and Extensive Properties . . . . . . . . . . . . 14
1.6 State and Equilibrium . . . . . . . . . . . . . . . . . . . . . . . 15
1.7 Thermal and Calorical Properties . . . . . . . . . . . . . . . . . 15
1.7.1 Specific Heat of an Incompressible Substance . . . . . . 17
1.7.2 Thermally Perfect Gas . . . . . . . . . . . . . . . . . . . 17
1.8 The Perfect Gas . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.10 Exercise Problems . . . . . . . . . . . . . . . . . . . . . . . . . 21
2 Conduction Heat Transfer 23
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2 Conduction Heat Transfer in a Stationary Medium . . . . . . . 27
2.2.1 Energy Flux by Conduction . . . . . . . . . . . . . . . . 27
2.3 Thermal Conductivity . . . . . . . . . . . . . . . . . . . . . . . 31
2.4 Boundary and Initial Conditions . . . . . . . . . . . . . . . . . 35
2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.6 Exercise Problems . . . . . . . . . . . . . . . . . . . . . . . . . 41
3 One-Dimensional, Steady-State Conduction 43
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.2 Steady-State Conduction in a Plane Wall . . . . . . . . . . . . 43
3.2.1 Thermal Resistance . . . . . . . . . . . . . . . . . . . . 48
3.3 Heat Conduction across a Cylindrical Shell . . . . . . . . . . . 57
3.3.1 Critical Thickness of Insulation . . . . . . . . . . . . . . 64
3.4 Steady Conduction in a Spherical Shell . . . . . . . . . . . . . . 65
3.4.1 Critical Thickness of Insulation for a Spherical Shell . . 71
3.5 Heat Transfer from Extended Surface . . . . . . . . . . . . . . . 74
3.5.1 Fins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.5.2 Infinitely Long Fin . . . . . . . . . . . . . . . . . . . . . 78
3.5.3 Fin Efficiency or Fin Effectiveness . . . . . . . . . . . . 79
3.6 The Conduction Shape Factor . . . . . . . . . . . . . . . . . . . 86
3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.8 Exercise Problems . . . . . . . . . . . . . . . . . . . . . . . . . 99
4 Unsteady Heat Conduction 107
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.2 Transient Conduction in an Infinite Wall . . . . . . . . . . . . . 108
4.2.1 The Dimensionless Groups . . . . . . . . . . . . . . . . 109
4.2.2 Transient Heating of Bodies with Negligible Internal Resistance
. . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.3 Lumped System Analysis . . . . . . . . . . . . . . . . . . . . . 123
4.3.1 Convection Boundary Condition . . . . . . . . . . . . . 125
4.3.2 Criteria for Lumped System Analysis . . . . . . . . . . 129
4.3.3 Penetration Depth-Significance of Thermal Diffusivity . 132
4.3.4 Surface Heat Flux from a Semi-Infinite Solid . . . . . . 135
4.3.5 The Significance of Thermal Diffusivity α . . . . . . . . 139
4.4 Multidimensional Systems . . . . . . . . . . . . . . . . . . . . . 143
4.5 Product Solution . . . . . . . . . . . . . . . . . . . . . . . . . . 146
4.5.1 The Concept of Product Solution . . . . . . . . . . . . . 146
4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
4.7 Exercise Problems . . . . . . . . . . . . . . . . . . . . . . . . . 158
5 Convective Heat Transfer 163
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
5.2 The Convection Boundary Layers . . . . . . . . . . . . . . . . . 165
5.3 The Convection Heat Transfer Equations . . . . . . . . . . . . 167
5.3.1 The Velocity Boundary Layer . . . . . . . . . . . . . . . 167
5.3.2 Thermal Boundary Layer . . . . . . . . . . . . . . . . . 173
5.4 Approximation and Special Conditions . . . . . . . . . . . . . . 177
5.5 Solving Convection Problems . . . . . . . . . . . . . . . . . . . 179
5.5.1 Similarity Parameters in Heat Transfer . . . . . . . . . . 179
5.6 Boundary Layer Similarity Parameters . . . . . . . . . . . . . . 181
5.7 Physical Significance of Dimensionless Parameters . . . . . . . 184
5.8 Boundary Layer Concepts . . . . . . . . . . . . . . . . . . . . . 187
5.9 Thermal Boundary Layer for Flow Past a Heated Plate . . . . 196
5.9.1 Turbulent Flow . . . . . . . . . . . . . . . . . . . . . . . 206
5.9.2 Transition Flow. . . . . . . . . . . . . . . . . . . . . . . 209
5.10 Free Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
5.10.1 Local Nusselt Number . . . . . . . . . . . . . . . . . . . 220
5.10.2 Free Convection Correlations . . . . . . . . . . . . . . . 222
5.11 Free Convection on Vertical Planes and Cylinders . . . . . . . . 224
5.11.1 UniformWall Temperature . . . . . . . . . . . . . . . . 224
5.11.2 UniformWall Heat Flux . . . . . . . . . . . . . . . . . . 225
5.12 Free Convection on a Horizontal Plate . . . . . . . . . . . . . . 231
5.12.1 Effects of Turbulence . . . . . . . . . . . . . . . . . . . . 234
5.13 Free Convection fromInclined Surfaces . . . . . . . . . . . . . . 235
5.13.1 Free Convection on Inclined Cylinders . . . . . . . . . . 236
5.13.2 Free Convection on a Sphere . . . . . . . . . . . . . . . 237
5.13.3 Simplified Equations for Air . . . . . . . . . . . . . . . . 237
5.14 Free Convection in Enclosed Spaces . . . . . . . . . . . . . . . . 237
5.14.1 Correlation for Free Convection in Enclosed Spaces . . . 240
5.14.2 Vertical Layer . . . . . . . . . . . . . . . . . . . . . . . . 241
5.14.3 Inclined Layer . . . . . . . . . . . . . . . . . . . . . . . 245
5.14.4 Horizontal Cylindrical Annulus . . . . . . . . . . . . . . 246
5.14.5 Spherical Annulus . . . . . . . . . . . . . . . . . . . . . 248
5.14.6 Non-Newtonian Fluids . . . . . . . . . . . . . . . . . . . 250
5.14.7 Combined Natural and Forced Convection . . . . . . . . 251
5.15 Vortex behind a Circular Cylinder . . . . . . . . . . . . . . . . 257
5.15.1 Drag Coefficient . . . . . . . . . . . . . . . . . . . . . . 259
5.15.2 Variation of h around a Cylinder . . . . . . . . . . . . . 263
5.16 Flow Past a Noncircular Cylinder . . . . . . . . . . . . . . . . . 265
5.17 Flow Past a Sphere . . . . . . . . . . . . . . . . . . . . . . . . . 266
5.17.1 Drag Coefficient . . . . . . . . . . . . . . . . . . . . . . 266
5.17.2 Heat Transfer Coefficient . . . . . . . . . . . . . . . . . 267
5.18 Flow across a Bundle of Tubes . . . . . . . . . . . . . . . . . . 268
5.18.1 Heat Transfer Correlations . . . . . . . . . . . . . . . . 269
5.18.2 PressureDrop Correlations . . . . . . . . . . . . . . . . 273
5.18.3 LiquidMetals . . . . . . . . . . . . . . . . . . . . . . . . 277
5.19 Heat Transfer in High-Speed Flow over a Flat Plate . . . . . . 278
5.20 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
5.21 Exercise Problems . . . . . . . . . . . . . . . . . . . . . . . . . 287
6 Radiation Heat Transfer 297
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297
6.2 RadiationMechanism . . . . . . . . . . . . . . . . . . . . . . . 297
6.3 Radiation Parameters . . . . . . . . . . . . . . . . . . . . . . . 299
6.3.1 Properties of Surfaces . . . . . . . . . . . . . . . . . . . 301
6.4 The Greenhouse Effect . . . . . . . . . . . . . . . . . . . . . . . 305
6.4.1 Blackbody Radiation . . . . . . . . . . . . . . . . . . . . 306
6.4.2 Emissive Power . . . . . . . . . . . . . . . . . . . . . . . 307
6.5 The View or Configuration Factor . . . . . . . . . . . . . . . . 309
6.5.1 View Factor Relation . . . . . . . . . . . . . . . . . . . 318
6.6 Blackbody Radiation Exchange . . . . . . . . . . . . . . . . . . 321
6.7 Radiation Exchange in an Enclosure . . . . . . . . . . . . . . . 322
6.7.1 Net Radiation Exchange at a Surface . . . . . . . . . . . 323
6.7.2 Radiation Exchange between Surfaces . . . . . . . . . . 325
6.7.3 Two-Surface Enclosure . . . . . . . . . . . . . . . . . . . 328
6.8 Radiation Shields . . . . . . . . . . . . . . . . . . . . . . . . . . 337
6.8.1 Radiating Surface . . . . . . . . . . . . . . . . . . . . . 341
6.9 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
6.10 Gas Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344
6.11 Radiation from Real Surfaces . . . . . . . . . . . . . . . . . . . 345
6.12 Solar Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . 346
6.13 Radiation Properties of the Environment . . . . . . . . . . . . . 347
6.14 Radiation Absorption in Water . . . . . . . . . . . . . . . . . . 350
6.15 Radiation Effect on Temperature Measurement . . . . . . . . . 352
6.16 Radiation Heat Transfer Coefficient . . . . . . . . . . . . . . . . 354
6.17 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
6.18 Exercise Problems . . . . . . . . . . . . . . . . . . . . . . . . . 361
7 Mass Transfer 367
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367
7.2 Mass Transfer Process . . . . . . . . . . . . . . . . . . . . . . . 367
7.3 Fick’s Law of Diffusion . . . . . . . . . . . . . . . . . . . . . . . 373
7.4 Species Conservation Equation . . . . . . . . . . . . . . . . . . 375
7.5 Steady-State Diffusion in Dilute Solutions in Stationary Media 379
7.6 Transient Diffusion in Dilute Solution in Stationary Media . . . 382
7.7 Diffusion in a Semi-Infinite Slab . . . . . . . . . . . . . . . . . . 386
7.8 Diffusion in Nondilute Gases . . . . . . . . . . . . . . . . . . . 389
7.9 Convective Mass Transfer . . . . . . . . . . . . . . . . . . . . . 393
7.10 Counterdiffusion in Gases . . . . . . . . . . . . . . . . . . . . . 397
7.11 Evaporation of Water . . . . . . . . . . . . . . . . . . . . . . . 403
7.12 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406
7.13 Exercise Problems . . . . . . . . . . . . . . . . . . . . . . . . . 411
8 Boiling and Condensation 413
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413
8.2 Boiling Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . 413
8.2.1 Pool Boiling . . . . . . . . . . . . . . . . . . . . . . . . . 416
8.3 Heat Transfer Correlations in Pool Boiling . . . . . . . . . . . . 418
8.4 Peak Heat Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . 422
8.5 Minimum Heat Flux . . . . . . . . . . . . . . . . . . . . . . . . 425
8.6 Film Boiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425
8.7 Flow Boiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427
8.8 CondensationHeat Transfer . . . . . . . . . . . . . . . . . . . . 429
8.9 Film Condensation . . . . . . . . . . . . . . . . . . . . . . . . . 429
8.9.1 Flow Regimes . . . . . . . . . . . . . . . . . . . . . . . . 432
8.9.2 Flow Condensation Heat Transfer Correlations . . . . . 433
8.10 Wavy Laminar Flow over a Vertical Plate . . . . . . . . . . . . 440
8.11 Turbulent Flow on Vertical Plates . . . . . . . . . . . . . . . . 441
8.11.1 Inclined Plate . . . . . . . . . . . . . . . . . . . . . . . . 445
8.11.2 Vertical Tubes . . . . . . . . . . . . . . . . . . . . . . . 445
8.11.3 Horizontal Tubes and Spheres . . . . . . . . . . . . . . . 449
8.11.4 Horizontal Tube Banks . . . . . . . . . . . . . . . . . . 449
8.12 Film Condensation inside Horizontal Tubes . . . . . . . . . . . 452
8.13 Dropwise Condensation . . . . . . . . . . . . . . . . . . . . . . 453
8.14 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453
8.15 Exercise Problems . . . . . . . . . . . . . . . . . . . . . . . . . 459
9 Heat Exchangers 463
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463
9.2 Types of Heat Exchangers . . . . . . . . . . . . . . . . . . . . . 463
9.3 The OverallHeat Transfer Coefficient . . . . . . . . . . . . . . 467
9.4 Fouling Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . 470
9.5 Heat Exchanger Performance . . . . . . . . . . . . . . . . . . . 472
9.6 Log Mean Temperature Difference Method . . . . . . . . . . . . 474
9.6.1 Counter-FlowHeat Exchanger . . . . . . . . . . . . . . 478
9.6.2 Multipass and Cross-Flow Heat Exchanger . . . . . . . 479
9.7 The Effective-NTU Method . . . . . . . . . . . . . . . . . . . . 481
9.7.1 Use of -NTU Relations for Rating and Sizing of Heat
Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . 489
9.8 Compact Heat Exchangers . . . . . . . . . . . . . . . . . . . . . 495
9.9 Analysis for Variable Properties . . . . . . . . . . . . . . . . . . 499
9.10 Boilers and Condensers . . . . . . . . . . . . . . . . . . . . . . 500
9.11 Selection of Heat Exchangers . . . . . . . . . . . . . . . . . . . 500
9.11.1 Heat Transfer Rate . . . . . . . . . . . . . . . . . . . . . 502
9.11.2 Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502
9.11.3 Size andWeight . . . . . . . . . . . . . . . . . . . . . . 502
9.11.4 Pumping Power . . . . . . . . . . . . . . . . . . . . . . . 502
9.11.5 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . 503
9.12 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503
9.13 Exercise Problems . . . . . . . . . . . . . . . . . . . . . . . . . 507
Appendix 509
Index 527

Preface

This book is developed to serve as a text for a course on heat transfer at the
introductory level for an undergraduate course and for an advanced course
at the graduate level. The basic aim of this book is to make a complete text
covering both the basic and applied aspects of heat transfer. The philosophy
followed in this book is that the subject of heat transfer is covered combining
the theoretical analysis, physical features and the application aspects.
The principles of heat transfer are covered as the subject is treated at
the undergraduate level. Beginning with introducing the elementary ideas of
the heat transfer process which results in change of flow parameters, such as
pressure and temperature, and developing the methods to achieve the desired
state, are presented in depth, together with their limitations and the features
influencing them.
Basic concepts and definitions, which form the basis for learning the science
of heat transfer, are discussed precisely to the point. Basic principles
of thermodynamics are discussed in the first chapter to make the readers
comfortable with heat transfer principles, processes and application aspects
covered in the rest of the book. The treatment of the material is such that it
emphasizes both the theory and application simultaneously.
The entire spectrum of heat transfer is presented, with necessary explanations
on every aspect, introducing the subject in a simple and effective
manner, in Chapter 2. One-dimensional, steady-state conduction is presented
in the subsequent Chapter 3. All aspects of the conduction process, and the associated
theory and application are discussed with appropriate examples. The
simplifying assumptions rendering conduction through a plane wall, cylindrical
and spherical shells are stated explicitly to gain an insight into the theory,
application and its limitation.
Unsteady heat conduction is discussed in Chapter 4. Beginning with the
transient conduction through simple geometry of infinite plane wall, the subject
is taken to an advanced level of transient conduction through multidimensional
systems. At every stage, the parameters influencing the heat transfer
process and their grouping, leading to different dimensionless parameters and
the physical significance of those dimensionless numbers, are systematically
presented. Suitable examples involving these parameters are included to assimilate
and enhance the understanding of the theory studied.
Convective heat transfer is discussed in Chapter 5. This is the theory involving
a significant amount of flow physics; a thorough treatment of the science
of flow physics is presented along with a large number of solved examples
to make the reader comfortable with this involved process of heat transfer.
Chapter 6 on radiation heat transfer deals with the theory and application
aspects of the mechanism of thermal radiation. Chapter 7 on mass transfer
presents all the important aspects of mass diffusion process. Chapter 8 on
boiling and condensation deals with the different regimes of boiling and condensation
and the calculation of heat flux associated with these regimes.
The chapter on heat exchanger, Chapter 9, deals with the classification,
performance and design aspects of heat exchangers. The popular methods
used for calculating the performance of heat exchangers are discussed in detail,
along with their merits and demerits.
The material covered in this book is designed so that any beginner can
easily follow it. The topics covered are broad-based, starting from the basic
principle and progressing towards the physical aspects which govern the heat
transfer process. The book is organized in a logical manner and the topics are
discussed in a systematic way.
The student, or reader, is assumed to have the background on the basics
of fluid mechanics and thermodynamics. Advanced undergraduate students
should be able to handle the subject material comfortably. Sufficient details
have been included so that the text can be used for self-study. Thus, the
book can be useful for scientists and engineers working in the field of thermal
science in industries and research laboratories.
My sincere thanks to my undergraduate and graduate students at the
Indian Institute of Technology Kanpur, who are directly and indirectly responsible
for the development of this book. My special thanks to my doctoral
students, Mrinal Kaushik and Arun Kumar, for checking the initial version of
the manuscript.
I thank Shashank Khurana, doctoral student, Graduate School of Frontier
Sciences, the University of Tokyo, Kashiwa Campus, Japan, and Yasumasa
Watanabe, doctoral student, Department of Aeronautics and Astronautics,
the University of Tokyo, Hongo Campus, Japan, for their valuable help in
checking the manuscript of the book and its solutions manual.
I would like to place on record my sincere thanks to my friend Professor
Kojiro Suzuki, Department of Advanced Energy, the Graduate School of
Frontier Sciences, the University of Tokyo, Kashiwa, Japan, for extending his
full-hearted help in the finalization of this book, during my stay in his lab, in
the year 2011, as Visiting Professor.
For instructors only, a companion Solutions Manual is available from Taylor
& Francis, CRC Press, that contains typed solutions to all the end-ofchapter
problems. I am grateful for the financial support extended by the
Continuing Education Centre of the Indian Institute of Technology Kanpur,
for the preparation of the manuscript.