## PREFACE TO THE THIRD EDITION

Professor Obert has observed in his famous treatise on Thermodynamics that concepts are

better understood by their repeated applications to real life situations. A firm conviction of

this principle has prompted the author to arrange the text material in each chapter in the

following order.

In the first section after enunciating the basic concepts and laws mathematical models

are developed leading to rate equations for heat transfer and determination of temperature

field, simple and direct numerical examples are included to illustrate the basic laws. More

stress is on the model development as compared to numerical problems.

Optimisation of the shape of the fin of specified volume for maximum

heat flow is discussed. Circumferential fins and variable area fins are analysed. The use of

numerical method is illustrated. Error in measurement of temperature using thermometer is

well discussed. The possibility of measurement of thermal conductivity and convective heat

transfer coefficient using fins is illustrated.

Two dimensional steady state conduction is discussed in the fifth chapter. Exact analysis

is first developed for two types of boundary conditions. The use of numerical method is illustrated

by developing nodal equations. The concept and use of conduction shape factor is illustrated

for some practical situations.

One dimensional transient (unsteady) heat conduction is discussed in Chapter 6. Three

types of models arise in this case namely lumped heat capacity system, semi-infinite solid and

infinite solid. Lumped heat capacity model for which there are a number of industrial

applications is analysed in great detail and problems of practical interest are shown solved.

The condition under which semi-infinite solid model is applicable as compared to infinite solid

model is clearly explained. Three types of boundary conditions are analysed. Infinite solid

model for three geometric shapes is analysed next. The complexity of the analytical solution is

indicated. Solution using charts is illustrated in great detail. Real solids are of limited

dimensions and these models cannot be applied directly in these cases. In these cases product

solution is applicable. A number of problems of practical interest for these types of solids are

worked out in this section. In both cases a number of problems are solved using numerical

methods. Periodic heat flow problems are also discussed.

Concepts and mechanism of convection are discussed in the seventh chapter. After

discussing the boundary layer theory continuity, momentum and energy equations are derived.

Next the different methods of solving these equations are discussed. In addition to the exact

analysis approximate integral method, analogy method and dimensional analysis are also

discussed and their applicability is indicated. General correlations for convective heat transfer

coefficient in terms of dimensionless numbers are arrived at in this chapter.

In Chapter 8, in addition to the correlations derived in the previous chapter, empirical

correlations arrived at from experimental results are listed and applied to flow over surfaces

like flat plate, cylinder, sphere and banks of tubes. Both laminar and turbulent flows situation

are discussed.

Flow through ducts is discussed in Chapter 9. Empirical correlations for various situations

are listed. Flow developing region, fully developed flow conditions, constant wall temperature

and constant wall heat flux are some of the conditions analysed. Flow through non-circular

pipes and annular flow are also discussed in this chapter.

Natural convection is dealt with in Chapter 10. Various geometries including enclosed

space are discussed. The choice of the appropriate correlation is illustrated through a number

of problems. Combined natural and forced convection is also discussed.

Chapter 11 deals with phase change processes. Boiling, condensation, freezing and

melting are discussed. Basic equations are derived in the case of freezing and melting and

condensation. The applicable correlations in boiling are listed and their applicability is

illustrated through numerical examples.

Chapter 12 deals with heat exchangers, both recuperative and regenerative types. The

LMTD and NTU-effectiveness methods are discussed in detail and the applicability of these

methods is illustrated. Various types of heat exchangers are compared for optimising the size.

Thermal radiation is dealt with in Chapter 13. The convenience of the use of electrical

analogy for heat exchange among radiating surfaces is discussed in detail and is applied in

almost all the solved problems. Gas radiation and multi-body enclosures are also discussed.

Chapter 14 deals with basic ideas of mass transfer in both diffusion and convection

modes. A large number of problems with different fluid combinations are worked out in this

chapter.

## CONTENTS

Preface to the Third Edition v

1 AN OVERVIEW OF HEAT TRANSFER 1–25

1.0 Introduction 1

1.1 Heat Transfer 1

1.2 Modes of Heat Transfer 2

1.3 Combined Modes of Heat Transfer 8

1.4 Dimensions and Units 10

1.5 Closure 11

Solved Problems 11

Exercise Problems 22

2 STEADY STATE CONDUCTION 26–98

2.0 Conduction 26

2.1 The General Model for Conduction Study 26

2.2 Steady Conduction in One Direction (One Dimensional) 30

2.3 Conduction in Other Shapes 41

2.4 One Dimensional Steady State Heat Conduction with Variable Heat

Conductivity or Variable Area Along the Section 42

2.5 Critical Thickness of Insulation 48

2.6 Mean Area Concept 50

2.7 Parallel Flow 51

Solved Problems 53

Objective Questions 92

Exercise Problems 93

3 CONDUCTION WITH HEAT GENERATION 99–127

3.0 Introduction 99

3.1 Steady State One Dimensional Conduction in a Slab with Uniform Heat

Generation 99

3.2 Steady State Radial Heat Conduction in Cylinder with Uniform Heat Generation 103

3.3 Radial Conduction in Sphere with Uniform Heat Generation 107

3.4 Conclusion 109

Solved Problems 110

Objective Questions 125

Exercise Problems 125

4 HEAT TRANSFER WITH EXTENDED SURFACES (FINS) 128–175

4.0 Introduction 128

4.1 Fin Model 129

4.2 Temperature Calculation 130

4.3 Heat Flow Calculation 134

4.4 Fin Performance 139

4.5 Circumferential Fins and Plate Fins of Varying Sections 142

4.6 Optimisation 145

4.7 Fin with Radiation Surroundings 146

4.8 Contact Resistance 146

4.9 Numerical Method 147

Solved Problems 148

Objective Questions 170

Exercise Problems 172

5 TWO DIMENSIONAL STEADY HEAT CONDUCTION 176–201

5.0 Introduction 176

5.1 Solution to Differential Equation 176

5.2 Graphical Method 182

5.3 Numerical Method 184

5.4 Electrical Analogy 187

5.5 In the Finite Difference Formulation 187

Solved Problems 188

Exercise Problems 199

6 TRANSIENT HEAT CONDUCTION 202–284

6.0 Introduction 202

6.1 A Wall Exposed to the Sun 202

6.2 Lumped Parameter Model 203

6.3 Semi Infinite Solid 207

6.4 Periodic Heat Conduction 213

6.5 Transient Heat Conduction in Large Slab of Limited Thickness, Long Cylinders

and Spheres 215

6.6. Product Solution 227

6.7 Numerical Method 230

6.8 Graphical Method 233

Solved Problems 234

Objective Questions 278

Exercise Problems 280

7 CONVECTION 285–333

7.0 Introduction 285

7.1 Mechanism of Convection 285

7.2 The Concept of Velocity Boundary Layer 287

7.3 Thermal Boundary Layer 289

7.4 Laminar and Turbulent Flow 291

7.5 Forced and Free Convection 292

7.6 Methods Used in Convection Studies 293

7.7 Energy Equation 299

7.8 Integral Method 302

7.9 Dimensional Analysis 303

7.10 Analogical Methods 306

7.11 Correlation of Experimental Results 307

Solved Problems 308

Objective Questions 331

Exercise Problems 332

8 CONVECTIVE HEAT TRANSFER—PRACTICAL CORRELATIONS

—FLOW OVER SURFACES 334–384

8.0 Introduction 334

8.1 Flow Over Flat Plates 334

8.2 Turbulent Flow 343

8.3 Flow Across Cylinders 348

8.4 Flow Across Spheres 356

8.5 Flow Over Bluff Bodies 359

8.6 Flow Across Bank of Tubes 360

Solved Problems 363

Objective Questions 380

Exercise Problems 381

9 FORCED CONVECTION 385–433

9.0 Internal Flow 385

9.1 Hydrodynamic Boundary Layer Development 386

9.2 Thermal Boundary Layer 387

9.3 Laminar Flow 388

9.4 Turbulent Flow 399

9.5 Liquid Metal Flow 402

9.6 Flow Through Non-circular Sections 404

9.7 The Variation of Temperature Along the Flow Direction 406

Solved Problems 408

Objective Questions 431

Exercise Problems 432

10 NATURAL CONVECTION 434–479

10.0 Introduction 434

10.1 Basic Nature of Flow Under Natural Convection Conditions 435

10.2 Methods of Analysis 437

10.3 Integral Method 439

10.4 Correlations from Experimental Results 442

10.5 A More Recent Set of Correlations 446

10.6 Constant Heat Flux Condition—Vertical Surfaces 447

10.7 Free Convection from Inclined Surfaces 451

10.8 Horizontal Cylinders 454

10.9 Other Geometries 455

10.10 Simplified Expressions for Air 456

10.11 Free Convection in Enclosed Spaces 458

10.12 Rotating Cylinders, Disks and Spheres 459

10.13 Combined Forced and Free Convection 460

Solved Problems 461

Objective Questions 477

Exercise Problems 477

11 PHASE CHANGE PROCESSES—BOILING, CONDENSATION

FREEZING AND MELTING 480–520

11.0 Introduction 480

11.1 Boiling or Evaporation 480

11.2 The correlations 483

11.3 Flow Boiling 485

11.4 Condensation 488

11.5 Freezing and Melting 494

Solved Problems 494

Objective Questions 516

Exercise Problems 518

12 HEAT EXCHANGERS 521–577

12.0 Introduction 521

12.1 Over All Heat Transfer Coefficient 521

12.2 Classification of Heat Exchangers 524

12.3 Mean Temperature Difference—Log Mean Temperature Difference 526

12.4 Regenerative Type 531

12.5 Determination of Area in Other Arrangements 531

12.6 Heat Exchanger Performance 535

12.7 Storage Type Heat Exchangers 547

12.8 Compact Heat Exchangers 550

Solved Problems 550

Objective Questions 572

Exercise Problems 574

13 THERMAL RADIATION 578–655

13.0 Introduction 578

13.1 Black Body 579

13.2 Intensity of Radiation 583

13.3 Real Surfaces 584

13.4 Radiation Properties of Gases—Absorbing, Transmitting and Emitting Medium 587

13.5 Heat Exchange by Radiation 595

13.6 Radiant Heat Exchange Between Black Surfaces 604

13.7 Heat Exchange by Radiation Between Gray Surfaces 606

13.8 Effect of Radiation on Measurement of Temperature by a Bare Thermometer 613

13.9 Multisurface Enclosure 614

13.10 Surfaces Separated by an Absorbing and Transmitting Medium 617

Solved Problems 618

Objective Questions 648

Exercise Problems 650

14 MASS TRANSFER 656–701

14.0 Introduction 656

14.1 Properties of Mixture 656

14.2 Diffusion Mass Transfer 657

14.3 Fick’s Law of Diffusion 657

14.4 Equimolal Counter Diffusion 659

14.5 Stationary Media with Specified Surface Concentration 660

14.6 Diffusion of One Component into a Stationary Component or

Unidirectional Diffusion 661

14.7 Unsteady Diffusion 661

14.8 Convective Mass Transfer 662

14.9 Similarity Between Heat and Mass Transfer 664

Solved Problems 664

Exercise Problems 680

Fill in the Blanks 682

State True or False 699

Short Questions 702

Appendix 707

References 712