HEAT AND MASS TRANSFER

(A Text Book for B.Tech./B.E. Students of all Indian UniversitiesAlso useful for IES/IAS/GATE and other competitive Examinations)

HEAT ANDMASS TRANSFER

By

Dr. C.P. AroraEx-Professor of Mechanical Engineering

Indian Institute of Technology,Hauz Khas, New Delhi

Revised, Updated and Edited By

Dr. Sadhu SinghEx-Professor and Head, Mechanical Engineering Department

and Ex-Dean, Faculty of Engineering and TechnologyGovind Ballabh Pant University of Agriculture and Technology,

Pantnagar-263 145 (Uttarakhand)Ex-Director (Colleges), Punjab Technical University,

Jalandhar

KP

KHANNA PUBLISHERS4575/15, ONKAR HOUSE, OPP. HAPPY SCHOOL

DARYAGANJ, NEW DELHI-110002Phone : 2324 30 42 ; Fax : 2722 41 79

Published by :Romesh Chander Khannafor KHANNA PUBLISHERS2-B, Nath Market, Nai Sarak,Delhi-110006 (India).

All Rights Reserved[This book or part thereof cannot be translated or reproduced in anyform (except for review or criticism) without the written permission ofthe Authors and the Publishers.]

ISBN NO. : 978-81-7409-290-8

Fourth Edition : 2011

Price : Rs. 225.00

Text Composition by : Excellent Graphics, Delhi.

Printed at: Bright Printers Turkman Gate, Dellhi—110006.

Dedicatedto

Mywife

Smt. Manjit Kaurand

MyParents

Preface To The Fourth Edition

Heat and Mass Transfer is a comprehensive Text Book forB.Tech./B.E. students of all Universities and Institutions. It is alsouseful for candidates preparing for IES/IAS/GATE and othercompetitive examinations.

The book in its present form contains twelve chapters comprisingof Basic Concepts of Heat Transfer, General Heat Conduction Equation;Steady State Heat Conduction; Conduction with Internal HeatGeneration; Theory of Fins; Unsteady–State Conduction; ForcedConvection; Free Convection; Boiling and Condensation; ThermalRadiation; Heat Exchangers and Mass Transfer.

The book contains a large number of solved and unsolvedproblems. Many problems have been taken from IES/IAS/Gate andother competitive examinations. Multi–choice Questions from theseexaminations have been given at the end of the book with explanatorynotes. These shall be quite helpful to the candidates preparing for theseexaminations.

A large number of books were consulted during the preparationof manuscript. The author expresses his gratitude to all thesepublishers and authors. Although utmost care has been exercisedduring proof reading, still some errors might have been leftinadvertently. The author and the publishers shall be thankful to thereaders if these errors are brought to their knowledge.

The author expresses his sincere thanks to his family membersfor their encouragement and support. My grand children Kanupreetand Amitoej have been a source of great inspiration during the writingof the book.

The publishers provided the necessary help as and whenrequired. The support provided by Mr. Vineet Khanna is dulyacknowledged.

The suggestions from the readers for the improvement of thebook are welcome and shall be duly acknowledged.

Dr. Sadhu Singh

Preface To The First Edition

Heat transfer now forms an integral part of the curriculum ofboth mechanical and chemical engineering education. The subject isgenerally taken up towards the penultimate years so that theknowledge of basic mathematics including differential equations, fluidmechanics and thermodynamics may form the base for developing thevaried approaches to the subject.

Many texts follow the extremely rigorous approach, whereasothers are restricted to elementary and empirical form. A consciouseffort has been made in this text to maintain a reasonable level ofrigour, but at the same time to apply simple techniques to solve fairlycomplex problems. A sound physical basis has been laid for obtainingthe first estimate of the heat and mass transfer equipment.

Also at the outset in the text, an approach based on electricalanalogy has been emphasised, thus eliminating the confusionexperienced by the readers in deriving expressions for overall heattransfer coefficients in compound thermal resistance and multi-modeheat transfer problems.

Numerical methods, now-a-days, provide a powerful tool for thesolution, more particularly, of un-steady state heat transfer problems.Therefore, heat transfer by conduction has been treated from bothanalytical and numerical viewpoint.

Integral analysis of both free and forced convection is providedto present a clear picture of convection processes. From this, inferencescan be drawn leading to the well known empirical and experimentalcorrelations for evaluating the heat transfer coefficients.

In the case of heat exchange between bodies by radiation,electrical network method has been used extensively as it affords aneasier approach to understand and solve intricate problems. In heatexchangers analysis, log mean temperature difference, andeffectiveness-number of transfer units approach have been employedsince both are widely used these days and each affords its ownadvantages.

A treatment on mass transfer is presented establishing firmlythe similarities between heat and mass transfer. As far as possiblesimilar nomenclature has been used for both to minimise additionaleffort to learn mass transfer.

The book also includes topics on the measurement of thermalconductivity, the problem of buried cables, optimum design of fins,

shell-side, heat transfer coefficient, solution of differential equationsof boundary layer over a flat plate, concept of displacement andmomentum thickness, etc. A few items such as the types of boundaryconditions in the solution of heat conduction equation, solution forheat transfer in pipes for constant wall temperature, monochromaticemissive power in a given wavelength range, etc., have been elaborated.

It is intended that it should cover the syllabus of anundergraduate programme. The author sincerely hopes that readersof the text will benefit from the approach presented, and will obligewith useful suggestions.

C.P. ARORA

About the Author

Dr. Chandra Prakash Arora received his Bachelor’s degreein Mechanical Engineering in 1956 and Postgraduate Diploma inApplied Thermodynamics in 1957 from Roorkee University. He wasawarded Master of Science in 1961 from University of Illinois, U.S.A.,and Doctor of Philosophy in 1968 from Indian Institute of Technology,Delhi. He has taught for nearly twentyfour years at Indian Institutesof Technology, Bombay and Delhi. He has guided a large number of B.Tech., M. Tech., and Ph. D. thises and has over 60 research publicationsin national and international journals to his credit. Dr. Arora is thefounder President of Indian Society of Mechanical Engineers. He hasbeen head of Mechanical Engineering Department and Dean,Undergraduate Studies at IIT Delhi. He is also the editor of the Journalof Thermal Engineering, an international ISME quarterly, and holdsthe position of Vice-President (Technical) of the Indian Society ofHeating, Refrigerating and Air Conditioning Engineers. He has alsoauthored a book on Refrigeration and Air Conditioning in S.I. units.

Dr. Sadhu Singh is a retired Professor of MechanicalEngineering of Govind Ballabh Pant University of Agriculture andTechnology, Pantnagar. He is B.Sc. Mechanical Engineering with Hons.from Punjab University, Chandigarh ; M.Sc. (Mechanical Design andProduction Engineering) and Ph.D. from Kurukshetra University,Kurukshetra. His teaching experience spans 15 years at RegionalEngineering College (now NIT), Kurukshetra and 19 years atPantnagar University. He has been Professor and Head, MechanicalEngineering Department and Dean, Faculty of Engineering andTechnology at Pantnagar. He has been Director (Colleges), PunjabTechnical University, Jalandhar. He has published more than 50research papers in national and international jounals of repute. He isthe author of many text books on Mechanical Engineering. He is arenowned academician, research worker, writer and an ableadministrator.

Contents

Chapter 1 Basic Concepts of Heat Transfer ........................ 1–33

1.1 Introduction ................................................................................ 11.2 Differences between Thermodynamics and Heat Transfer ...... 11.3 Applications of Heat Transfer.................................................... 21.4 Modes of Heat Transfer .............................................................. 31.5 Fourier’s Law of Heat Conduction ............................................. 4

1.5.1 Assumptions of Fourier’s law ........................................... 51.5.2 Thermal conductivity ........................................................ 61.5.3 Guarded hot plate apparatus for measurement

of thermal conductivity ..................................................... 81.5.4 Thermal resistance ............................................................ 8

1.6 Newton’s Law of Cooling for Convection ................................... 91.6.1 Film heat transfer coefficient ......................................... 10

1.7 Stefan–Boltzmann Law for Thermal Radiation ..................... 121.7.1 Radiation coefficient ........................................................ 13

1.8 Heat Transfer through Composite Bodies............................... 141.8.1 Resistances in series ....................................................... 141.8.2 Resistances in parallel .................................................... 14

Highlights ...................................................................... 27Multi-choice Questions .................................................. 28Review Questions .......................................................... 31Exercises ........................................................................ 31

Chapter 2 General Heat Conduction Equation .................. 34–45

2.1 Introduction .............................................................................. 342.2 General Heat Conduction Equation in Cartesian

Coordinates ............................................................................... 342.2.1 General heat conduction equation with constant

thermal conductiviy ......................................................... 362.2.2 Other simplified forms of heat conduction equation ..... 37

2.3 General Heat Conduction Equation in CylindricalCoordinates ............................................................................... 37

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2.4 General Heat Conduction Equation in SphericalCoordinates ............................................................................... 40

2.5 Thermal Diffusivity .................................................................. 432.6 Initial and Boundary Conditions ............................................. 43

Highlights ........................................................................ 44Review Questions ............................................................ 45Exercises .......................................................................... 45

Chapter 3 Steady State Heat Conduction ......................... 46–132

3.1 Introduction .............................................................................. 463.2 Heat Conduction through a Slab or a Plane Wall .................. 463.3 Heat Transfer through Composite Wall .................................. 53

3.2.1 Composite plane wall with convective boundaries ........ 533.2.2 Composite plane wall with series and parallel

resistances ....................................................................... 543.3.3 Overall heat transfer coefficient ..................................... 733.3.4 Heat flow through wall with variable thermal

conductiviity .................................................................... 743.4 Heat Flow Through Cylinders ................................................. 77

3.4.1 The logarithmic mean area ............................................. 793.4.2 Composite cylindrical wall convective boundaries ........ 803.4.3 Overall heat transfer coefficient ..................................... 813.4.4 Hollow cylinder with variable conductivity ................... 92

3.5 Heat Conduction Through Hollow Sphere .............................. 943.5.1 Logarithmic mean area for a hollow sphere .................. 963.5.2 Heat conduction through a hollow sphere ..................... 963.5.3 Heat conduction through hollow sphere with

variable conductivity ....................................................... 973.5.4 Overall heat transfer coefficient ..................................... 99

3.6 Thermal Contact Resistance .................................................. 1033.7 Conductive Shape Factor ....................................................... 105

3.7.1 Conduction through edges and corners of walls .......... 1083.8 Critical Thickness of Insulation ............................................ 112

3.8.1 Cylindrical pipe ............................................................. 1123.8.2 Hollow sphere ................................................................ 114

Highlights ...................................................................... 123Multi-Choice Questions ................................................. 125Eeview Questions .......................................................... 127Exercises ........................................................................ 128

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Chapter 4 Conduction with Internal Heat Generation ... 133–184

4.1 Introduction ............................................................................ 1334.2 Plane Wall with Uniform Heat Source .................................. 1334.3 Dielectric Heating .................................................................. 1504.4 Cylinder with Uniform Heat Generation .............................. 154

4.4.1 Solid cylinder ................................................................. 1554.4.2 Hollow cylinder with insulated outer surface .............. 1584.4.3 Hollow cylinder with inside surface insulated ............. 1604.4.4 Hollow cylinder with specified temperature on

the lnside and outside surfaces ................................... 1614.5 Heat Transfer through a Piston Crown ................................ 1634.6 Heat Conduction with Heat Generation in Nuclear

Cylindrical Fuel Rod .............................................................. 1664.6.1 Without cladding ........................................................... 1664.6.2 With cladding ................................................................ 168

4.7 Sphere with Uniform Heat Generation ................................. 1724.7.1 Solid sphere ................................................................... 1724.7.2 Hollow sphere with inside surface insulated ............... 175

Highlights ...................................................................... 179Multi-choice Questions .................................................. 182Review Questions .......................................................... 182Exercises ........................................................................ 183

Chapter 5 Theory of Fins ................................................. 185–259

5.1 Introduction ............................................................................ 1855.2 Types of Fins and Spines ....................................................... 1855.3 Applications of Fins and Spines ............................................ 1875.4 Assumptions made for Heat Transfer through Fins ............ 1875.5 Heat flow along a Rectangular Fin ........................................ 188

5.5.1 Infinitely long rectangular fin ...................................... 1895.5.2 Infinitely long circular fin ............................................. 1915.5.3 Comparison of fins ......................................................... 1925.5.4 Heat dissipation from a fin insulated at the tip

(fin of finite length) ....................................................... 1945.5.5 Fin of short length ......................................................... 1955.5.6 Temperature distribution along a pin fin .................... 2065.5.7 Circular fin .................................................................... 208

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5.6 Fin Performance ..................................................................... 2085.6.1 Relation between fin efficiency and fin effectiveness .. 210

5.7 Optimum Design of Fins ........................................................ 2155.7.1 Space considerations ..................................................... 2155.7.2 Weight considerations ................................................... 216

5.8 Heat Transfer Through Straight Triangular Fins ................ 2235.9 Parabolic Fins ......................................................................... 228

5.10 Temperature Measurement of Flow Through Pipes ............. 2325.10.1 Determination of error in temperature

measurement ................................................................. 2335.11 Heat Transfer From a Bar Connected to Two Heat

Sources at Different Temperatures ....................................... 236Highlights ...................................................................... 247Multi-choice Questions .................................................. 251Review Questions .......................................................... 255Exercises ........................................................................ 255

Chapter 6 Unsteady-State Conduction ........................... 260–315

6.1 Introduction ............................................................................ 2606.2 Solids of Infinite Thermal Conductivity—Lumped

Heat Capacity Analysis .......................................................... 2616.2.1 Temperature distribution ............................................. 2616.2.2 Instaneous heat flow rate ............................................. 2636.2.3 Total heat flow rate ....................................................... 2636.2.4 Significance of Fourier Number ................................... 2646.2.5 Significance of Biot Number ......................................... 2646.2.6 Transient temperature measurements and

determination of the heat transfer coefficient ............. 2676.2.7 Time constant and response of

temperature measuring instruments ........................... 2736.2.8 Analogous electrical system—the R.C. circuit ............. 276

6.3 Transient Heat Conduction in Solids with FiniteConduction and Convective Resistance ................................. 277

6.4 Transient Heat Conduction in Semi-infiniteSolids ....................................................................................... 2916.4.1 Penetration depth and penetration time...................... 294

6.5 System with Periodic Variation of Surface Temperature ... 300Highlights ...................................................................... 305Multi-choice Questions .................................................. 307Review Questions .......................................................... 308Exercises ........................................................................ 309

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Chapter 7 Forced Convection ......................................... 316–409

7.1 Introduction ............................................................................ 3167.2 Hydrodynamic Boundary Layer ............................................ 316

7.2.1 Laminar and turbulant flow ......................................... 3177.3 Thermal Boundary Layer ...................................................... 3197.4 Dimensional Analysis ............................................................ 320

7.4.1 Dimensional homogeneity ............................................. 3207.4.2 Buckingham’s π—theorem ............................................ 3217.4.3 Selection of repeating variables .................................... 3217.4.4 Dimensionless numbers ................................................ 3227.4.5 Determination of dimensionless correlation

for forced convection ...................................................... 3237.5 Bulk and Mean Film Temperatures ...................................... 3257.6 Local and Average Convective Coefficients .......................... 3267.7 Empirical Correlations for Forced Convection...................... 327

7.7.1 Laminar flow past flat plates and walls ....................... 3277.7.2 Laminar flow inside tubes ............................................ 3277.7.3 Turbulent flow over flat plate ....................................... 3287.7.4 Turbulent flow in tubes ................................................. 3297.7.5 Empirical correlation for flow outside tubes ................ 3317.7.6 Shell–side heat transfer coefficient .............................. 3327.7.7 Turbulent flow over spheres ......................................... 333

7.8 Differential Equations of Boundary Layeron a Flat Plate ........................................................................ 3447.8.1 Continuity equation of hydrodynamic boundry layer .. 3447.8.2 Momentum equation of hydrodynamic

boundary layer ............................................................... 3467.8.3 Energy equation of thermal boundary layer ................ 3477.8.4 Comparison of momentum and energy equations ....... 349

7.9 Solution of Differential Equations of Boundary Layer ......... 3507.9.1 Velocity distribution and momentum transfer in

laminar flow over a flat plate ....................................... 3507.9.2 Temperature distribution and heat transfer

in laminer flow over flat plate ...................................... 3537.10 The Integral Equations of the Boundary Layer .................... 357

7.10.1 Displacement thickness ................................................ 3587.10.2 Momentum thickness .................................................... 359

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7.10.3 Momentum integral equation ofhydrodynamic boundary ............................................... 360

7.10.4 Von-Karman solution of momentumintegral equation ........................................................... 362

7.10.5 Energy integral equation of thermal boundary layer .. 3647.10.6 Solution of integral energy equation ............................ 3657.10.7 Heat transfer coefficient and Nusselt number ............ 367

7.11 Analogy between Fluid Friction and Heat Transfer ............. 3707.12 Heat Transfer in Turbulent Flow .......................................... 3717.13 Heat Transfer in Laminar Flow in Tubes ............................. 372

7.13.1 Solution for constant wall heat flux ............................. 3747.13.2 The bulk mean temperature ......................................... 3757.13.3 Heat transfer coefficient ............................................... 376

7.14 Solution for Constant Wall Temperature .............................. 3797.15 Heat Transfer in Turbulent Flow in Tubes ........................... 379

Highlights ...................................................................... 398Multi-choice Questions .................................................. 401Review Questions .......................................................... 403Exercises ........................................................................ 403

Chapter 8 Free or Natural Convection............................ 410–446

8.1 Introduction ............................................................................ 4108.2 Characteristic Parameters in Natural Convection ............... 4108.3 Determination of Dimensionless Correlation

for Free Convection ................................................................ 4128.4 Empirical Correlation for Free Convection ........................... 413

8.4.1 Inclined surface ............................................................. 4158.4.2 Simplified correlation for air ........................................ 4158.4.3 Free convection in enclosed spaces ............................... 4168.4.4 Constant heat flux ......................................................... 4178.4.5 Combined free and forced convection ........................... 418

8.5 Momentum and Energy Equations For Laminar FreeConvection Heat Transfer on a Vertical Flat Plate .............. 4238.5.1 Differential equations for momentum and energy

energy on a flat plate .................................................... 4248.6 Integral Equations for Momentum and Energy

on a Flat Plate ........................................................................ 4248.6.1 Velocity and temperature profiles on a

vertical flat plate from integral equations ................... 425

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8.6.2 Solution for boundary layer thicknesson vertical flat plate ...................................................... 427

8.7 Free Convection Heat Transfer Coefficient for aVertical Walls ......................................................................... 427

Highlights ...................................................................... 441Multi-choice Questions .................................................. 443Review Questions .......................................................... 443Exercises ........................................................................ 444

Chapter 9 Convection with Phase Change(Boiling and Condensation) .......................... 447–489

9.1 Introduction ............................................................................ 4479.2 Applications of Boiling and Condensation Processes ........... 4489.3 Special Features of Boiling and

Condensation Processes ......................................................... 4489.4 Condensation .......................................................................... 449

9.4.1 Modes of Condensation ................................................. 4499.5 Laminar Film Condensation on a Vertical Plate .................. 450

9.5.1 Velocity Distribution .................................................... 4519.5.2 Mass Flow Rate ............................................................. 4529.5.3 Heat Flux ....................................................................... 4539.5.4 Film Heat Transfer Coefficient ..................................... 4559.5.5 Total Heat Transfer and Condensation Rates ............. 4559.5.6 Inclined Flat Surfaces ................................................... 4559.5.7 Horizontal Plate ............................................................ 4569.5.8 Horizontal Versus Vertical Surfaces ............................ 456

9.6 Turbulent Film Condensation ............................................... 4569.7 Condensation on Tube ............................................................ 4589.8 Condensation Number and Correlations .............................. 4589.9 Film Condensation Inside Horizontal Tubes ........................ 460

9.10 Fundamentals of Boiling Heat Transfer ............................... 4719.10.1 Regimes of Pool Boiling ................................................. 472

9.11 Correlation of Pool Boiling Heat Transfer Data ................... 4749.12 Forced Convection Boiling ..................................................... 4779.13 Simplified Correlations .......................................................... 477

9.13.1 Simplified Correlations for Boiling of Water ............... 4779.13.2 Dembi, Dhar and Arora’s Correlation .......................... 479

Highlights ...................................................................... 483Multi-choice Questions .................................................. 485

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Review Questions .......................................................... 486Exercises ........................................................................ 486

Chapter 10 Thermal Radiation ........................................ 490–566

10.1 Introduction ............................................................................ 49010.2 Characteristics of Radiation .................................................. 49010.3 Definitions .............................................................................. 49110.4 Radiation Properties .............................................................. 49210.5 A Black Body .......................................................................... 49310.6 Planck’s Law for Monochromatic Thermal Radiation

of a Black Body ....................................................................... 494 10.7 Emissive Power and Radiation Intensity .............................. 494

10.7.1 Lambert’s Cosine Law ................................................... 49510.8 Monochromatic Emissive Power of Black Body .................... 49510.9 Stefan–Boltzmann Law of Black Body Radiation ................ 49910.10 Wien’s Diplacement Law........................................................ 50010.11 Calculation of Black Body Emissive Power Within

a Wavelength Band ................................................................ 50010.12 Radiation from Real Surfaces ................................................ 50810.13 Kirchhoff’s Identity ................................................................ 50910.14 Heat Exchange by Radiation between Black Surfaces ......... 51110.15 Radiation Shape Factor and Reciprocity Theorem ............... 513

10.15.1 Shape factors for regular geometries ........................... 51410.16 Heat Exchange between Non-black Bodies ........................... 51910.17 Heat Exchange by Radiation between Gray Surfaces .......... 520

10.17.1 Heat Exchange between two gray Surfaces ................. 52110.17.2 Heat Exchange between three gray Surfaces .............. 52210.17.3 Heat Exchange between two gray Surfaces

enclosed by a third inculated surface ........................... 52210.17.4 Heat Exchange between infinite parallel planes ......... 523

10.18 Radiation Shields ................................................................... 52810.19 Radiation from Gases and Vapours ....................................... 542

10.19.1 Absorptivity of gases ..................................................... 54310.19.2 Mean beam length ......................................................... 54510.19.3 Radiant heat exchange between gas bolume

and black enclosure ....................................................... 553Highlights ...................................................................... 558Multi-choice uestions .................................................... 559

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Review Questions .......................................................... 561Exercises ........................................................................ 562

Chapter–11 Heat Exchangers .......................................... 567–640

11.1 Introduction ............................................................................ 56711.2 Types of Heat Exchangers ..................................................... 56711.3 Design Considerations ........................................................... 57311.4 Overall Heat Transfer Coefficient ......................................... 57311.5 Fouling Factors ....................................................................... 57511.6 Thermal Design Procedures ................................................... 57611.7 Log Mean Temperature Difference (LMTD) ......................... 577

11.7.1 LMTD correction factors ............................................... 59711.8 Effectiveness—Number of Transfer Units Method .............. 607

11.8.1 Heat exchanger effectiveness ....................................... 60811.8.2 Effectiveness of counter–flow heat exchanger ............. 60911.8.3 Number of transfer units .............................................. 610

11.9 Finned Heat Exchangers ....................................................... 626Highlights ...................................................................... 630Multi-choice Questions .................................................. 631Review Questions .......................................................... 632Exercises ........................................................................ 632

Chapter–12 Mass Transfer .............................................. 641–693

12.1 Introduction ............................................................................ 64112.2 Modes of Mass Transfer ......................................................... 64212.3 Mass Transfer by Molecular Diffusion .................................. 642

12.3.1 Fick’s law of diffusion .................................................... 64212.3.2 Diffusion coefficient ....................................................... 64312.3.3 Molecular diffusion in gases ......................................... 64412.3.4 Molecular diffusion in liquids and solids ..................... 64512.3.5 Measurement of diffusion coefficient ........................... 64612.3.6 Definitions of quantities ............................................... 64712.3.7 Fick’s law in terms of mass and mole fractions ........... 64912.3.8 Equivalence of diffusion coefficients ............................ 65012.3.9 Equation of mass diffusion in stationary media-

species conservation equation....................................... 65112.3.10 Steady–state diffusion through a plain membrane ..... 652

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12.3.11 Diffusion in binary gas mixtures .................................. 65412.3.12 Equimolal counter-diffusion in gases ........................... 65512.3.13 Diffusion of gas A through a stationary gas B ............. 65812.3.14 Transient diffusion in a semi-infinite medium ............ 66112.3.15 Drying of solids .............................................................. 663

12.4 Mass Transfer by Convection ................................................ 66512.4.1 Governing equation of diffusion with convection......... 66612.4.2 Concentration boundary layer and

mass transfer coefficient ............................................... 66912.4.3 Unit of mass transfer coefficient .................................. 67012.4.4 Analogy between momentum, heat and mass

transfer .......................................................................... 67112.4.5 Forced convection mass transfer in

Laminar flow over a flat plate ...................................... 67412.4.6 Forced convection mass transfer in laminar

flow in a tube ................................................................. 67412.5 Mass Transfer in Turbulent Flow ......................................... 677

12.5.1 Analogy and experimental results ................................ 67712.6 Simultaneous Heat and Mass Transfer ................................ 68212.7 Simultaneous Heat and Mass Transfer in a Wet

Bulb Thermometer ................................................................. 682Highlights ...................................................................... 687Multi-choice Questions .................................................. 689Review Questions .......................................................... 689Exercises ........................................................................ 690

Appendix–I Heat Transfer Data .................................... 694–707Appendix–II Solved Questions from Engineering

Services Examinations ............................. 708–773Appendix–III Multi–choices Questions from

Engineering Services Examinations ..... 774–847Subject Index ............................................... 848-855

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1

1Basic Concepts of

Heat Transfer

1.1 INTRODUCTION

Heat transfer may be defined as the science that predicts thetransfer of energy from one body to another by virtue of temperaturedifference. Thermodynamics is the science which deals with the systemsin equilibrium. It predicts the extent of heat and work interactionswhen a system passes from one equilibrium state to another. Heattransfer provides the answers to the questions to the extent andmanner of transfer of heat in any process.

There must be a potential difference for the transfer of heat.The difference in temperature provides the necessary potentialdifference. According to the second law of thermodynamics, heat cannotflow from a body at low temperature to a body at higher temperaturewithout employing external work. Thus, heat must flow from a highertemperature region to a lower temperature region until equilibrium isreached when the two bodies attain the same temperature. Thus heattransfer is essentially an irreversible process.

1.2 DIFFERENCES BETWEEN THERMODYNAMICS ANDHEAT TRANSFER

The basic differences between thermodynamics and heattransfer may be summarised as given in Table 1.1.

Heat And Mass Transfer

Publisher : KHANNAPUBLISHERS ISBN : 9788174092908 Author : C.P. Arora and

Sadhu Singh

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