Heat Transfer Basics E-Book

Jamil Ghojel

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 584

Veröffentlichungsjahr: 2023

Beschreibung

HEAT TRANSFER BASICS Concise introduction to heat transfer, with a focus on worked example problems to aid in reader comprehension and student learning Heat Transfer Basics covers the essential topics of heat transfer in a focused manner, starting with an introduction to heat transfer that explains its relationship to thermodynamics and fluid mechanics and continuing on to key topics such as free convection, boiling and condensation, radiation, heat exchangers, and more, for an accessible and reader-friendly yet comprehensive treatment of the subject. Each chapter features multiple worked out example problems, including derivations of key governing equations and comparisons of worked solutions with computer modeled results, which helps students become familiar with the types of problems they will encounter in the field. Throughout the book, figures and diagrams liberally illustrate the concepts discussed, and practice problems allow students to test their understanding of the content. The text is accompanied by an online instructor's manual. Heat Transfer Basics includes information on: * One-dimensional, steady-state conduction, covering the plane wall, the composite wall, solid and hollow cylinders and sphere, conduction with and without internal energy generation, and conduction with constant and temperature-dependent thermal conductivity * Heat transfer from extended surfaces, fins of uniform and variable cross-sectional area, fin performance, and overall fin efficiency * Transient conduction, covering general lumped capacitance solution method, one- and multi-dimensional transient conduction, and the finite-difference method for solving transient problems * Free and forced convection, covering hydrodynamic and thermal considerations, the energy balance, and thermal analysis and convection correlations More advanced than introductory textbooks yet not as overwhelming as textbooks targeted at specialists, Heat Transfer Basics is ideal for students in introductory and advanced heat transfer courses who do not intend to specialize in heat transfer, and is a helpful reference for advanced students and practicing engineers.

Leseprobe

Heat Transfer Basics

A Concise Approach to Problem Solving

By

Jamil Ghojel

Copyright © 2024 by John Wiley & Sons, Inc. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

Published simultaneously in Canada.

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Library of Congress Cataloging-in-Publication Data:

Names: Ghojel, J., author. | John Wiley & Sons, publisher.

Title: Heat transfer basics : a concise approach to problem solving / by Jamil Ghojel.

Description: Hoboken, New Jersey : John Wiley & Sons, [2024] | Includes bibliographical references and index.

Identifiers: LCCN 2023013359 (print) | LCCN 2023013360 (ebook) | ISBN 9781119840268 (hardback) | ISBN 9781119840275 (adobe pdf) | ISBN 9781119840282 (epub)

Subjects: LCSH: Heat--Transmission--Textbooks. | Heat--Transmission--Problems, exercises, etc.

Classification: LCC QC320.34 .G46 2023 (print) | LCC QC320.34 (ebook) | DDC 621.402/2--dc23/eng/20230928

LC record available at https://lccn.loc.gov/2023013359

LC ebook record available at https://lccn.loc.gov/2023013360

Cover image(s): © Etienne Outram/Shutterstock

Cover design: Wiley

Set in 9.5/12.5pt STIXTwoText by Integra Software Services Pvt. Ltd., Pondicherry, India

Contents

Cover

Title Page

Copyright Page

Preface

Acknowledgements

List of Symbols

About the Companion Website

1 Basic Concepts of Heat and Mass Transfer

1.1 Heat Transfer and Its Relationship With Thermodynamics

1.2 Heat Conduction

1.3 Heat Convection

1.4 Thermal Radiation

1.5 Mass Transfer

2 One-Dimensional Steady-State Heat Conduction

2.1 General Heat Conduction Equation

2.1.1 Cartesian Coordinate System

2.1.2 Cylindrical Coordinate System

2.1.3 Spherical Coordinate System

2.2 Special Conditions of the General Conduction Equation

2.2.1 Constant Thermal Conductivity k With Energy Storage and Generation

2.2.2 Variable Thermal Conductivity and No Internal Energy Storage and Generation

2.2.3 Variable Thermal Conductivity With Internal Energy Generation and No Energy Storage

2.3 One-Dimensional Steady-State Conduction

2.3.1 Plane Wall (or Plate) Without Heat Generation and Storage

2.3.1.1 Constant Thermal Conductivity

2.3.1.2 Temperature-Dependent Thermal Conductivity

2.3.1.3 Composite Plane Wall

2.3.2 Boundary Conditions

2.3.3 Hollow Cylinder (Tube) Without Heat Generation and Storage

2.3.3.1 Constant Thermal Conductivity

2.3.3.2 Temperature-Dependent Thermal Conductivity

2.3.3.3 Composite Cylinder

2.3.3.4 Critical Thickness of Cylinder Insulation

2.3.3.5 Effect of Order of Insulation Material

2.3.4 Hollow Spherical Shell Without Heat Generation and Storage

2.3.4.1 Constant Thermal Conductivity

2.3.4.2 Temperature-Dependent Thermal Conductivity

2.3.4.3 Composite Spherical Shell

2.3.5 Plate With Internal Heat Generation, No Heat Storage, and Uniform Heat Dissipation By Convection

2.3.5.1 Constant Thermal Conductivity

2.3.5.2 Temperature-Dependent Thermal Conductivity

2.3.6 Plate With Internal Heat Generation and Non-Uniform Heat Dissipation By Convection

2.3.6.1 Constant Thermal Conductivity

2.3.6.2 Temperature-Dependent Thermal Conductivity

2.3.7 Solid Cylinder With Internal Heat Generation and Heat Dissipation By Convection

2.3.7.1 Constant Thermal Conductivity

2.3.7.2 Temperature-Dependent Thermal Conductivity

2.3.8 Hollow Cylinder With Internal Heat Generation and Heat Dissipation By Convection From the Outer Surface

2.3.8.1 Constant Thermal Conductivity

2.3.8.2 Temperature-Dependent Thermal Conductivity

2.3.9 Hollow Cylinder With Internal Heat Generation and Heat Dissipation By Convection From the Inner Surface

2.3.9.1 Constant Thermal Conductivity

2.3.9.2 Temperature-Dependent Thermal Conductivity

2.3.10 Hollow Cylinder With Internal Heat Generation and Heat Dissipation By Convection From Both Inner and Outer Surfaces

2.3.10.1 Constant Thermal Conductivity

2.3.10.2 Temperature-Dependent Thermal Conductivity

2.3.11 Solid Sphere With Internal Heat Generation and Heat Dissipation By Convection and No Heat Storage

2.3.11.1 Constant Thermal Conductivity

2.3.11.2 Temperature-Dependent Thermal Conductivity

2.3.12 Hollow Sphere With Internal Heat Generation and Heat Dissipation By Convection From the Outer Surface and No Heat Storage

2.3.12.1 Constant Thermal Conductivity

2.3.12.2 Temperature-Dependent Thermal Conductivity

2.3.13 Hollow Sphere With Internal Heat Generation and Heat Dissipation By Convection From the Inner Surface and No Heat Storage

2.3.13.1 Constant Thermal Conductivity

2.3.13.2 Temperature-Dependent Thermal Conductivity

2.3.14 Hollow Sphere With Internal Heat Generation and Heat Dissipation By Convection From Both the Inner and Outer Surfaces and No Heat Storage

2.3.14.1 Constant Thermal Conductivity

2.3.14.2 Temperature-Dependent Thermal Conductivity With Specified Inner and Outer Surface Temperature

2.4 Interface Contact Resistance

3 Heat Transfer From Extended Surfaces

3.1 Pin Fin of Rectangular Profile and Circular Cross-Section

3.1.1 Pin Fin of Finite Length and Un-Insulated Tip

3.1.2 Pin Fin of Finite Length and Insulated Tip

3.1.3 Pin Fin of Infinite Length

3.1.4 Fin Efficiency

3.2 Straight Fin of Rectangular Profile and Uniform Thickness

3.3 Pin Fin of Triangular Profile and Circular Cross-Section (Conical Pin Fin)

3.4 Straight Fins of Variable Cross-Sectional Area

3.4.1 Fin of Trapezoidal Profile

3.4.2 Direct Solution of the Straight Fin of Trapezoidal Profile

3.4.3 Straight Fin of Triangular Profile

3.4.4 Correction Factor Solution Method for Straight Fins of Variable Cross-Sectional Area

3.4.5 Straight Fin of Convex Parabolic Profile

3.4.6 Straight Fin of Concave Parabolic Profile

3.5 Annular Fins

3.5.1 Straight Annular Fin of Uniform Thickness

3.5.2 Direct Solution of the Straight Annular Fin of Uniform Thickness

3.5.3 Correction Factor Solution Method for Annular Fins of Uniform Thickness

3.5.4 Circular (Annular) Fin of Triangular Profile

3.5.5 Annular Fin of Hyperbolic Profile

3.6 Other Fin Shapes

3.7 Heat Transfer Through Finned Walls

4 Two-Dimensional Steady-State Heat Conduction

4.1 Analytical Method

4.1.1 Two-Dimensional Plate With Finite Length and Width and Constant Boundary Conditions

4.1.1.1 Temperature Distribution

4.1.1.2 Rate of Heat Transfer

4.1.2 Two-Dimensional Plate With Finite Length and Nonconstant Boundary Conditions

4.1.2.1 Temperature Distribution

4.1.2.2 Rate of Heat Transfer

4.1.3 Two-Dimensional Plate With Semi-Infinite Length

4.1.4 Other Boundary Conditions

4.1.5 Two-Dimensional Semi-Circular Plate (Or Cylinder) With Prescribed Boundary Conditions

4.2 Conduction Shape Factor Method

4.3 Numerical Solution of Two-Dimensional Heat Conduction Problems

4.3.1 Interior Node

4.3.2 Plane-Surface Node

4.3.3 Interior Node Near Curved Surface

4.3.4 Finite Difference Formulation in Cylindrical Coordinates

4.4 Solution Methods for Finite-Difference Models

4.4.1 Matrix Inversion Method

4.4.2 Iterative Methods (Gauss–Seidel Method)

5 Transient Conduction

5.1 Analytical Solutions of One-Dimensional Distributed Systems

5.1.1 Heating or Cooling of an Infinite Plate

5.1.2 Analysis of the Plate Solution

5.1.2.1 Other Boundary Conditions

5.1.3 Heating or Cooling of an Infinite Solid Cylinder

5.1.4 Heating or Cooling of a Sphere

5.1.5 Heisler Charts

5.2 Time-Dependent and Spatially Uniform Temperature Distribution

5.2.1 Lumped Capacitance Method

5.3 Multi-Dimensional Transient Conduction Systems

5.3.1 Long Rectangular Bar

5.3.2 Short Cylinder

5.3.3 Rectangular Parallelepiped

5.4 Finite-Difference Method for Solving Transient Conduction Problems

5.4.1 Explicit Finite-Difference Method

5.4.1.1 One-Dimensional Transient Conduction

5.4.1.2 Two-Dimensional Transient Conduction

5.4.2 Implicit Finite-Difference Method

5.4.2.1 One-Dimensional Transient Conduction

5.4.2.2 Two-Dimensional Transient Conduction

5.4.3 Finite Difference Formulation in Cylindrical Coordinates

6 Fundamentals of Convection Heat Transfer

6.1 Convection Governing Equation

6.2 Viscosity

6.3 Types of Flow

6.4 The Hydrodynamic (Velocity) Boundary Layer

6.4.1 Flow Over a Flat Plate

6.4.2 Flow Inside a Cylindrical Tube

6.4.3 Flow Over Tube or Sphere

6.5 The Thermal Boundary Layer

6.6 Dimensional Analysis

6.6.1 The Rayleigh Method

6.6.2 Buckingham Pi (Π or π) Theorem

6.7 Geometric Similarity and Other Considerations

7 Forced Convection – External Flows

7.1 Flow Over a Flat Plate

7.1.1 Laminar Flow Over a Flat Plate

7.1.2 Turbulent Flow Over a Flat Plate

7.2 Flow Over a Cylindrical Tube

7.3 Tube Banks in Crossflow

7.3.1 Banks of Smooth Tubes

7.3.2 Banks of Rough Staggered Tubes

7.4 Flow Over Non-Circular Tubes

7.5 Flow Over Spheres

8 Forced Convection – Internal Flows

8.1 Forced Convection Inside Tubes

8.2 Laminar Forced Convection (Region I)

8.2.1 Fully Developed Flow

8.2.2 Non-Circular Tubes

8.2.3 Laminar Forced Convection Correlations

8.3 Turbulent Forced Convection (Region III)

8.3.1 Forced Convection for Flow in the Transition Region (Region II)

9 Natural (Free) Convection

9.1 Boundary Layer in Free Convection

9.2 Governing Equation for Laminar Boundary Layer

9.3 Application of Dimensional Analysis to Natural Convection

9.4 Empirical Correlations for Natural Convection

9.4.1 Vertical Plates

9.4.2 Horizontal Plates

9.4.3 Inclined Plates

9.4.4 Long Horizontal Cylinder

9.4.5 Spheres

9.4.6 Flow in Channels

9.4.7 Flow in Closed Spaces

9.4.7.1 Vertical Rectangular Cavity

9.4.7.2 Horizontal Fluid Layer

9.4.7.3 Concentric Cylinders

9.4.7.4 Concentric Spheres

9.5 Mixed Free and Forced Convection

10 Thermal Radiation

10.1 The Electromagnetic Spectrum

10.2 Definitions and Radiation Properties

10.3 Shape Factors

10.3.1 Reciprocity Rule

10.3.2 Summation Rule

10.3.3 Superposition Rule

10.3.4 Symmetry Rule

10.3.5 String Rule

10.4 Determination of Shape Factors for Finite Surfaces

10.5 Shape Factor Equations

11 Thermal Radiation

11.1 Radiation Exchange Between Two Grey Surfaces

11.2 Thermal Radiation Networks

11.2.1 Grey Object in Grey Enclosure

11.2.2 Radiation Exchange Between Two Grey Surfaces

11.2.3 Three Infinitely Long Parallel Planes

11.2.4 Radiation Exchange Between Several Grey Surfaces

11.2.5 Enclosure With Four Long Grey Surfaces That See Each Other

11.2.6 Enclosure With Three Long Grey Surfaces That See Each Other

11.2.7 Three Surfaces With One of Them Insulated

11.2.8 Two Parallel Flat Plates of Equal Finite Size in Very Large Room

11.2.9 Two Surfaces With One of Them Insulated in Large Room

11.3 Radiation Exchange With Participating Medium

11.3.1 Absorption of Radiation

11.3.2 Gaseous Emission

11.3.3 Gas-Mass to Surface Radiation Heat Transfer

11.4 Combined Radiation and Convection

12 Heat Exchangers

12.1 Overall Heat Transfer Coefficient

12.2 The LMTD Method of Heat Exchanger Analysis

12.2.1 Double-Pipe Heat Exchangers

12.2.2 Shell-and-Tube Heat Exchangers

12.2.3 Cross-Flow Heat Exchangers

12.2.4 LMTD Thermal Design Procedure

12.3 The Effectiveness-NTU Method of Heat-Exchanger Analysis

12.3.1 Effectiveness-NTU Relation for Parallel-Flow Exchanger

12.3.2 Effectiveness-NTU Relation for Counter-Flow Exchanger

12.3.3 Other Types of Heat Exchangers

12.3.4 Effectiveness-NTU Thermal Design Procedure

13 Heat Transfer With Phase Change

13.1 Heat Transfer in Condensing Vapours

13.1.1 Filmwise Condensation

13.1.2 Flow Regimes of the Condensate Film

13.1.2.1 Laminar Flow Regime

13.1.2.2 Laminar Wavy Regime

13.1.2.3 Turbulent Flow Regime

13.1.3 Film Condensation Outside Horizontal Tubes

13.1.4 Film Condensation Inside Horizontal Tubes

13.1.4.1 Laminar Flow

13.1.4.2 Turbulent Flow

13.1.5 Dropwise Condensation

13.2 Boiling Heat Transfer

13.2.1 Pool Boiling

13.2.2 Film Boiling

13.2.3 Forced-Convection Boiling

14 Mass Transfer

14.1 Species Concentrations

14.2 Diffusion Mass Transfer

14.3 Steady Mass Diffusion Through a Plane Wall

14.4 Diffusion of Vapour Through a Stationary Gas

14.5 Steady-State Equimolar Counter Diffusion

14.6 Mass Convection

14.6.1 Forced Mass Convection Correlations

14.6.2 Natural (Free) Mass Convection Correlations

14.7 Simultaneous Mass and Heat Transfer

Appendices

Appendix B

Appendix C

Appendix D

Appendix N

References

Index

End User License Agreement

List of Tables

APPENDIX 01

Table B.1 Bessel functions.

Table B.2 Modified Bessel functions.

Table B.3 Correlations for...

Table B.4 Correlations for...

Table B.5 Correlations for...

Table B.6 Correlations for...

APPENDIX 03

Table D.1 Positive roots of...

Table D.2 Positive roots of...

Table D.3 Positive roots of...

APPENDIX 04

Table N.1 Thermophysical properties...

Table N.2 Thermophysical properties...

CHAPTER 01

Table 1.1 Energy balance...

Table 1.2 Thermal conductivity...

Table E1.1 Calculated heat flux ...

Table 1.3 Heat transfer coefficient...

Table 1.4 Emissivity of selected...

Table 1.5 Diffusion coefficients...

CHAPTER 02

Table 2.1 Maximum and wall...

Table E2.4 Results of calculations...

Table 2.2 Selected values...

CHAPTER 03

Table E3.1 Modified Bessel...

Table 3.1 Coefficients for...

Table E3.5 Bessel functions...

Table E3.6 Bessel functions...

Table 3.2 Coefficients for...

Table 3.3 Coefficients for...

Table 3.4 Examples of calculation...

Table 3.5 Coefficients for correlation...

Table 3.6 Methodologies for determining...

Table 3.7 Efficiency correlations...

CHAPTER 04

Table E4.1 Calculation methodology...

Table E4.5 Calculation methodology...

Table 4.1 Shape factors for...

Table E4.6 Summary of calculations...

Table 4.2 Nodal temperature equations...

Table E4.9.1 Solution of...

Table E4.9.2 Effect of grid size...

Table E4.10 Comparison of the inverse...

CHAPTER 05

Table 5.1 Variation of Biot number...

Table 5.2 Spatial temperature variation...

Table E5.4 Calculated average...

Table 5.3 Explicit nodal equations...

Table 5.4 Implicit nodal equations...

Table E5.8.1 Selected results of the...

Table E5.8.2 Comparison of results...

CHAPTER 06

Table 6.1 Symbols, units, and dimensions...

Table 6.2 Dimensionless numbers.

CHAPTER 07

Table 7.1 Constant C and exponent...

Table 7.2 Determination of Umax...

Table 7.3 Correction factor for...

Table 7.4 Constant n and exponent...

CHAPTER 08

Table 8.1 Heat transfer and fluid...

CHAPTER 09

Table E9.2 Calculation results using...

CHAPTER 10

Table 10.1 Blackbody radiation...

Table 10.2 Shape factor equations...

CHAPTER 11

Table 11.1 Selected values of the mean...

CHAPTER 12

Table 12.1 Fouling factors for selected...

Table 12.2 Heat exchanger effectiveness...

Table 12.3 Heat exchanger effectiveness...

CHAPTER 13

Table 13.1 Selected values of constants...

Table 13.2 Comparison of indicative heat...

CHAPTER 14

Table 14.1 Diffusion coefficients for...

List of Illustrations

APPENDIX 01

Figure B.1 Efficiency chart of straight...

Figure B.2 Efficiency chart of straight...

Figure B.3 Correction factor chart for...

Figure B.4 Efficiency chart of straight ...

Figure B.5 Efficiency chart of straight...

Figure B.6 Correction factor chart for...

Figure B.7 Efficiency chart of annular...

Figure B.8 Efficiency chart of annular...

APPENDIX 02

Figure C.1 Screen shot of spreadsheet...

Figure C.2 Screen shot of spreadsheet...

APPENDIX 03

Figure D.1 Screen shot of...

Figure D.2 Screen shot of...

CHAPTER 01

Figure 1.1 Heat transfer modes...

Figure 1.2 Conduction heat transfer...

Figure 1.3 Analogy between:...

Figure 1.4 Schematic diagrams...

Figure 1.5 Analogy between electrical...

Figure 1.6 Emissive power of heated...

Figure 1.7 Convex black object...

Figure 1.8 Concentration profile...

Figure 1.9 Schematic diagram of...

CHAPTER 02

Figure 2.1 Elemental control volume...

Figure 2.2 Elemental control volume...

Figure 2.3 Elemental control volume...

Figure 2.4 Heat conduction through...

Figure 2.5 Effect of variability of...

Figure 2.6 Three-layer composite...

Figure 2.7 Computer model of three-layer...

Figure 2.8 Examples of boundary conditions...

Figure 2.9 Comparison between electrical...

Figure 2.10 Thermal circuits for combined...

Figure 2.11 Hollow cylinder and its thermal...

Figure 2.12 Effect of variability of the...

Figure 2.13 Two-layer composite hollow...

Figure 2.14 Results of computer model...

Figure 2.15 Two-layer hollow composite...

Figure 2.16 Thermal resistance versus...

Figure 2.17 Effect of the critical radius...

Figure 2.18 Thermal circuit for an electrical...

Figure 2.19 Computer modelling of the effect...

Figure 2.20 Spherical shell and its thermal...

Figure 2.21 Effect of variability of the...

Figure 2.22 Thermal circuit for conduction...

Figure 2.23 Computer modelling of five-layer...

Figure E2.4.2 Temperature plots for cases...

Figure E2.4.1 (a) Single-layer and...

Figure 2.24 Plate with internal heat generation...

Figure 2.25 Temperature distribution...

Figure 2.26 Plate with internal heat...

Figure 2.27 Temperature profiles in...

Figure 2.28 Solid cylinder with internal...

Figure 2.29 Solid cylinder with internal...

Figure 2.30 Heat transfer in a hollow...

Figure 2.31 Temperature profiles in a...

Figure 2.32 Heat transfer in a hollow...

Figure 2.33 Temperature profiles in...

Figure 2.34 Heat dissipation by...

Figure 2.35 Hollow cylinder with...

Figure 2.36 Hollow cylinder with...

Figure 2.37 Conduction heat transfer...

Figure 2.38 Solid sphere with heat...

Figure 2.39 Temperature profiles in...

Figure 2.40 Conduction heat transfer...

Figure 2.41 Hollow sphere with internal...

Figure 2.42 Temperature profiles in...

Figure 2.43 Conduction heat transfer...

Figure 2.44 Hollow sphere with heat...

Figure 2.45 Temperature profiles in...

Figure 2.46 Hollow sphere with heat...

Figure 2.47 Hollow sphere with heat...

Figure E2.7.1 Graphical method for...

Figure E2.7.2 Temperature profile...

Figure 2.48 Hollow sphere with heat...

Figure 2.49 Interfacial contacts...

Figure 2.50 Steel–concrete...

Figure 2.51 Inverse two-dimensional...

Figure 2.52 Effect of contact...

Figure P2.5 Composite wall.

Figure P2.12 Steel tube with...

CHAPTER 03

Figure 3.1 Heat transfer enhancement...

Figure 3.2 Heat transfer enhancement...

Figure 3.3 Mixed-mode heat transfer...

Figure 3.4 Effect of fin material on...

Figure 3.5 Effect of coefficient of...

Figure 3.6 Effect of increasing the...

Figure 3.7 Temperature profiles in...

Figure 3.8 Fin efficiency versus...

Figure 3.9 Straight fin with constant...

Figure 3.10 Temperature profile of...

Figure 3.11 Pin fin of triangular...

Figure 3.12 Second-order modified...

Figure 3.13 Fin efficiency of conical...

Figure 3.14 Straight fin with trapezoidal...

Figure 3.15 Modified Bessel functions...

Figure 3.16 Efficiency of straight fin...

Figure E3.1 Temperature profiles in the...

Figure 3.17 Straight fin with triangular...

Figure 3.18 Straight fin with:...

Figure 3.19 Correction factor chart...

Figure 3.20 Straight fin of convex...

Figure 3.21 Efficiency of straight...

Figure 3.22 Plots of modified...

Figure E3.5 Temperature profile...

Figure 3.24 Efficiency of straight...

Figure 3.25 Straight annular fin...

Figure 3.26 Efficiency chart of...

Figure E3.6 Temperature profile...

Figure 3.27 Straight annular fin...

Figure 3.28 Correction factor chart...

Figure 3.29 plots for the efficiency...

Figure 3.30 plots for the efficiency...

Figure 3.31 Efficiency of pin (spine)...

Figure 3.32 Efficiency of straight...

Figure 3.33 Plane wall with an array...

Figure 3.34 Thermal circuit of the heat...

Figure 3.35 Computer modelling results...

Figure 3.36 Computer modelling results...

Figure P3.20 Schematic diagram...

CHAPTER 04

Figure 4.1 Schematics of heat...

Figure 4.2 Schematic diagram of...

Figure 4.3 Temperature profiles:...

Figure E4.1 Two-dimensional model...

Figure 4.4 Rate of heat transfer...

Figure 4.5 Schematic diagram of...

Figure E4.3 Two-dimensional model...

Figure 4.7 Temperature profiles...

Figure 4.6 Schematic diagram of...

Figure E4.5 Two-dimensional model...

Figure 4.9 Two-dimensional...

Figure P4.14 Two-dimensional plate...

Figure 4.8 Computer simulation...

Figure E4.7 Schematic diagram...

Figure E4.6 Schematic diagram...

Figure 4.10 Nomenclature used...

Figure 4.11 Schematic diagram...

Figure E4.8 Schematic diagram...

Figure 4.12 Exterior plane-surface...

Figure 4.13 Node near curved...

Figure 4.14 Two-dimensional...

Figure E4.9.1 Finite-difference ...

Figure E4.9.2 Computer modelling...

Figure E4.10 Model for Example...

Figure P4.5 Two-dimensional model...

Figure P4.9 Steel pipe encased...

Figure P4.12 Two-dimensional...

Figure P4.13 Two-dimensional...

CHAPTER 05

Figure 5.1 One-dimensional...

Figure 5.2 Temperature response...

Figure 5.3 Effect of Fourier number...

Figure 5.4 Transient conduction model...

Figure 5.5 One-dimensional transient...

Figure 5.6 Effect of Biot number on...

Figure 5.7 Formation of long rectangular...

Figure E5.5 Schematic diagram...

Figure 5.8 Formation of solid...

Figure E5.6 Schematic diagram...

Figure 5.9 The formation of a...

Figure E5.7 Schematic diagram...

Figure 5.10 One-dimensional...

Figure 5.11 Surface control...

Figure 5.12 Schematic diagram...

Figure 5.13 Exterior...

Figure 5.14 Two-dimensional...

Figure E5.8 Schematic diagram...

Figure P5.14 Schematic diagram...

Figure P5.16 Heated short...

Figure P5.17 Conduction in...

Figure P5.18 Fin of circular...

Figure P5.19 Cross-section...

CHAPTER 06

Figure 6.1 Schematic diagram...

Figure 6.2 Flow velocity profiles...

Figure 6.3 Flow velocity profiles...

Figure 6.4 Cross laminar flow over...

Figure 6.5 Cross flow over a tube...

Figure 6.6 Temperature profiles...

Figure 6.7 Relative positions of...

Figure P6.6 Schematic diagram of...

Figure P6.11 Schematic diagram of...

CHAPTER 07

Figure 7.1 Velocity profile in...

Figure 7.2 Temperature distribution...

Figure E7.1 Temperature variation...

Figure 7.3 Transition of laminar...

Figure 7.4 Velocity fluctuations...

Figure 7.5 Horizontal cylinder...

Figure 7.6 Variation of local...

Figure 7.7 Tube bank configurations...

Figure P7.12 Air flow across...

Figure P7.15 Air flow across...

Figure P7.16 Air flow across...

Figure P7.17 Air flows over...

CHAPTER 08

Figure 8.1 Schematic diagram...

Figure 8.2 Relationship between Nusselt...

Figure 8.3 Flow in a heated tube:...

Figure 8.4 Effect of application...

Figure 8.5 Effect of application...

Figure 8.6 Computer modelling of...

Figure 8.7 Heat exchanger...

Figure 8.8 Flow structure...

Figure 8.9 Correction factor...

Figure 8.10 Laminar and turbulent...

Figure 8.11 Flow in the transient...

Figure P8.7 Flow in a long...

Figure P8.8 Flow of air in...

CHAPTER 09

Figure 9.1 Development of boundary...

Figure 9.2 Force balance on...

Figure 9.3 Convection flow...

Figure 9.4 Convection flow...

Figure 9.5 Convection flow...

Figure 9.6 Natural convection...

Figure 9.7 Natural convection...

Figure 9.8 Horizontal fluid...

Figure E9.2 Double vertical...

Figure 9.9 Natural convection...

Figure E9.3 Insulated thin-walled...

Figure 9.10 Relative directions...

Figure P9.16 Double vertical wall...

Figure P9.19 Steam flow in insulated...

CHAPTER 10

Figure 10.1 Electromagnetic...

Figure 10.2 Radiation on the...

Figure 10.3 Monochromatic emissive...

Figure 10.4 Monochromatic emissive...

Figure 10.5 Model for deriving...

Figure 10.6 Thermal radiation...

Figure 10.7 Radiation energy...

Figure 10.8 Enclosure with...

Figure 10.9 Radiation exchange...

Figure 10.19 Parallel strip...

Figure 10.20 Rectangular plate...

Figure 10.22 Disk 1 radiating to...

Figure 10.23 Two concentric cylinders...

Figure 10.21 Rectangle 1 radiating...

Figure 10.10 Representation of...

Figure 10.11 Three infinitely...

Figure 10.12 Radiation exchange...

Figure E10.3b Cross-section of...

Figure E10.3a Long heating...

Figure 10.13 Definition of...

Figure 10.14 Plane and solid...

Figure 10.15 Schematic diagram...

Figure 10.16 Two arbitrary...

Figure E10.4 Schematic diagram...

Figure 10.18 Concentric cylinder...

Figure 10.24 Two concentric...

Figure 10.17 Infinite plate...

Figure P10.4 Schematic diagram...

Figure P10.12 Three configurations...

Figure P10.13 Geometry...

Figure P10.14 Radiation...

Figure P10.15 Two long parallel...

Figure P10.16 Two long parallel...

Figure P10.17 Geometrical...

Figure P10.18 Two concentric...

Figure P10.19 Two coaxial discs...

Figure P10.21 Parallel rectangles...

CHAPTER 11

Figure 11.1 Schematic diagram...

Figure 11.2 Surface resistance...

Figure 11.3 Two grey surfaces...

Figure 11.4 Space resistance...

Figure 11.5 Grey object in grey...

Figure 11.6 Radiation network...

Figure 11.7 Two parallel plates...

Figure 11.8 Enclosure with several...

Figure 11.9 Enclosure of four grey...

Figure 11.10 Long three-sided duct...

Figure 11.11 Three surfaces exchanging...

Figure 11.12 Two parallel plates...

Figure 11.13 Two perpendicular...

Figure E11.3.2 Radiation network...

Figure 11.14 Absorption of radiation...

Figure 11.15 Radiation from hemispherical...

Figure 11.16 Standard emissivity of...

Figure 11.17 Standard emissivity of...

Figure 11.18 Standard emissivity of...

Figure 11.19 Pressure correction...

Figure 11.20 Correction charts for...

Figure P11.1 Long duct with a heating...

Figure P11.8 Three shields between...

Figure P11.10 Two isothermal concentric...

Figure P11.12 Schematic representation...

Figure P11.16 Radiation exchange...

Figure P11.17 Schematic diagram...

Figure P11.18 Radiation exchange...

Figure P11.22 Schematic diagram...

CHAPTER 12

Figure 12.1 (a) Parallel-flow heat...

Figure 12.2 Temperature profiles in...

Figure 12.3 Temperature profiles for...

Figure 12.4 Schematic diagram of 1:1...

Figure 12.5 Schematic diagram of 1:2...

Figure 12.6 Shell-and-tube heat exchanger...

Figure 12.7 Correction factor for...

Figure 12.8 Correction factor for...

Figure 12.9 Correction factor for...

Figure 12.10 Correction factor fo...

Figure 12.11 Cross-flow heat...

Figure 12.12 Correction factor...

Figure 12.13 Correction factor...

Figure 12.14 Correction factor...

Figure 12.15 Schematic diagrams...

Figure 12.16 Heat rate and effectiveness...

Figure 12.17 Temperature profiles...

Figure 12.27 Effectiveness of...

Figure 12.18 Effectiveness of...

Figure 12.19 Effectiveness of...

Figure 12.20 Effectiveness of...

Figure 12.21 Effectiveness of...

Figure 12.22 Effectiveness of...

Figure 12.23 Effectiveness of...

Figure 12.24 Effectiveness of...

Figure 12.25 Effectiveness of...

Figure 12.26 Effectiveness of...

Figure E12.5 Temperature profiles...

Figure P12.5 Counterflow heat...

Figure P12.13 Schematic diagram...

Figure P12.16 Schematic diagram...

Figure P12.17 Schematic diagram...

CHAPTER 13

Figure 13.1 Condensing double-pipe...

Figure 13.2 Filmwise condensation...

Figure 13.3 Flow regimes in film...

Figure 13.4 Plots of versus for...

Figure 13.5 Chart for the estimation...

Figure 13.6 (a) Condenser shell-and-tube heat...

Figure 13.7 Film condensation on a single...

Figure 13.8 Film condensation inside horizontal...

Figure 13.9 Film condensation inside horizontal...

Figure 13.10 Average heat transfer coefficient...

Figure 13.11 Heat flux as a function of temperature...

Figure 13.12 Heat flux and heat transfer coefficient...

Figure 13.13 Forced convection boiling stages...

Figure P13.10 Schematic representation of the...

CHAPTER 14

Figure 14.1 Concentration profile...

Figure 14.2 Schematic diagram of...

Figure 14.3 Steady mass transfer...

Figure 14.4 Diffusion of vapour...

Figure 14.5 Equimolar isothermal...

Figure E14.4 Representation of...

Figure 14.6 Concentration boundary...

Figure 14.7 Air passing over wetted...

Figure P14.5 Representation of...

Figure P14.7 Representation of...

Figure P14.14 Thin plastic membrane...

Guide

Cover

Title Page

Copyright Page

Table of Contents

Preface

Acknowledgements

List of Symbols

About the Companion Website

Begin Reading

Appendices

Appendix B

Appendix C

Appendix D

Appendix N

References

Index

End User License Agreement

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Preface

As the title implies, the book covers basic but essential material for heat transfer courses at different levels. The book has been made self-contained so that certain parts can be used as introductory material and others as material for more advanced levels. The book is also intended for use by practicing professionals in various engineering fields. Basic also implies concise coverage of a wide range of topics at sufficient depth without blowing up the number of pages and cost to extremes, as has been the case with many excellent textbooks in recent years.

The book is primarily concerned with conduction, convection, and radiation heat transfer. The book consists of 14 chapters and 14 appendices. Chapter 1 is a general brief introduction to heat transfer concepts. Chapters 2 and 3 cover the topics of one-dimensional steady-state conduction and extended surfaces, which are presented in considerably more detail and depth than most other similar textbooks. Chapter 4 deals with two-dimensional steady-state conduction issues and Chapter 5 discusses one- and multi-dimensional non-steady (transient) conduction in some detail. Numerical methods of solving steady and transient conduction problems are presented with a number of illustrative examples and spreadsheet screenshots. Following an introduction to fundamentals of convection heat transfer in Chapter 6, forced convection in external and internal flows are discussed in Chapters 7 and 8, respectively. Natural (free) convection is covered in Chapter 9. Chapters 10 and 11 deal with fundamentals of radiation heat transfer, shape factors, and the exchange of thermal radiation between surfaces separated by transparent and non-transparent media. In dealing with radiation in participating gaseous media, the conventional Hottel charts have been replaced by recently developed charts by Alberti et al. (2016, 2018. 2020) on the basis of more accurate spectral data. The comprehensive set of charts include gas emissivity of water vapour, carbon dioxide, and carbon monoxide together with pressure and binary gas-overlap correction factors. Essentials of heat exchangers and the classical thermal analysis using the log-mean-temperature-difference and NTU-effectiveness approaches is presented in Chapter 12.

Heat transfer with phase change, and mass transfer are also covered in Chapters 13 and 14, respectively. The book has 14 appendices (A to N) four of which (B, C, D, and N) are included in the text and the remainder can be accessed online at “www.wiley.com/go/ghojel/heat_transfer.”

Since the primary goal of the book is to provide students with the knowledge and skills needed for practical engineering practice, both analytical and graphical solution techniques are presented. For the latter approach, most charts in the text are duplicated with enlarged versions in the appendices. Also, since computer applications play an integral role in solving complex problems, “Solaria Thermal” software package (Harley Thermal) is used in the book, where applicable, to reinforce the relevance of computer-aided solutions of heat transfer problems.

Acknowledgements

The author wishes to acknowledge and thank Dave Rosato, president and founder of Harley Thermal, for kindly providing access to the “Solaria Thermal” computer modelling software package which has been used in this book to model selected conduction and convection examples. His insight and advice on the use of Solaria throughout the preparation of the manuscript is greatly appreciated.

Thanks are also due to Dr David Trujillo (TRUCOMP – Inverse Problems) for providing the latest version of INTEMP (Inverse heat conduction software package), which was used to update the simulation of steel-concrete contact resistance in cylindrical structural columns.

About Solaria Thermal

Solaria is a general-purpose thermal modelling software package incorporating model generation, solving and post processing functions. It incorporates Finite Difference and Conjugate Gradient solvers to solve steady-state and transient models of constant, temperature-dependent, or time-dependent thermophysical properties. It can also handle anisotropic (three-dimensional) material conductivities. The software is relatively easy to learn and model generation and post processing is mostly intuitive. A free demo version with a limited number of nodes can be obtained from https//www. solariathermal. com.

List of Symbols

Area,

Area of unfinned surface (prime area),

Cross-sectional area,

Fin profile area,

Fin profile area,

Surface area,

Molar concentration, ; gas emissivity pressure correction factor

Drag coefficient

Specific heat at constant pressure,

Capacitance ratio

Thermal capacitance,

Specific heat at constant volume,

Diameter,

Binary mass diffusivity,

Hydraulic diameter,

Emissive power,

Blackbody emissive power,

Blackbody emissive power per unit wave length (monochromatic),

Eckert number

Rate of energy generation,

Shape factor; drag force, ; correction factor for heat exchangers

Euler number

Fouling factor,

Fourier number

Froud number

Friction factor, coefficient of friction or friction coefficient

Irradiation,

Grashof number

Gravitational acceleration,

Heat transfer coefficient, ; conductance,

Surface-average heat transfer coefficient

Latent heat of vaporization,

Modified heat of vaporization,

Convection mass transfer coefficient,

Radiation heat transfer coefficient,

Electric current,

Radiation intensity,

Radiosity, ; mass diffusion flux,

Molar diffusion flux,

Jacob number

Thermal conductivity,

Effective conductivity,

Length,

Log mean temperature difference

Molar mass,

Molar flow rate,

Mass,

Mass flow rate,

Number of moles of substance, number of tubes

Nusselt number

Number of transfer units

species molar transfer rate,

Perimeter,

Peclet number

Prandtl number

Pressure, ,

Energy transfer,

Rate of energy transfer,

Heat flux,

Rate of energy generation per unit volume,

Cylinder radius, gas constant, electric resistance,

Universal gas constant,

Rayleigh number

Reynolds number

Thermal contact resistance,

Thermal resistance,

Radius,

Inner radius,

Outer radius,

Conduction shape factor,

Diagonal pitch of a tube bank,

Longitudinal pitch of a tube bank,

Traverse pitch of a tube bank,

Schmidt number

Sherwood number

Stanton number

Temperature,

Temperature, ; time,

Fluid velocity, ; overall heat transfer coefficient, ; internal energy,

Volume,

Specific volume,

Width,

Weber number

Species mass fraction

Vapour quality

Mole fraction of a species

Greek letters

Thermal diffusivity, ; absorptivity

Coefficient of volume thermal expansion,

Hydrodynamic boundary layer thickness, ; thickness (slab, plate),

Thermal boundary layer thickness,

Emissivity; heat exchanger effectiveness; average roughness height,

Fin effectiveness

Correction factor (heat exchangers)

Efficiency

Fin efficiency

Overall efficiency

Temperature difference,

Relative humidity

Wavelength,

Dynamic viscosity, ; molecular (molar) mass,

Kinematic viscosity, ; frequency of radiation,

Mass density, ; reflectivity

Stefan-Boltzmann constant, surface tension,

Shear stress, ; transmissivity; time step

Solid angle, (steradian)

Subscripts

Species in binary mixture

Atmosphere

Species in binary mixture

Blackbody; bulk temperature,

Cross-sectional; cold fluid; characteristic; corrected; convective

Critical

Conduction

Convection

Drag

Effective;

Fluid properties; fin condition; film (temperature)

ɡ

Generation

Hydrodynamic; hot fluid

Insulation

Isothermal

Length,

Saturated liquid conditions

Mean value

Maximum

Centre condition; outlet; outer

Radiation

Root

Surface conditions, storage

Saturated conditions

Thermal, tip

Saturated vapour conditions

Local conditions

Wall

Total

Free stream conditions

Superscripts

Standard emissivity

About the Companion Website

Heat Transfer Basics: A Concise Approach to Problem Solving is accompanied by a companion website:

www.wiley.com/go/ghojel/heat_transfer

This website includes:

Instructor’s Manual

Solution Manual

Appendices A, E to M

1 Basic Concepts of Heat and Mass Transfer

1.1 Heat Transfer and Its Relationship With Thermodynamics

Heat transfer can be looked at as a branch of classical thermodynamics with specific distinguishing features. This can best be explained by considering the processes taking place in the cylinder of the internal combustion engine schematically shown in Figure 1.1a.

Figure 1.1 Heat transfer modes in the cylinder of internal combustion engine: (a) engine cylinder schematic; (b) control volume.

The thermodynamic processes taking place in the cylinder are elegantly and succinctly stated by the first law of thermodynamics (principle of conservation of energy) in the form

(1.1)

where

is the heat generated by the combustion of the injected fuel in the cylinder at the end of the compression process, resulting in high-pressure, high temperature gaseous products

is the work done by the piston as the combustion products expand with the piston moving downwards

is the balance of the heat left from the combustion process to raise the internal energy and temperature of the gases inside the cylinder.

The first law of thermodynamics states that energy can be converted (transformed) from one form (heat) to another (work) but cannot be created or destroyed and that the process takes place between two states at equilibrium. The first law does not provide information on the amount of energy that can be transformed, energy transformation direction, and its effectiveness. This gap is filled by the second law of thermodynamics which stipulates that only part of the heat will be converted to work, heat will flow spontaneously from a high temperature source to a lower temperature sink, and the flow will be accompanied by irreversible changes that degrade the resultant energy making it difficult to be utilized further. Applied to the example under consideration, indicative heat balance in internal combustion engines is given in Table 1.1.

Table 1.1 Energy balance in internal combustion engines.

% Energy supplied

Component

Petrol engine

Diesel engine

Useful work

32

45

Exhaust system

38

28

Cooling system and surface losses

30

27

The disposal of the heat component shown under “losses” in Table 1.1 is the domain of the science of heat transfer. This process of disposal is explained below and some new terms are introduced without explanation at this stage to be defined in greater detail later.

The system shown in Figure 1.1b is essentially heat exchange between the high-temperature combustion gases and the circulating cooling water in the water jacket. Heat is first transferred from the hot gases at temperature to the inner cylinder wall at temperature by convection and radiation followed by conduction through the inner wall of the jacket with the temperature dropping to . Heat is then transferred to the circulating water at temperature by convection, followed by transfer by convection to the inner surface of the outer jacket wall at temperature . The final conduction process takes place through the outer water jacket wall with a temperature drop to followed by heat losses from the outer cylinder surface by both convection and radiation to the atmosphere. A parallel heat exchange process takes place in the engine cooling system (not shown here), whereby the cooling water is circulated by a pump in a heat exchanger (radiator) to be cooled and returned to the engine. The flow rate and corresponding dimensions of the components of the cooling system must be selected to maintain optimum operating conditions of engine components.

From the above description of the processes in the cylinder, it is apparent that heat flow involves time-dependent factors and the fluids are in temperature nonequilibrium states. Therefore, the basic laws of thermodynamics are not adequate to assess the heat transfer processes described and proper analysis requires the use of tools that are provided by other branches of science, such as fluid dynamics, physics, and mathematics.

In heat transfer, the first law of thermodynamics is widely used, albeit without the work component and is generally known as the principle of conservation of energy (in short, energy or heat balance). Applied to the control volume in Figure 1.1, the heat balance can be expressed as

Rate of heat transfer into the control volume,

Rate of heat removed by the cooling water,

Rate of heat loss to the surrounding media,

(1.2)

More generally, taking into account that heat transfer processes may be accompanied by internal energy generation and/or energy storage (accumulation) within the control volume , the energy balance equation for a control volume can be written as

(1.3)

Internal heat generation could be due to electrical heating, chemical processes, or nuclear reactions.

The field of applications of heat transfer is wide and diverse covering, for example, energy generation, transport, process industry, building industry, agriculture, medical industry, and aviation and space industries. In the following sections, the three modes of heat transfer will be discussed separately but it should be kept in mind that they continually interact and rarely occur independently.

1.2 Heat Conduction

Consider a solid layer or static liquid layer contained between two long vertical plates at two different temperatures and (Figure 1.2). The molecules of the medium between the plates are depicted as small circles, with the molecules at higher temperature in black. The molecules exist in continuous agitated random motion indicated by the small arrows, with the degree of agitation being directly proportional to the temperature. According to the second law of thermodynamics, there is a net molecular energy transfer from the hotter side of the layer to the colder side and, consequently, net thermal energy (heat) transfer and this process is known as conduction.

Figure 1.2 Conduction heat transfer and sign convention: (a) positive temperature gradient; (b) negative temperature gradient.

The heat conduction process is governed by Fourier’s law, stated in terms of the rate of heat transfer

(1.4)

where

is the area through which heat flows,

is the temperature gradient in the direction, , and

is the constant of proportionality known as the thermal conductivity, which is a physical property of the conduction medium and could vary significantly with temperature,

Often, Eq. (1.4) is written in terms of the heat flux , defined as

(1.5)

The negative sign in Fourier’s law is deliberately introduced to obtain a positive heat flow when the temperature gradient is negative (decreasing temperature in the -direction) (Figure 1.2b) and a negative heat flow when the temperature gradient is positive (increasing temperature in the -direction) (Figure 1.2a).

For a slab of thickness δ and finite temperature gradient of , Eq. (1.4) can be rearranged as

(1.6)

This equation is analogous to the equation relating voltage potential to resistance and current in electrical circuits (Figure 1.3)

(1.7)

Figure 1.3 Analogy between: (a) electrical and (b) thermal conduction circuits.

The thermal resistance for the conduction process is then

(1.8)

Similar to electrical resistances, thermal resistances can be arranged in series or in parallel, depending on the physical model of the heat transfer problem.

For steady-state one-dimensional problems, in which the thickness of a plate is much smaller than its height, the temperature gradient in Eqs (1.4) and (1.5) can be approximated by the temperature difference divided by the thickness of the one-dimensional layer

(1.9)

Table 1.2 shows some indicative values of the thermal conductivity for some materials. More comprehensive data on thermal conductivity is provided in Appendix A.

Table 1.2 Thermal conductivity for selected materials.

Material

Thermal conductivity

Air

0.0625

Aluminium alloy

168

Carbon steel

64

Copper

386

Fibreglass

0.028

Water

0.611

Example 1.1 In the model shown in Figure 1.2, the distance between the two plates is 100 mm, the left plate is maintained at and the right plate at . Calculate the heat flux through the plate if the space between the plates is filled with air, water, fibreglass, and copper.

Solution

Since the temperature gradient is constant, the flux is directly proportional to the thermal conductivity

The results of the calculations are shown in Table E1.1.

Table E1.1 Calculated heat flux for air, water, and fibreglass.

Material

Thermal conductivity

Air

0.0625

0.01875

Water

0.611

0.1833

Fibreglass (insulating material)

0.028

0.084

Copper

386

115.8

It is apparent that the higher the thermal conductivity, the less resistant the material is to heat flow. Most resistance (least heat flux) is exhibited by insulating materials. Air and water can be used as insulating materials under certain circumstances to reduce heat losses.

1.3 Heat Convection

Convection is the process of heat transfer between fluids and solid boundaries. Referring to Figure 1.1, we observe the following heat transfer processes that come under this definition:

From high-temperature gases to the inner walls of the cylinder

From heated cylinder wall to the circulating water in the water jacket

From the heated circulating water to the cooler outer cylinder wall

From heated outer wall to the surrounding air at ambient temperature.

In all these processes, heat transfer is due to the combined effect of molecular motion, as illustrated in Figure 1.2, and macroscopic motion of the fluid portions. The macroscopic motion in the cylinder is caused by the turbulent motion of the combustion products as the piston moves downwards at high speed and in the water jacket by the action of the water pump. Macroscopic motion is the motion of fluid portions (parcels) from one position to another, resulting in enthalpy exchange between high- and low-temperature zones in the fluid, as a result of which the rate of heat transfer in the fluid as a whole and to the solid wall increases and the process is referred to as forced convection. The rate of heat transfer can be increased at will simply by increasing the rapidity of motion of fluid parcels by external means such as pumps and blowers. In some cases, moderate fluid motion may be caused by the density gradient in the fluid, in which case heat transfer is by free convection. In our example of the engine cylinder, this can occur at the exterior walls if the engine is stationary. If the engine is powering a motor vehicle, heat will be dissipated to the atmosphere by forced convection.

Convection heat transfer is more complex than conduction due to the interaction of fluid motion with surface effects and the formation of hydrodynamic and thermal boundary layers and the presence of velocity and temperature profiles. Figure 1.4 shows velocity and temperature profiles for forced and free convection.

Figure 1.4 Schematic diagrams of velocity and temperature profiles over heated plates: (a) forced convection from horizontal plate; (b) free convection from vertical plate.

Despite the aforementioned complications, the convective heat transfer rate and heat flux can be calculated by a simple equation known as Newton’s law of cooling

(1.10)

(1.11)

where

rate of convective heat transfer,

heat flux,

area through which heat flows,

difference between the surface temperature and the free stream temperature ,

proportionality factor known as the heat transfer coefficient,

The thermal circuit for a simple heat transfer by convection is shown in Figure 1.5. The convection resistance is

(1.12)

Figure 1.5 Analogy between electrical (a) and thermal convection (b) circuits.

The heat transfer coefficient is determined from experimental results and, strictly speaking, in Eqs (1.10) and (1.11) should be an average value over area . The direction of the heat flux (Figure 1.4) depends on whether the plate temperature is higher or lower than the free stream temperature .

Values of heat transfer coefficient for selected fluids in contact with a solid surface are shown in Table 1.3.

Table 1.3 Heat transfer coefficient for selected fluids.

Heat transfer coefficient

Fluid

Air (free convection)

Air (forced convection)

Water (free convection)

Water (forced convection)

Oil (forced convection)

Superheated steam (forced convection)

Example 1.2 A solid cylindrical element 2 m long and 2.5 cm diameter is heated electrically by passing 1.5 current at 80 voltage until it reaches a steady surface temperature . If the temperature of the surrounding air is 16, estimate the average heat transfer coefficient for the heat transfer process between the tube surface and the surrounding air.

Solution

We assume that there is no energy storage and no other heat transfer modes. Hence, applying the energy equation

The surface area of the element is

From Newton’s law of cooling

1.4 Thermal Radiation

Radiation heat transfer in the example of Figure 1.1 is shown by the curly arrows inside the cylinder and at the exterior surface of the cylinder. Compared to the two heat transfer models discussed so far, radiation heat transfer has the following distinctive features:

All surfaces above absolute zero temperature emit electromagnetic radiation energy in all directions (

Figure 1.6

). The higher the temperature, the more energy is emitted

Figure 1.6 Emissive power of heated surfaces and radiation energy exchange.

The emitted energy is attributed to changes in the electron configurations of the constituent atoms and molecules at the atomic scale

Radiation energy is transported by electromagnetic waves travelling at the speed of light

When radiation emitted by one surface falls on a recipient surface and is absorbed, the random molecular energy increases causing the temperature of the recipient to increase

The presence of a material medium is not a requirement for radiation energy transfer and can occur efficiently in vacuum

Radiation energy is exchanged between emitting surfaces, resulting in net energy direction from the high-temperature source to the low-temperature target.

The upper limit to the emitted energy is given by the Stefan–Boltzmann law, which states that any blackbody surface above a temperature of absolute zero radiates heat at a rate proportional to the fourth power of the absolute temperature

(1.13)

The constant of proportionality is the Stefan–Boltzmann constant , subscript (for black) denotes idealized blackbody or black surface, and subscript denotes surface. A net transfer of radiant heat can take place between any two bodies if a temperature gradient exists. If a convex small black body at temperature exchanges radiation energy with a large black enclosure at temperature , as shown in Figure 1.7, all the radiant energy incident upon surface 1 is fully absorbed and the net rate of radiant heat transfer to that surface is given by

(1.14)

Figure 1.7 Convex black object in black enclosure.

Real surfaces, or grey surfaces, are not blackbody surfaces and the emitted energy (heat flux) by a real surface is less than that of a blackbody emission at the same temperature, and Eq. (1.13) acquires the form

(1.15)

where is a property termed emissivity or emittance that has a value less than unity. If the surfaces of objects 1 and 2 in Figure 1.7 are assumed grey, all the radiation emitted from object 1 is absorbed by the surrounding enclosure (object 2) and the latter behave like a black body at . The net radiative heat transfer to object 1 is given by

(1.16)

If the two objects exchanging radiation have a specific geometry and finite size (Figure 1.6) and different emissivities, the radiation heat flow rate between them is

(1.17)

is known as the shape factor, view factor, configuration factor, or transfer factor and it accounts for the emissivities and relative geometries of actual bodies. The term “shape factor” will be used in this book. Determination of shape factors for some geometries could be mathematically challenging, and some examples will be presented in Chapter 10. Table 1.4 shows selected values of emissivity.

Table 1.4 Emissivity of selected materials and surfaces.

Surface

Temperature,

Emissivity,

Aluminium (polished)

500

0.04

Aluminium (anodized)

310

0.94

Copper (polished)

340

0.041

Copper (dull)

320

0.15

Stainless steel (polished)

310

0.25

Asphalt

310

0.93

Glass

420

0.88

Light-coloured surfaces

530–800

0.25–0.5

Dark-coloured surfaces

530–800

0.4–0.8

Example 1.3 A spherical object of diameter and temperature is placed centrally inside an evacuated spherical shell with a nearly black wall that is maintained at temperature . Calculate the net rate of radiation heat transfer from the small sphere to the inner wall of the spherical shell for surface emissivities and .

Solution

Applying Eq. (1.12), we obtain for

For

1.5 Mass Transfer