Heat Transfer

Preface to the Springer Edition
Preface to the Second Edition
Acknowledgements
Contents
About the Author
Nomenclature
	Latin Alphabet Symbols
	Greek Symbols
	Subscripts
1 Introduction to the Study of Heat Transfer
	1.1 Introduction
	1.2 Basic Assumptions in the Study of Heat Transfer
	1.3 Basic Heat Transfer Processes and Examples
		1.3.1 Basic Definitions
	1.4 Exercises
2 Steady Conduction in One Dimension
	2.1 Preliminaries
		2.1.1 On Thermal Conductivity Values
		2.1.2 Approaches to the Study of Conduction Heat Transfer
	2.2 Steady One Dimensional Conduction
		2.2.1 One-Dimensional Conduction in a Uniform Area Bar
		2.2.2 Steady One-Dimensional Conduction in Cylindrical Coordinates
		2.2.3 Steady Radial Conduction in a Solid Cylinder with Internal Heat Generation
		2.2.4 One-Dimensional Radial Conduction in Spherical Coordinates
	2.3 Generalization
	2.4 Exercises
3 Unsteady Heat Transfer in Lumped Systems
	3.1 Preliminaries
	3.2 Governing Equation and the General Solution
		3.2.1 Governing Equation
		3.2.2 Electrical Analogy
		3.2.3 Characteristic Length Scale
		3.2.4 General Solution
		3.2.5 Response of a First-Order System in Particular Cases
	3.3 Second-Order Thermal System: Response to Step Input
	3.4 Exercises
4 Heat Transfer from Extended Surfaces
	4.1 Introduction
	4.2 Fins of Uniform Area
		4.2.1 Analysis
		4.2.2 Solution to the Fin Equation
		4.2.3 Uniform Area Fin Subject to Third Kind Boundary Condition at the Tip
	4.3 Variable Area Fins
		4.3.1 General Analysis of Variable Area Fins
		4.3.2 Particular Cases of Variable Area Fins
	4.4 Fins of Minimum Mass
		4.4.1 Uniform Fin of Optimum Proportions
		4.4.2 Uniform Spine (pin Fin) of Optimum Proportions
	4.5 Heat Transfer from Fin Arrays
		4.5.1 Overall Surface Efficiency of a fin array
		4.5.2 Effectiveness of a Fin Array
		4.5.3 Fin Array Applications
	4.6 Exercises
5 Multidimensional Conduction Part I
	5.1 Introduction
		5.1.1 Integral Form of Governing Equation
		5.1.2 Differential Form of Governing Equation
		5.1.3 Simplified Form of Energy Equation
		5.1.4 Thermal Diffusivity
	5.2 One-Dimensional Transient Conduction
		5.2.1 Transients in a Semi-infinite Solid
		5.2.2 Approximate Integral Method Due to Goodman
		5.2.3 One-Dimensional Transient Problem: Space Domain Finite
	5.3 Steady Conduction in Two Dimensions
		5.3.1 Steady Conduction in a Rectangle
		5.3.2 Steady Conduction in a Rectangle With Heat Generation
		5.3.3 Steady Two-Dimensional Conduction in Cylindrical Co-Ordinates
		5.3.4 Shape Factors for Some Useful Configurations
		5.3.5 Solution to Laplace Equation in a Cylinder
		5.3.6 Solution to a Practical Problem
		5.3.7 Solution to Laplace Equation in Spherical Co-ordinates
	5.4 Exercises
6 Multidimensional Conduction Part II
	6.1 Preliminaries
		6.1.1 Introduction
		6.1.2 Basic Problem in Cartesian Coordinates
		6.1.3 Basic Problem in Cylindrical Coordinates
		6.1.4 Basic Problem in Spherical Co-Ordinates
	6.2 One-Term Approximation and Heisler Charts
	6.3 Transient Conduction in More Than One Dimension
		6.3.1 Introduction
		6.3.2 Transient Conduction in an Infinitely Long Rectangular Bar
		6.3.3 Transient Heat Conduction in a Rectangular Block  in the form of a brick
		6.3.4 Transient Heat Conduction in a Circular Cylinder  of Finite Length
	6.4 Exercises
7 Numerical Solution of Conduction Problems
	7.1 Introduction
		7.1.1 A Simple Example: One-Dimensional Steady Conduction
		7.1.2 Numerical Solution of a Fin Problem
		7.1.3 Solution of Nodal Equations by TDMA
		7.1.4 Steady Radial Conduction in a Cylinder
		7.1.5 Steady Radial Conduction in a Spherical Shell
	7.2 Conduction in Two Dimensions
		7.2.1 Steady Heat Conduction in Two Dimensions: Cartesian Coordinates
		7.2.2 Steady Heat Conduction in Two Dimensions: Cylindrical Coordinates
		7.2.3 One-Dimensional Transient in a Bar
		7.2.4 Transient Heat Transfer in a Conducting Convecting Fin
		7.2.5 One-Dimensional Transient in a Solid Cylinder
		7.2.6 One-Dimensional Transient in a Solid Sphere
	7.3 Transient Conduction in Two and Three Dimensions
		7.3.1 Transient Conduction in a Rectangle: Explicit Formulation
		7.3.2 ADI Method
		7.3.3 Modification of the ADI Method for Three Dimensional Transient Conduction
	7.4 Exercises
8 Basics of Thermal Radiation
	8.1 Introduction
		8.1.1 Fundamental Ideas
		8.1.2 Preliminaries and Definitions
	8.2 Cavity or Black Body Radiation
		8.2.1 Basic Ideas
		8.2.2 Thermodynamics of Black Body Radiation
	8.3 Wavelength Distribution of Black Body Radiation
		8.3.1 About Waves
		8.3.2 Number of Degenerates Modes in a Three-Dimensional Cavity
		8.3.3 Planck Distribution
		8.3.4 Properties of the Planck Distribution Function
	8.4 Exercises
9 Surface Radiation
	9.1 Introduction
		9.1.1 Surface Types
	9.2 Spectral and Hemispherical Surface Properties
		9.2.1 Spectral Hemispherical Quantities
		9.2.2 Total Hemispherical Quantities
		9.2.3 Band Model for a Non-gray Surface
		9.2.4 Equilibrium Temperature of a Surface
		9.2.5 Selective Surfaces
	9.3 Angle-Dependent Surface Properties
		9.3.1 Some Results from Electromagnetic Theory
		9.3.2 Specular Surface
		9.3.3 Hemispherical Reflectance
		9.3.4 Real or Engineering Surfaces
	9.4 Exercises
10 Radiation in Enclosures
	10.1 Introduction
	10.2 Evacuated Enclosure with Gray Diffuse Walls
		10.2.1 Assumptions
		10.2.2 Diffuse Radiation Interchange Between Two Surfaces
		10.2.3 Angle Factor Algebra and Its Applications
		10.2.4 Three-Dimensional Enclosures
	10.3 Radiation Heat Transfer in Enclosures with Gray Diffuse Walls
		10.3.1 Method of Detailed Balancing
		10.3.2 Radiation Shields
		10.3.3 Radiosity Irradiation Method of Enclosure Analysis
		10.3.4 Electrical Analogy
	10.4 Enclosure Analysis Under Special Circumstances
		10.4.1 Enclosure Containing Diffuse Non-gray Surfaces
		10.4.2 Gray Enclosures Containing Diffuse and Specular Surfaces
		10.4.3 Enclosure Analysis with Surfaces of Non-uniform Radiosity
	10.5 Exercises
11 Radiation in Participating Media
	11.1 Introduction
	11.2 Preliminaries
		11.2.1 Definitions
		11.2.2 Equation of Transfer
	11.3 Absorption of Radiation in Different Media
		11.3.1 Transmittance of a Solid Slab
		11.3.2 Absorption of Radiation by Liquids
		11.3.3 Absorption of Radiation by Gases
		11.3.4 Radiation in an Isothermal Gray Gas Slab  and the Concept of Mean Beam Length
	11.4 Modeling of Gas Radiation
		11.4.1 Basics of Gas Radiation Modeling
		11.4.2 Band Models
	11.5 Radiation in a Non-isothermal Participating Medium
		11.5.1 Radiation Transfer in a Gray Slab:
		11.5.2 Radiation Equilibrium
		11.5.3 Solution of Integral Equation
		11.5.4 Discrete Ordinate Method
	11.6 Enclosure Analysis in the Presence of an Absorbing and Emitting Gas
		11.6.1 Zone Method
		11.6.2 Example of Zone Analysis
		11.6.3 Application of DOM to Two-Surface Enclosure with a Non-isothermal Participating Medium
	11.7 Exercises
12 Laminar Convection In Internal Flow
	12.1 Introduction
		12.1.1 Classification of Flows
		12.1.2 Fluid Properties and Their Variation
	12.2 Dimensional Analysis and Similarity
		12.2.1 Dimensional Analysis of a Flow Problem
		12.2.2 Notion of ``Similarity\'\'
		12.2.3 Dimensional Analysis of Heat Transfer Problem
	12.3 Internal Flow Fundamentals
		12.3.1 Fundamentals of Steady Laminar Tube Flow
		12.3.2 Governing Equation Starting from First Principles
		12.3.3 Governing Equation Starting with the NS Equations
		12.3.4 Solution
		12.3.5 Fully Developed Flow in a Parallel Plate Channel
		12.3.6 Concept of Fluid Resistance
	12.4 Laminar Heat Transfer in Tube Flow
		12.4.1 Bulk Mean Temperature
		12.4.2 Variation of the Bulk Mean Temperature
		12.4.3 Tube Flow with Uniform Wall Heat Flux
		12.4.4 Fully Developed Temperature with Uniform Wall Heat Flux
		12.4.5 Tube Flow with Constant Wall Temperature
		12.4.6 Fully Developed Tube Flow with Constant Wall Temperature
	12.5 Laminar Fully Developed Flow and Heat Transfer in Non-circular Tubes and Ducts
		12.5.1 Introduction
		12.5.2 Parallel Plate Channel with Asymmetric Heating
		12.5.3 Parallel Plate Channel with Symmetric Heating
		12.5.4 Fully Developed Flow in a Rectangular Duct
		12.5.5 Fully Developed Heat Transfer in a Rectangular Duct: Uniform Wall Heat Flux Case
		12.5.6 Fully Developed Flow and Heat Transfer Results in Several Important Geometries
	12.6 Laminar Fully Developed Heat Transfer to Fluid Flowing in an Annulus
		12.6.1 Fully Developed Flow in an Annulus
		12.6.2 Fully Developed Temperature in an Annulus
	12.7 Flow and Heat Transfer in Laminar Entry Region
		12.7.1 Heat Transfer in Entry Region of Fully Developed Tube Flow
		12.7.2 Mean Nusselt Number and Useful Correlations
	12.8 Exercises
13 Laminar Convection in External Flow
	13.1 Introduction
	13.2 Laminar Boundary Layer Flow Past a Surface
		13.2.1 Order of Magnitude Analysis and the Boundary Layer Approximation
		13.2.2 Laminar Boundary Layer over a Flat Plate: Velocity Boundary Layer
		13.2.3 Laminar Thermal Boundary Layer over a Flat Plate
	13.3 Boundary Layer Flow in the Presence of Stream-Wise Pressure Variation
		13.3.1 Inviscid Flow Past the Wedge
		13.3.2 Flow Within the Boundary Layer
		13.3.3 Temperature Profiles in Falkner–Skan Flows
	13.4 Integral Form of Boundary Layer Equations
		13.4.1 Momentum and Energy Integral Equations
		13.4.2 Approximate Solution for Boundary Layer Flow Past a Flat Plate Using a Polynomial Profile for Velocity
		13.4.3 Approximate Solution for Boundary Layer Temperature Profile for Flow Past a Flat Plate Using a Polynomial Profile for Temperature
		13.4.4 Integral Method Applied to Boundary Layer Flow with Axial Pressure Gradient
		13.4.5 Thwaites\'s Method
	13.5 Cylinder in Cross Flow
		13.5.1 Introduction
		13.5.2 Laminar Flow Normal to a Cylinder
		13.5.3 Laminar Boundary Layer Flow Past a Cylinder
		13.5.4 Effect of Pressure Gradient on Boundary Layer Flow
		13.5.5 Drag Force on a Cylinder in Cross Flow
	13.6 Exercises
14 Convection in Turbulent Flow
	14.1 Introduction
	14.2 Time-Averaged Equations
		14.2.1 Turbulent Shear Stress and Turbulent Heat Flux
		14.2.2 Turbulent Boundary Layer Equations
	14.3 Turbulence Models
		14.3.1 Prandtl\'s Mixing Length Theory
		14.3.2 Universal Velocity Distribution
		14.3.3 Velocity Profiles in Pipe Flow
	14.4 Pressure Drop and Heat Transfer in Turbulent Pipe Flow
		14.4.1 Pressure Drop in Turbulent Pipe Flow
		14.4.2 Heat Transfer in Turbulent Pipe Flow
		14.4.3 Application of Average Heat Transfer Coefficient Concept to a Practical Application
	14.5 Turbulent Boundary Layer over a Flat Plate
		14.5.1 Approximate Analysis of Turbulent Flow Parallel to a Flat Plate
		14.5.2 Heat Transfer in the Turbulent Boundary Layer over a Flat Plate
		14.5.3 Calculation of Drag with Flow Being Partly Laminar and Partly Turbulent
	14.6 Cylinder in Cross Flow
		14.6.1 Heat Transfer for Flow Normal to a Tube Bank
	14.7 Exercises
15 Heat Exchangers
	15.1 Introduction
	15.2 Analysis of Heat Exchangers
		15.2.1 Thermodynamic Analysis of a Co-Current Heat Exchanger
		15.2.2 Thermal Analysis of a Co-Current Heat Exchanger
		15.2.3 Overall Heat Transfer Coefficient
		15.2.4 Alternate Approach—ε-NTU Relationship for a Co-Current Heat Exchanger
		15.2.5 Counter-Current Heat Exchanger
	15.3 Other Types of Heat Exchangers
		15.3.1 Analysis of Shell and Tube Heat Exchanger
		15.3.2 Analysis of a Cross Flow Heat Exchanger by the ε-NTU Approach
		15.3.3 Analysis of a Cross Flow Heat Exchanger by LMTD Correction Factor Approach
		15.3.4 General Remarks on Heat Exchangers
	15.4 Exercises
16 Natural Convection
	16.1 Introduction
	16.2 Laminar Natural Convection from a Vertical Isothermal Plate
		16.2.1 Isothermal Vertical Plate—Integral Solution
		16.2.2 Exact Solution of Ostrach
		16.2.3 Comparison with Experimental Results
	16.3 Turbulent Natural Convection from a Vertical Isothermal Plate
		16.3.1 Approximate Integral Analysis
		16.3.2 Useful Nusselt Number Correlations
	16.4 Natural Convection from Other Geometries
		16.4.1 Correlation for Horizontal Plates
		16.4.2 Correlation for Vertical Cylinders
		16.4.3 Correlation for Horizontal Cylinders
	16.5 Heat Transfer Across Fluid Layers
		16.5.1 Horizontal Fluid Layers
		16.5.2 Vertical Fluid Layers
		16.5.3 Inclined Air Layers
	16.6 Exercises
17 Special Topics in Heat Transfer
	17.1 Introduction
	17.2 Multi-mode Problem Involving Radiation
		17.2.1 Transient Cooling of a Lumped System
		17.2.2 Radiation Error in Thermometry
		17.2.3 Duct Type Space Radiator
		17.2.4 Uniform Area Fin Losing Heat by Convection and Radiation
		17.2.5 Radiating-Conducting-Convecting Fin With Linearized Radiation
	17.3 Heat Transfer During Melting or Solidification
		17.3.1 Stefan Problem
		17.3.2 Neumann Problem
		17.3.3 Phase Change in a Finite Domain
	17.4 Heat Transfer During Condensation
		17.4.1 Film Condensation Over An Isothermal Vertical Surface
		17.4.2 Film Condensation Inside and Outside Tubes
		17.4.3 Condensation in the Presence of Flowing Vapor
	17.5 Heat Transfer During Boiling
		17.5.1 Pool Boiling
		17.5.2 Some Useful Relations in Pool Boiling
		17.5.3 Flow Boiling
		17.5.4 Heat Transfer Correlation in Flow Boiling
	17.6 Mixed Convection
		17.6.1 Laminar Mixed Convection For Flow Over A Vertical Isothermal Flat Plate
		17.6.2 Laminar Mixed Convection in a Parallel Plate Channel
		17.6.3 Laminar Mixed Convection in a Vertical Parallel Plate Channel: Fully Developed Solution
	17.7 Heat Transfer in a Particle Bed
		17.7.1 Flow Characteristics of a Particle Bed
		17.7.2 Heat Transfer Characteristics of a Particle Bed
	17.8 Heat Transfer in High Speed Flows
		17.8.1 Compressible Boundary Layer Flow Parallel to a Flat Plate
	17.9 Current Topics of Interest in Heat Transfer
	17.10 Exercises
Appendix A Note on Bessel Functions
A.1  Background
A.1.1  Bessel Equation with Non-integer ν
A.1.2  Gamma Function: A Short Digression
A.1.3  Bessel Function of the First Kind
A.2  Bessel Equation When ν is an Integer: Bessel Function of the Second Kind
A.3  Asymptotic Behavior of Bessel Functions
A.4  Orthogonal Property of Bessel Functions
A.5  Modified Bessel Functions
A.6  General Form of Equation Solvable in Terms of Bessel Functions
A.7  Some Useful Results
A.8  Tables of Bessel Functions and Modified Bessel Functions
Appendix B Note on Legendre Functions
B.1  Background
B.1.1  Special Simple Case of Legendre Equation
B.1.2  Legendre Equation with nge1
B.1.3  Legendre Function of Second Kind
B.1.4  Some Useful Relations Involving Legendre Polynomials
B.1.5  Orthogonality property and Fourier Legendre series
Appendix C Basics of Complex Variables
C.1  Introduction
C.1.1  Definitions
C.1.2  Conditions for the Existence of Derivative of w
C.1.3  Complex Potential
C.2  Examples of Complex Potentials
C.2.1  Complex Potential w=z
C.2.2  Complex Potential w=Ln(z)
C.2.3  Complex Potential w=ez
C.3  Superposition of Complex Potentials
C.3.1  Combination of Complex Potentials Considered in Sects. C.2.1 and C.2.2
C.3.2  Flow Past a Cylinder
C.3.3  General Comments
Appendix D Heisler Charts
D.1  One Term Approximation of the Slab Transient
D.2  One Term Approximation of the Cylinder Transient
D.3  One Term Approximation of the Sphere Transient
Appendix E Numerical Solution of Algebraic and Differential Equations
E.1  Introduction
E.2  Solution of Algebraic Equations
E.2.1  Solution of a Single Algebraic Equation
E.2.2  Solution of Several Algebraic Equations
E.2.3  Solution of Equations Involving Sparse Matrix—TDMA
E.2.4  Point by Point Iteration Methods
E.2.5  Iteration With Over or Under Relaxation
E.3  Solution of Ordinary Differential Equations (ODE)
E.3.1  First Order ODE
E.4  Higher Order ODE
E.4.1  Second-Order ODE: Initial Value Problem
E.4.2  Second-Order ODE: Boundary Value Problem
Appendix F Exponential Integrals
F.1  Introduction
F.2  Useful Ways of Calculating Exponential Integrals
F.2.1  Approximation of E3(t):
Appendix G Angle Factors and Mean Beam Lengths
G.1  Angle Factors
G.1.1  Angle Factors Between Rectangles
G.1.2  Angle Factor Between Equal and Parallel Rectangles
G.1.3  Angle Factor Between Perpendicular Rectangles
G.1.4  Angle Factor Between Coaxial Disks
G.2  Mean Beam Lengths in a Parallelepiped Enclosure
G.2.1  Mean Beam Length Between Equal and Parallel Rectangles
G.2.2  Mean Beam Length Between Perpendicular Rectangles Sharing a Common Edge
Appendix H Basic Equations of Convection Heat Transfer
H.1  Introduction
H.1.1  NS Equations in Cartesian Coordinates
H.1.2  Ideal Fluid Flow
H.2  NS Equations in Cylindrical and Spherical Coordinates
H.2.1  NS Equations in Cylindrical Coordinates
H.2.2  NS Equations in Spherical Coordinates
Appendix I Useful Tables
Index