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Heat Conduction 3rd ed. 2009 [Hardback]

  • Format: Hardback, 418 pages, height x width: 235x155 mm, weight: 1730 g, XV, 418 p., 1 Hardback
  • Pub. Date: 05-Sep-2009
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642012663
  • ISBN-13: 9783642012662
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Heat Conduction 3rd ed. 2009Larger Image
  • Format: Hardback, 418 pages, height x width: 235x155 mm, weight: 1730 g, XV, 418 p., 1 Hardback
  • Pub. Date: 05-Sep-2009
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642012663
  • ISBN-13: 9783642012662
Other books in subject:
Permanent link: https://www.kriso.ee/db/9783642012662.html
Keywords:
This textbook presents the classical topics of conduction heat transfer and extends the coverage to include chapters on perturbation methods, heat transfer in living tissue, and microscale conduction. This makes the book unique among the many published textbook on conduction heat transfer. Other noteworthy features of the book are:















The material is organized to provide students with the tools to model, analyze and solve a wide range of engineering applications involving conduction heat transfer.







Mathematical techniques are presented in a clear and simplified fashion to be used as instruments in obtaining solutions.







The simplicity of one-dimensional conduction is used to drill students in the role of boundary conditions and to explore a variety of physical conditions that are of practical interest.









Examples are carefully selected to illustrate the application of principles and the construction of solutions.









Students are trained to follow a systematic problem solving methodology with emphasis on thought process, logic, reasoning and verification. Solutions to all examples and end-of-chapter problems follow an orderly problems solving approach.

Extensive training material is available on the web

The author provides an extensive solution manual for verifiable course instructors on request. Please send your request to heattextbook@gmail.com
Preface vii
CHAPTER 1: BASIC CONCEPTS 1
1.1 Examples of Conduction Problems
1
1.2 Focal Point in Conduction Heat Transfer
2
1.3 Fourier's Law of Conduction
2
1.4 Conservation of Energy: Differential Formulation of the Heat Conduction in Rectangular Coordinates
5
1.5 The Heat Conduction Equation in Cylindrical and Spherical Coordinates
9
1.6 Boundary Conditions
10
1.6.1 Surface Convection: Newton's Law of Cooling
10
1.6.2 Surface Radiation: Stefan-Boltzmann Law
11
1.6.3 Examples of Boundary Conditions
12
1.7 Problem Solving Format
15
1.8 Units
16
REFERENCES
17
PROBLEMS
18
CHAPTER 2: ONE-DIMENSIONAL STEADY-STATE CONDUCTION 24
2.1 Examples of One-dimensional Conduction
24
2.2 Extended Surfaces: Fins
34
2.2.1 The Function of Fins
34
2.2.2 Types of Fins
34
2.2.2 Heat Transfer and Temperature Distribution in Fins
35
2.2.4 The Fin Approximation
36
2.2.5 The Fin Heat Equation: Convection at Surface
37
2.2.6 Determination of dAs/dx
39
2.2.7 Boundary Conditions
40
2.2.8 Determination of Fin Heat Transfer Rate qf
40
2.2.9 Steady State Applications: Constant Area Fins with Surface Convection
41
2.2.10 Corrected Length Lc
44
2.2.11 Fin Efficiency ηf
44
2.2.12 Moving Fins
45
2.2.13 Application of Moving Fins
47
2.2.14 Variable Area Fins
49
2.3 Bessel Differential Equations and Bessel Functions
52
2.3.1 General Form of Bessel Equations
52
2.3.2 Solutions: Bessel Functions
52
2.3.3 Forms of Bessel Functions
54
2.3.4 Special Closed-form Bessel Functions: n = odd integer/2
54
2.3.5 Special Relations for n = 1, 2, 3,
55
2.3.6 Derivatives and Integrals of Bessel Functions
56
2.3.7 Tabulation and Graphical Representation of Selected Bessel Functions
56
2.4 Equidimensional (Euler) Equation
58
2.5 Graphically Presented Solutions to Fin Heat Transfer Rate of qf
59
REFERENCES
60
PROBLEMS
61
CHAPTER 3: TWO-DIMESIONAL STEADY STATE CONDUCTION 72
3.1 The Heat Conduction Equation
72
3.2 Method of Solution and Limitations
72
3.3 Homogeneous Differential Equations and Boundary Conditions
72
3.4 Sturm-Liouville Boundary-Value Problem: Orthogonality
74
3.5 Procedure for the Application of Separation of Variables Method
76
3.6 Cartesian Coordinates: Examples
83
3.7 Cylindrical Coordinates: Examples
97
3.8 Integrals of Bessel Functions
102
3.9 Non-homogeneous Differential Equations
103
3.10 Non-homogeneous Boundary Conditions: The Method of Superposition
109
REFERENCES
111
PROBLEMS
111
CHAPTER 4: TRANSIENT CONDUCTION 119
4.1 Simplified Model: Lumped-Capacity Method
119
4.1.1 Criterion for Neglecting Spatial Temperature Variation
119
4.1.2 Lumped-Capacity Analysis
121
4.2 Transient Conduction in Plates
124
4.3 Non-homogeneous Equations and Boundary Conditions
128
4.4 Transient Conduction in Cylinders
132
4.5 Transient Conduction in Spheres
138
4.6 Time Dependent Boundary Conditions: Duhamel's Superposition Integral
141
4.6.1 Formulation of Duhamel's Integral
142
4.6.2 Extension to Discontinuous Boundary Conditions
144
4.6.3 Applications
145
4.7 Conduction in Semi-infinite Regions: The Similarity Transformation Method
150
REFERENCES
154
PROBLEMS
154
CHAPTER 5: POROUS MEDIA 163
5.1 Examples of Conduction in Porous Media
163
5.2 Simplified Heat Transfer Model
164
5.2.1 Porosity
164
5.2.2 Heat Conduction Equation: Cartesian Coordinates
165
5.2.3 Boundary Conditions
167
5.2.4 Heat Conduction Equation: Cylindrical Coordinates
168
5.3 Applications
168
REFERENCES
174
PROBLEMS
175
CHAPTER 6: CONDUCTION WITH PHASE CHANGE: MOVING BOUNDARY PROBLEMS 184
6.1 Introduction
184
6.2 The Heat Equation
185
6.3 Moving Interface Boundary Conditions
185
6.4 Non-linearity of the Interface Energy Equation
188
6.5 Non-dimensional Form of the Governing Equations: Governing Parameters
189
6.6 Simplified Model: Quasi-Steady Approximation
190
6.7 Exact Solutions
197
6.7.1 Stefan's Solution
197
6.7.2 Neumann's Solution: Solidification of Semi-Infinite Region
200
6.7.3 Neumann's Solution: Melting of Semi-Infinite Region
203
6.8 Effect of Density Change on the Liquid Phase
204
6.9 Radial Conduction with Phase Change
205
6.10 Phase Change in Finite Regions
209
REFERENCES
210
PROBLEMS
210
CHAPTER 7: NON-LINEAR CONDUCTION PROBLEMS 215
7.1 Introduction
215
7.2 Sources of Non-linearity
215
7.2.1 Non-linear Differential Equations
215
7.2.2 Non-linear Boundary Conditions
216
7.3 Taylor Series Method
216
7.4 Kirchhoff Transformation
220
7.4.1 Transformation of Differential Equations
220
7.4.2 Transformation of Boundary Conditions
221
7.5 Boltzmann Transformation
224
7.6 Combining Boltzmann and Kirchhoff Transformations
226
7.7 Exact Solutions
227
REFERENCES
230
PROBLEMS
230
CHAPTER 8: APPROXIMATE SOLUTIONS: THE INTEGRAL METHOD 236
8.1 Integral Method Approximation: Mathematical Simplification
236
8.2 Procedure
236
8.3 Accuracy of the Integral Method
237
8.4 Application to Cartesian Coordinates
238
8.5 Application to Cylindrical Coordinates
246
8.6 Non-linear Problems
251
8.7 Energy Generation
260
REFERENCES
264
PROBLEMS
264
CHAPTER 9: PERTURBATION SOLUTIONS 269
9.1 Introduction
269
9.2 Solution Procedure
270
9.3 Examples of Perturbation Problems in Conduction
271
9.4 Perturbation Solutions: Examples
273
9.5 Useful Expansions
296
REFERENCES
296
PROBLEMS
297
CHAPTER 10: HEAT TRANSFER IN LIVING TISSUE 302
10.1 Introduction
302
10.2 Vascular Architecture and Blood Flow
302
10.3 Blood Temperature Variation
304
10.4 Mathematical Modeling of Vessels-Tissue Heat Transfer
305
10.4.1 Pennes Bioheat Equation
305
10.4.2 Chen-Holmes Equation
312
10.4.3 Three-Temperature Model for Peripheral Tissue
313
10.4.4 Weinbaum-Jiji Simplified Bioheat Equation for Peripheral Tissue
315
10.4.5 The s-Vessel Tissue Cylinder Model
323
REFERENCES
332
PROBLEMS
334
CHAPTER 11: MICROSCALE CONDUCTION 347
11.1 Introduction
347
11.1.1 Categories of Microscale Phenomena
348
11.1.2 Purpose and Scope of this
Chapter
350
11.2 Understanding the Essential Physics of Thermal Conductivity Using the Kinetic Theory of Gases
351
11.2.1 Determination of Fourier's Law and Expression for Thermal Conductivity
351
11.3 Energy Carriers
355
11.3.1 Ideal Gas: Heat is Conducted by Gas Molecules
355
11.3.2 Metals: Heat is Conducted by Electrons
359
11.3.3 Electrical Insulators and Semiconductors: Heat is Conducted by Phonons (Sound Waves)
361
11.3.4 Radiation: Heat is Carried by Photons (Light Waves)
372
11.4 Thermal Conductivity Reduction by Boundary Scattering: The Classical Size Effect
376
11.4.1 Accounting for Multiple Scattering Mechanisms: Matthiessen's Rule
377
11.4.2 Boundary Scattering for Heat Flow Parallel to Boundaries
379
11.4.3 Boundary Scattering for Heat Flow Perpendicular to Boundaries
387
11.5 Closing Thoughts
391
REFERENCES
394
PROBLEMS
397
APPENDIX A: Ordinary Differential Equations 402
(1) Second Order Differential Equations with Constant Coefficients
402
(2) First Order Ordinary Differential Equations with Variable Coefficients
404
APPENDIX B: Integrals of Bessel Functions 405
APPENDIX C: Values of Bessel Functions 406
APPENDIX D: Fundamental Physical Constants and Material Properties 412
D-1 Fundamental Physical Constants
412
D-2 Unit conversions
412
D-3 Properties of Helium Gas
412
D-4 Properties of Copper at 300 K
412
D-5 Properties of Fused Silica
412
(Amorphous Silicon Dioxide, SiO2) at 300 K
413
D-6 Properties of Silicon
413
D-7 Measured Thermal Conductivity of a 56 nm Diameter Silicon Nanowire at Selected Temperatures
414
D-8 Calculated Thermal Conductivity of Single-Walled Carbon Nanotubes, Selected Values
414
INDEX 416