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El. knyga: Finite Difference Methods in Heat Transfer

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(Coppe - UFRJ, Brazil), (Coppe - UFRJ, Brazil), (Coppe - UFRJ, Brazil), (North Carolina State University, Raleigh, North Carolina, US)
  • Formatas: 600 pages
  • Serija: Heat Transfer
  • Išleidimo metai: 20-Jul-2017
  • Leidėjas: CRC Press Inc
  • Kalba: eng
  • ISBN-13: 9781482243468
Kitos knygos pagal šią temą:
Finite Difference Methods in Heat TransferDidesnis paveikslėlis
  • Formatas: 600 pages
  • Serija: Heat Transfer
  • Išleidimo metai: 20-Jul-2017
  • Leidėjas: CRC Press Inc
  • Kalba: eng
  • ISBN-13: 9781482243468
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Finite Difference Methods in Heat Transfer, Second Edition focuses on finite difference methods and their application to the solution of heat transfer problems. Such methods are based on the discretization of governing equations, initial and boundary conditions, which then replace a continuous partial differential problem by a system of algebraic equations. Finite difference methods are a versatile tool for scientists and for engineers. This updated book serves university students taking graduate-level coursework in heat transfer, as well as being an important reference for researchers and engineering.

Features

Provides a self-contained approach in finite difference methods for students and professionals Covers the use of finite difference methods in convective, conductive, and radiative heat transfer Presents numerical solution techniques to elliptic, parabolic, and hyperbolic problems Includes hybrid analyticalnumerical approaches
Preface xv
Preface-First Edition xix
1 Basic Relations 1(22)
1.1 Classification of Second-Order Partial Differential Equations
2(3)
1.1.1 Physical Significance of Parabolic, Elliptic, and Hyperbolic Systems
4(1)
1.2 Parabolic Systems
5(2)
1.3 Elliptic Systems
7(1)
1.3.1 Steady-State Diffusion
7(1)
1.3.2 Steady-State Advection-Diffusion
7(1)
1.3.3 Fluid Flow
8(1)
1.4 Hyperbolic Systems
8(1)
1.5 Systems of Equations
9(3)
1.5.1 Characterization of System of Equations
10(1)
1.5.2 Wave Equation
11(1)
1.6 Boundary Conditions
12(3)
1.7 Uniqueness of the Solution
15(3)
Problems
18(5)
2 Discrete Approximation of Derivatives 23(42)
2.1 Taylor Series Formulation
24(10)
2.1.1 Finite Difference Approximation of First Derivative
25(2)
2.1.2 Finite Difference Approximation of Second Derivative
27(1)
2.1.3 Differencing via Polynomial Fitting
28(1)
2.1.4 Finite Difference Approximation of Mixed Partial Derivatives
29(2)
2.1.5 Changing the Mesh Size
31(2)
2.1.6 Finite Difference Operators
33(1)
2.2 Control Volume Approach
34(4)
2.3 Boundary and Initial Conditions
38(8)
2.3.1 Discretization of Boundary Conditions with Taylor Series
40(2)
2.3.1.1 Boundary Condition of the First Kind
41(1)
2.3.1.2 Boundary Conditions of the Second and Third Kinds
41(1)
2.3.2 Discretization of Boundary Conditions with Control Volumes
42(4)
2.3.2.1 Boundary Condition of the First Kind
43(1)
2.3.2.2 Boundary Condition of the Second Kind
44(1)
2.3.2.3 Boundary Condition of the Third Kind
44(2)
2.4 Errors Involved in Numerical Solutions
46(3)
2.4.1 Round-Off Errors
46(1)
2.4.2 Truncation Error
46(1)
2.4.3 Discretization Error
47(1)
2.4.4 Total Error
47(1)
2.4.5 Stability
48(1)
2.4.6 Consistency
48(1)
2.5 Verification and Validation
49(9)
2.5.1 Code Verification
50(4)
2.5.2 Solution Verification
54(4)
Problems
58(4)
Notes
62(3)
3 Methods of Solving Systems of Algebraic Equations 65(32)
3.1 Reduction to Algebraic Equations
65(5)
3.2 Direct Methods
70(5)
3.2.1 Gauss Elimination Method
71(1)
3.2.2 Thomas Algorithm
72(3)
3.3 Iterative Methods
75(9)
3.3.1 Gauss-Seidel Iteration
75(4)
3.3.2 Successive Overrelaxation
79(2)
3.3.3 Red-Black Ordering Scheme
81(2)
3.3.4 LU Decomposition with Iterative Improvement
83(1)
3.3.5 Biconjugate Gradient Method
83(1)
3.4 Nonlinear Systems
84(4)
Problems
88(9)
4 One-Dimensional Steady-State Systems 97(32)
4.1 Diffusive Systems
97(19)
4.1.1 Slab
97(1)
4.1.2 Solid Cylinder and Sphere
98(7)
4.1.3 Hollow Cylinder and Sphere
105(5)
4.1.4 Heat Conduction through Fins
110(6)
4.1.4.1 Fin of Uniform Cross Section
112(1)
4.1.4.2 Finite Difference Solution
113(3)
4.2 Diffusive-Advective Systems
116(8)
4.2.1 Stability for Steady-State Systems
118(1)
4.2.2 Finite Volume Method
119(10)
4.2.2.1 Interpolation Functions
121(3)
Problems
124(5)
5 One-Dimensional Transient Systems 129(78)
5.1 Diffusive Systems
129(40)
5.1.1 Simple Explicit Method
130(16)
5.1.1.1 Prescribed Potential at the Boundaries
131(1)
5.1.1.2 Convection Boundary Conditions
132(1)
5.1.1.3 Prescribed Flux Boundary Condition
133(1)
5.1.1.4 Stability Considerations
134(2)
5.1.1.5 Effects of Boundary Conditions on Stability
136(1)
5.1.1.6 Effects of r on Truncation Error
137(1)
5.1.1.7 Fourier Method of Stability Analysis
138(8)
5.1.2 Simple Implicit Method
146(2)
5.1.2.1 Stability Analysis
147(1)
5.1.3 Crank-Nicolson Method
148(4)
5.1.3.1 Prescribed Heat Flux Boundary Condition
151(1)
5.1.4 Combined Method
152(3)
5.1.4.1 Stability of Combined Method
154(1)
5.1.5 Cylindrical and Spherical Symmetry
155(1)
5.1.6 Application of Simple Explicit Method
156(8)
5.1.6.1 Solid Cylinder and Sphere
156(4)
5.1.6.2 Stability of Solution
160(2)
5.1.6.3 Hollow Cylinder and Sphere
162(2)
5.1.7 Application of Simple Implicit Scheme
164(2)
5.1.7.1 Solid Cylinder and Sphere
164(1)
5.1.7.2 Hollow Cylinder and Sphere
165(1)
5.1.8 Application of Crank-Nicolson Method
166(3)
5.2 Advective-Diffusive Systems
169(16)
5.2.1 Purely Advective (Wave) Equation
169(10)
5.2.1.1 Upwind Method
170(2)
5.2.1.2 MacCormack's Method
172(1)
5.2.1.3 Warming and Beam's Method
173(6)
5.2.2 Advection-Diffusion Equation
179(6)
5.2.2.1 Simple Explicit Scheme
179(3)
5.2.2.2 Implicit Finite Volume Method
182(3)
5.3 Hyperbolic Heat Conduction Equation
185(5)
5.3.1 Finite Difference Representation of Hyperbolic Heat Conduction Equation
186(4)
Problems
190(17)
6 Transient Multidimensional Systems 207(46)
6.1 Simple Explicit Method
207(12)
6.1.1 Two-Dimensional Diffusion
208(5)
6.1.2 Two-Dimensional Transient Convection-Diffusion
213(43)
6.1.2.1 FTCS Differencing
213(1)
6.1.2.2 Upwind Differencing
214(1)
6.1.2.3 Control Volume Approach
215(4)
6.2 Combined Method
219(1)
6.3 ADI Method
220(4)
6.4 ADE Method
224(4)
6.5 An Application Related to the Hyperthermia Treatment of Cancer
228(15)
Problems
243(8)
Notes
251(2)
7 Nonlinear Diffusion 253(38)
7.1 Lagging Properties by One Time Step
254(2)
7.2 Use of Three-Time-Level Implicit Scheme
256(5)
7.2.1 Internal Nodes
257(1)
7.2.2 Limiting Case R = 0 for Cylinder and Sphere
258(1)
7.2.3 Boundary Nodes
259(2)
7.3 Linearization
261(3)
7.3.1 Stability Criterion
263(1)
7.4 False Transient
264(4)
7.4.1 Simple Explicit Scheme
266(1)
7.4.2 Simple Implicit Scheme
267(1)
7.4.3 A Set of Diffusion Equations
267(1)
7.5 Applications in Coupled Conduction and Radiation in Participating Media
268(17)
7.5.1 One-Dimensional Problem with Diffusion Approximation
268(4)
7.5.2 Solution of the Three-Dimensional Equation of Radiative Transfer
272(13)
Problems
285(6)
8 Multidimensional Incompressible Laminar Flow 291(48)
8.1 Vorticity-Stream Function Formulation
291(18)
8.1.1 Vorticity and Stream Function
292(3)
8.1.2 Finite Difference Representation of Vorticity-Stream Function Formulation
295(3)
8.1.2.1 Vorticity Transport Equation
296(1)
8.1.2.2 Poisson's Equation for Stream Function
297(1)
8.1.2.3 Poisson's Equation for Pressure
298(1)
8.1.3 Method of Solution for omega and psi
298(3)
8.1.3.1 Solution for a Transient Problem
298(1)
8.1.3.2 Solution for a Steady-State Problem
299(2)
8.1.4 Method of Solution for Pressure
301(1)
8.1.5 Treatment of Boundary Conditions
302(6)
8.1.5.1 Boundary Conditions on Velocity
302(1)
8.1.5.2 Boundary Conditions on pis
303(1)
8.1.5.3 Boundary Condition on omega
304(3)
8.1.5.4 Boundary Conditions on Pressure
307(1)
8.1.5.5 Initial Condition
307(1)
8.1.6 Energy Equation
308(1)
8.2 Primitive Variables Formulation
309(20)
8.2.1 Determination of the Velocity Field: The SIMPLEC Method
314(6)
8.2.2 Treatment of Boundary Conditions
320(19)
8.2.2.1 Pressure
321(4)
8.2.2.2 Momentum and Energy Equations
325(4)
8.3 Two-Dimensional Steady Laminar Boundary Layer Flow
329(3)
Problems
332(7)
9 Compressible Flow 339(22)
9.1 Quasi-One-Dimensional Compressible Flow
339(15)
9.1.1 Solution with MacCormack's Method
342(6)
9.1.2 Solution with WAF-TVD Method
348(6)
9.2 Two-Dimensional Compressible Flow
354(4)
Problems
358(3)
10 Phase Change Problems 361(50)
10.1 Mathematical Formulation of Phase Change Problems
363(5)
10.1.1 Interface Condition
364(1)
10.1.2 Generalization to Multidimensions
365(1)
10.1.3 Dimensionless Variables
366(1)
10.1.4 Mathematical Formulation
367(1)
10.2 Variable Time Step Approach for Single-Phase Solidification
368(6)
10.2.1 Finite Difference Approximation
369(2)
10.2.1.1 Differential Equation
370(1)
10.2.1.2 Boundary Condition at x = 0
370(1)
10.2.1.3 Interface Conditions
371(1)
10.2.2 Determination of Time Steps
371(3)
10.2.2.1 Starting Time Step Deltat0
371(1)
10.2.2.2 Time Step Deltat1
371(1)
10.2.2.3 Time Step Deltatn
372(2)
10.3 Variable Time Step Approach for Two-Phase Solidification
374(9)
10.3.1 Finite Difference Approximation
376(1)
10.3.1.1 Equation for the Solid Phase
376(1)
10.3.1.2 Boundary Condition at x = 0
376(1)
10.3.1.3 Equation for the Liquid Phase
377(1)
10.3.1.4 Interface Conditions
377(1)
10.3.2 Determination of Time Steps
377(6)
10.3.2.1 Starting Time Step Ato
378(1)
10.3.2.2 Time Step Deltat1
379(1)
10.3.2.3 Time Steps Deltatn, (2 < or = to n < or = to N - 4)
380(1)
10.3.2.4 Time Step DeltatN-3
380(1)
10.3.2.5 Time Step DeltatN-2
381(1)
10.3.2.6 Time Step DeltatN-1
382(1)
10.4 Enthalpy Method
383(9)
10.4.1 Explicit Enthalpy Method: Phase Change with Single Melting Temperature
385(4)
10.4.1.1 Algorithm for Explicit Method
386(1)
10.4.1.2 Interpretation of Enthalpy Results
387(1)
10.4.1.3 Improved Algorithm for Explicit Method
388(1)
10.4.2 Implicit Enthalpy Method: Phase Change with Single Melting Temperature
389(3)
10.4.2.1 Algorithm for Implicit Method
390(2)
10.4.3 Explicit Enthalpy Method: Phase Change over a Temperature Range
392(1)
10.5 Phase Change Model for Convective-Diffusive Problems
392(17)
10.5.1 Model for the Passive Scalar Transport Equation
395(3)
10.5.2 Model for the Energy Equation
398(11)
Problems
409(2)
11 Numerical Grid Generation 411(66)
11.1 Coordinate Transformation Relations
413(6)
11.1.1 Gradient
415(1)
11.1.2 Divergence
415(1)
11.1.3 Laplacian
416(1)
11.1.4 Normal Derivatives
416(1)
11.1.5 Tangential Derivatives
417(2)
11.2 Basic Ideas in Simple Transformations
419(3)
11.3 Basic Ideas in Numerical Grid Generation and Mapping
422(7)
11.4 Boundary Value Problem of Numerical Grid Generation
429(7)
11.5 Finite Difference Representation of Boundary Value Problem of Numerical Grid Generation
436(3)
11.6 Steady-State Heat Conduction in Irregular Geometry
439(6)
11.7 Steady-State Laminar Free Convection in Irregular Enclosures-Vorticity-Stream Function Formulation
445(12)
11.7.1 The Nusselt Number
454(1)
11.7.2 Results
455(2)
11.8 Transient Laminar Free Convection in Irregular Enclosures-Primitive Variables Formulation
457(4)
11.9 Computational Aspects for the Evaluation of Metrics
461(8)
11.9.1 One-Dimensional Advection-Diffusion Equation
461(4)
11.9.2 Two-Dimensional Heat Conduction in a Hollow Sphere
465(4)
Problems
469(4)
Notes
473(4)
12 Hybrid Numerical-Analytical Solutions 477(50)
12.1 Combining Finite Differences and Integral Transforms
479(10)
12.1.1 The Hybrid Approach
480(1)
12.1.2 Hybrid Approach Application: Transient Forced Convection in Channels
481(8)
12.2 Unified Integral Transforms
489(16)
12.2.1 Total Transformation
491(2)
12.2.2 Partial Transformation
493(4)
12.2.3 Computational Algorithm
497(4)
12.2.4 Test Case
501(4)
12.3 Convective Eigenvalue Problem
505(12)
Problems
517(10)
Appendix A. Subroutine Gauss 527(2)
Appendix B. Subroutine Trisol 529(2)
Appendix C. Subroutine SOR 531(2)
Appendix D. Subroutine BICGM2 533(8)
Appendix E. Program to Solve Example 10.1 541(4)
Bibliography 545(20)
Index 565
Helcio Rangel Barreto Orlande was born in Rio de Janeiro on March 9, 1965. He obtained his B.S. in Mechanical Engineering from the Federal University of Rio de Janeiro (UFRJ) in 1987 and his M.S. in Mechanical Engineering from the same University in 1989. After obtaining his Ph.D. in Mechanical Engineering in 1993 from North Carolina State University, he joined the Department of Mechanical Engineering of UFRJ, where he was the department head during 2006 and 2007. His research areas of interest include the solution of inverse heat and mass transfer problems, as well as the use of numerical, analytical and hybrid numerical-analytical methods of solution of direct heat and mass transfer problems. He is the co-author of 4 books and more than 280 papers in major journals and conferences. He is a member of the Scientific Council of the International Centre for Heat and Mass Transfer and a Delegate in the Assembly for International Heat Transfer Conferences. He serves as an Associate Editor for the journals Heat Transfer Engineering, Inverse Problems in Science and Engineering and High Temperatures High Pressures.



Marcelo J. Colaco is an Associate Professor in the Department of Mechanical Engineering at the Federal University of Rio de Janeiro - UFRJ, Brazil. He received his Ph.D. from UFRJ in 2001. He then spent 15 months as a postdoctoral fellow at the University of Texas at Arlington working on optimization algorithms, inverse problems in heat transfer, and electro-magneto-hydrodynamics including solidification. Afterwards, he spent one year performing research at UFRJ/COPPE on a prestigious CNPq grant as an Instructor and a researcher. From there, he joined Brazilian Military Institute of Engineering where he was teaching and performing research for five years in numerical algorithms for analysis of MHD flows, EHD flows, solidification problems, optimization algorithms utilizing response surfaces, and fuel research. For the past years, he has been teaching and performing research in Brazil and helping to build a large and unique fuels and lubricants research center at the UFRJ. He is the co-author of some book-chapters, and more than 200 papers in major journals and conferences. He was the recipient of the Young Scientist Award, given by state of Rio de Janeiro, in 2007 and 2009 and the Scientist Award in 2013 and 2015. Prof. Colaco is also member of the Scientific Council of the International Centre for Heat and Mass Transfer.
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