Finite element simulation of heat transfer:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
ISTE [u.a.]
2008
|
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 279 S. Ill., graph. Darst. |
| ISBN: | 9781847040176 9781848210530 |
Internformat
MARC
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|---|---|---|---|
| 001 | BV041279382 | ||
| 003 | DE-604 | ||
| 005 | 20131015 | ||
| 007 | t | ||
| 008 | 130919s2008 ad|| |||| 00||| eng d | ||
| 020 | |a 9781847040176 |9 978-1-84704-017-6 | ||
| 020 | |a 9781848210530 |9 978-1-84821-053-0 | ||
| 024 | 3 | |a 9781848210530 | |
| 035 | |a (OCoLC)862802578 | ||
| 035 | |a (DE-599)BSZ276052706 | ||
| 040 | |a DE-604 |b ger | ||
| 041 | 0 | |a eng | |
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| 082 | 0 | |a 621.402/2015118 | |
| 084 | |a SK 910 |0 (DE-625)143270: |2 rvk | ||
| 084 | |a UG 2500 |0 (DE-625)145618: |2 rvk | ||
| 100 | 1 | |a Bergheau, Jean-Michel |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Simulation numérique des transferts thermiques par éléments finis |
| 245 | 1 | 0 | |a Finite element simulation of heat transfer |c Jean-Michel Bergheau ; Roland Fortunier |
| 264 | 1 | |a London |b ISTE [u.a.] |c 2008 | |
| 300 | |a 279 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 700 | 1 | |a Fortunier, Roland |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026252847&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-026252847 | ||
Datensatz im Suchindex
| _version_ | 1804150749709467648 |
|---|---|
| adam_text | Table of Contents
Introduction 11
Part 1. Steady State Conduction 17
Chapter 1. Problem Formulation 21
1.1. Physical modeling 21
1.1.1. Thermal equilibrium equation 21
1.1.2. Fourier law 22
1.1.3. Boundary conditions 23
1.2. Mathematical analysis 24
1.2.1. Weighted residual method 25
1.2.2. Weak integral formulation 27
1.3. Working example 30
1.3.1. Physical modeling 30
1.3.2. Direct methods 32
1.3.2.1. Analytical integration 32
1.3.2.2. The finite difference method 33
1.3.3. Collocation methods 34
1.3.3.1. Point collocation 35
1.3.3.2. Sub-domain collocation 36
1.3.4. Galerkin method 37
1.3.4.1. Polynomial functions 37
1.3.4.2. Piecewise linear functions 39
Chapter 2. The Finite Element Method 43
2.1. Finite element approximation 43
2.1.1. Mesh 43
2.1.2. Nodal approximation 46
2.2. Discrete problem formulation 48
6 Finite Element Simulation of Heat Transfer
2.2.1. Element quantities 49
2.2.2. Assembly 51
2.3. Solution 53
2.3.1. Application of temperature boundary conditions 53
2.3.2. Linear system solution 56
2.3.2.1. Direct methods 58
2.3.2.2. Iterative methods 60
2.3.3. Storing the linear system matrix 62
2.3.4. Analysis of results 63
2.3.4.1. Smoothing the heat flux density 64
2.3.4.2. Result accuracy 66
2.4. Working example 68
2.4.1. Finite element approximation 70
2.4.1.1. Mesh 70
2.4.1.2. Nodal approximation 71
2.4.2. Discrete problem formulation 72
2.4.2.1. Element quantities 72
2.4.2.2. Assembly 74
2.4.3. Solution 75
2.4.3.1. Application of boundary conditions 75
2.4.3.2. Solution 77
Chapter 3. Isoparametric Finite Elements 79
3.1. Definitions 79
3.1.1. Reference element 79
3.1.1.1. Triangular element with linear transformation functions ... 81
3.1.1.2. Quadrangle element with linear transformation functions . . 82
3.1.1.3. Quadrangle element with quadratic transformation functions 84
3.1.2. Isoparametric elements 85
3.1.3. Interpolation function properties 89
3.2. Calculation of element quantities 90
3.2.1. Expression in the reference frame 91
3.2.2. Gaussian quadrature 93
3.2.2.1. ID numerical integration 94
3.2.2.2. 2D and 3D numerical integration 97
3.3. Some finite elements 99
PART 2. Transient State, Non-linearities, Transport Phenomena 101
Chapter 4. Transient Heat Conduction 105
4.1. Problem formulation 105
4.1.1. The continuous problem 105
4.1.2. Finite element approximation 107
4.1.3. Linear case 109
Table of Contents 7
4.2. Time integration Ill
4.2.1. Modal method Ill
4.2.1.1. Determining the modal basis 112
4.2.1.2. Projection on the modal basis 114
4.2.2. Direct time integration 115
4.2.3. Accuracy and stability of a direct integration algorithm 119
4.2.3.1. Accuracy 120
4.2.3.2. Stability 121
4.2.3.3. Simplified analysis of the stability condition 122
4.2.4. Practical complementary rules 124
4.2.4.1. Space oscillations during thermal shock simulation 124
4.2.4.2. Discrete maximum principle 128
4.2.4.3. Initial temperatures during thermal contact simulation . ... 130
4.3. Working example 135
4.3.1. Physical modeling and approximation 135
4.3.2. Numerical applications 139
Chapter 5. Non-linearities 143
5.1. Formulation and solution techniques 143
5.1.1. Formulation 143
5.1.2. Non-linear equation system solution methods 144
5.1.2.1. Newton-Raphson method 147
5.1.2.2. Substitution method 149
5.1.2.3. Quasi-Newton methods 150
5.1.3. Line search method 152
5.2. Traditional non-linearities 153
5.2.1. Physical properties 153
5.2.2. Flux or volumetric heat source boundary conditions 155
5.2.3. Modeling state changes 157
5.2.3.1. Equivalent specific heat method 158
5.2.3.2. Enthalpy solution method 160
5.3. A temperature-enthalpy formulation 162
5.3.1. Mathematical formulation 163
5.3.2. Example 166
Chapter 6. Transport Phenomena 169
6.1. Highlighting instabilities 169
6.1.1. Thermal balance 169
6.1.2. Treating a simple case 171
6.2. Resolution techniques 174
6.2.1. Upwind technique 175
6.2.2. SUPG method 177
6.2.3. 2D and 3D Petrov-Galerkin formulation 180
8 Finite Element Simulation of Heat Transfer
Part 3. Coupled Phenomena 183
Chapter 7. Radiation Exchanges in a Chamber 189
7.1. Modeling radiative heat exchanges in a cavity 189
7.1.1. Posing the problem 190
7.1.2. Calculation of view factors 194
7.1.3. Diffusion-radiation coupling 197
7.1.3.1. Tangent matrix 198
7.1.3.2. Substitution matrix 199
7.2. Examples 200
7.2.1. Radiation between two walls 200
7.2.2. Cylinder quenching 203
Chapter 8. Fluid-Structure Coupling in a Pipe 207
8.1. Modeling the fluid 207
8.1.1. Physical model and mathematical formulation 207
8.1.2. Modeling the coupling 210
8.2. Example 212
8.2.1. Physical and geometric modeling 212
8.2.2. Results 213
Chapter 9. Thermometallurgical Coupling 215
9.1. Modeling phase changes 215
9.1.1. Rate of phase changes 215
9.1.1.1. Avrami kinetics 215
9.1.1.2. Martensitic kinetics 217
9.1.2. Numerical integration 217
9.1.3. The case of several phase changes 220
9.1.4. Modeling the coupling 221
9.2. Examples 222
9.2.1. Phase transformation diagrams 223
9.2.2. Steel quenching 227
Chapter 10. Thermochemical Coupling 231
10.1. Finite element simulation of simultaneous diffusion and precipitation 231
10.1.1. Governing equations 232
10.1.2. Finite element formulation 234
10.2. Calculation of precipitation 236
10.2.1. Mathematical formulation 236
10.2.2. Numerical scheme 238
10.3. Examples 239
10.3.1. Calculation of a phase diagram 239
10.3.2. Carbon diffusion in a titanium steel 240
Table of Contents 9
Chapter 11. Electrothermal Coupling 243
11.1. Electrokinetic modeling 243
11.1.1. Weak formulation 243
11.1.2. Modeling the coupling 244
11.1.3. Solving the coupled problem 246
11.2. Resistance welding 248
11.2.1. Implementing the model 249
11.2.2. Results 251
Chapter 12. Magnetothcrmal Coupling 253
12.1. Introduction 253
12.2. Magnetic vector potential formulation for magnetodynamics 254
12.3. Coupled finite element-boundary element method 257
12.3.1. Finite element formulation 259
12.3.2. Boundary element formulation 260
12.3.3. FEM-BEM coupling 261
12.4. A harmonic balance method for the magnetodynamic problem .... 261
12.5. Coupling magnetodynamics with heat transfer 263
12.5.1. Iterative coupling 263
12.5.2. A direct method for magnetothermal coupling 265
12.6. Application: induction hardening of a steel cylinder 266
Bibliography 269
Index 277
|
| any_adam_object | 1 |
| author | Bergheau, Jean-Michel Fortunier, Roland |
| author_facet | Bergheau, Jean-Michel Fortunier, Roland |
| author_role | aut aut |
| author_sort | Bergheau, Jean-Michel |
| author_variant | j m b jmb r f rf |
| building | Verbundindex |
| bvnumber | BV041279382 |
| classification_rvk | SK 910 UG 2500 |
| ctrlnum | (OCoLC)862802578 (DE-599)BSZ276052706 |
| dewey-full | 621.402/2015118 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 621 - Applied physics |
| dewey-raw | 621.402/2015118 |
| dewey-search | 621.402/2015118 |
| dewey-sort | 3621.402 72015118 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Physik Mathematik Energietechnik |
| format | Book |
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| id | DE-604.BV041279382 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:43:52Z |
| institution | BVB |
| isbn | 9781847040176 9781848210530 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026252847 |
| oclc_num | 862802578 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | 279 S. Ill., graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | ISTE [u.a.] |
| record_format | marc |
| spelling | Bergheau, Jean-Michel Verfasser aut Simulation numérique des transferts thermiques par éléments finis Finite element simulation of heat transfer Jean-Michel Bergheau ; Roland Fortunier London ISTE [u.a.] 2008 279 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Fortunier, Roland Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026252847&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bergheau, Jean-Michel Fortunier, Roland Finite element simulation of heat transfer |
| title | Finite element simulation of heat transfer |
| title_alt | Simulation numérique des transferts thermiques par éléments finis |
| title_auth | Finite element simulation of heat transfer |
| title_exact_search | Finite element simulation of heat transfer |
| title_full | Finite element simulation of heat transfer Jean-Michel Bergheau ; Roland Fortunier |
| title_fullStr | Finite element simulation of heat transfer Jean-Michel Bergheau ; Roland Fortunier |
| title_full_unstemmed | Finite element simulation of heat transfer Jean-Michel Bergheau ; Roland Fortunier |
| title_short | Finite element simulation of heat transfer |
| title_sort | finite element simulation of heat transfer |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026252847&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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