Fundamentals of the finite element method for heat and mass transfer:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester, West Sussex
Wiley
2016
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| Ausgabe: | Second edition |
| Schriftenreihe: | Wiley series in computational mechanics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | xiii, 450 Seiten Illustrationen |
| ISBN: | 9780470756256 |
Internformat
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| 245 | 1 | 0 | |a Fundamentals of the finite element method for heat and mass transfer |c P. Nithiarasu (Zienkiewicz Centre for Comutational Engineering, College of Engineering, Swansea University, UK), R.W. Lewis (Zienkiewicz Centre for Comutational Engineering, College of Engineering, Swansea University, UK), K.N. Seetharamu (Department of Mechanical Engineering, PESIT, Bangalore, Karnataka, India) |
| 250 | |a Second edition | ||
| 264 | 1 | |a Chichester, West Sussex |b Wiley |c 2016 | |
| 300 | |a xiii, 450 Seiten |b Illustrationen | ||
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Datensatz im Suchindex
| _version_ | 1804151360527007744 |
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| adam_text | Contents
p
Preface to the Second Edition xii
Series Editor’s Preface xiv
1 Introduction 1
1.1 Importance of Heat and Mass Transfer.................................... 1
1.2 Heat Transfer Modes..................................................... 2
1.3 The Laws of Heat Transfer............................................... 3
1.4 Mathematical Formulation of Some Heat Transfer Problems................. 5
1.4.1 Heat Transfer from a Plate Exposed to Solar Heat Flux....... 5
1.4.2 Incandescent Lamp............................................... 7
1.4.3 Systems with a Relative Motion and Internal Heat Generation. 8
1.5 Heat Conduction Equation............................................... 10
1.6 Mass Transfer.......................................................... 13
1.7 Boundary and Initial Conditions........................................ 13
1.8 S olution Methodology.................................................. 15
1.9 Summary................................................................ 15
1.10 Exercises.............................................................. 16
References................................................................... 17
2 Some Basic Discrete Systems 19
2.1 Introduction.......................................................... 19
2.2 Steady-state Problems.................................................. 20
2.2.1 Heat Flow in a Composite Slab.................................. 20
2.2.2 Fluid Flow Network............................................. 23
2.2.3 Heat Transfer in Heat Sinks.................................... 26
2.3 Transient Heat Transfer Problem........................................ 28
2.4 Summary................................................................ 31
2.5 Exercises............................................................. 31
References................................................................. 36 3
3 The Finite Element Method 39
3.1 Introduction........................................................... 39
3.2 Elements and Shape Functions........................................... 42
VI
CONTENTS
3.2.1 One-dimensional Linear Element................................. 43
3.2.2 One-dimensional Quadratic Element.............................. 46
3.2.3 Two-dimensional Linear Triangular Element...................... 49
3.2.4 Area Coordinates............................................... 53
3.2.5 Quadratic Triangular Element................................. 55
3.2.6 Two-dimensional Quadrilateral Elements......................... 58
3.2.7 Isoparametric Elements......................................... 63
3.2.8 Three-dimensional Elements..................................... 72
3.3 Formulation (Element Characteristics)................................. 76
3.3.1 Ritz Method (Heat Balance Integral Method - Goodman’s Method) 78
3.3.2 Rayleigh-Ritz Method (Variational Method)...................... 79
3.3.3 The Method of Weighted Residuals.............................. 82
3.3.4 Galerkin Finite Element Method................................. 86
3.4 Formulation for the Heat Conduction Equation........................... 89
3.4.1 Variational Approach........................................... 90
3.4.2 The Galerkin Method...................................... 93
3.5 Requirements for Interpolation Functions............................... 94
3.6 Summary............................................................... 100
3.7 Exercises............................................................. 100
References................................................................ 102
4 Steady-State Heat Conduction in One-dimension 105
4.1 Introduction.......................................................... 105
4.2 Plane Walls......................................................... 105
4.2.1 Homogeneous Wall.............................................. 105
4.2.2 Composite Wall............................................. 107
4.2.3 Finite Element Discretization................................. 108
4.2.4 Wall with Varying Cross-sectional Area........................ 110
4.2.5 Plane Wall with a Heat Source: Solution by Linear Elements.. 112
4.2.6 Plane Wall with Heat Source: Solution by Quadratic Elements- 115
4.2.7 Plane Wall with a Heat Source: Solution by Modified Quadratic
Equations (Static Condensation).............................. 117
4.3 Radial Heat Conduction in a Cylinder Wall............................. 118
4.4 Solid Cylinder with Heat Source....................................... 120
4.5 Conduction - Convection Systems....................................... 123
4.6 Summary............................................................... 126
4.7 Exercises............................................................. 127
References.................................................................. 129
5 Steady-state Heat Conduction in Multi-dimensions 131
5.1 Introduction......................................................... 131
5.2 Two-dimensional Plane Problems........................................ 132
5.2.1 Triangular Elements........................................... 132
5.3 Rectangular Elements................................................. 142
CONTENTS vii
5.4 Plate with Variable Thickness.......................................... 145
5.5 Three-dimensional Problems............................................ 146
5.6 Axisymmetric Problems.................................................. 148
5.6.1 Galerkin Method for Linear Triangular Axisymmetric Elements ... 150
5.7 Summary................................................................ 153
5.8 Exercises.............................................................. 153
References................................................................... 155
6 Transient Heat Conduction Analysis 157
6.1 Introduction........................................................... 157
6.2 Lumped Heat Capacity System........................................... 157
6.3 Numerical Solution..................................................... 159
6.3.1 Transient Governing Equations and Boundary and Initial
Conditions..................................................... 159
6.3.2 The Galerkin Method............................................ 160
6.4 One-dimensional Transient State Problem................................ 162
6.4.1 Time Discretization-Finite Difference Method (FDM)............. 163
6.4.2 Time Discretization-Finite Element Method (FEM)................ 168
6.5 Stability.............................................................. 169
6.6 Multi-dimensional Transient Heat Conduction............................ 169
6.7 Summary................................................................ 171
6.8 Exercises.............................................................. 171
References................................................................... 173
7 Laminar Convection Heat Transfer 175
7.1 Introduction........................................................... 175
7.1.1 Types of Fluid Motion Assisted Heat Transport.................. 176
7.2 Navier-Stokes Equations................................................ 177
7.2.1 Conservation of Mass or Continuity Equation.................... 177
7.2.2 Conservation of Momentum..................................... 179
7.2.3 Energy Equation................................................ 183
7.3 Nondimensional Form of the Governing Equations......................... 184
7.4 The Transient Convection-Diffusion Problem............................. 188
7.4.1 Finite Element Solution to the Convection-Diffusion Equation .... 189
7.4.2 A Simple Characteristic Galerkin Method for Convection-Diffusion
Equation...................................................... 191
7.4.3 Extension to Multi-dimensions.................................. 197
7.5 Stability Conditions................................................... 202
7.6 Characteristic Based Split (CBS) Scheme................................ 202
7.6.1 Spatial Discretization......................................... 208
7.6.2 Time-step Calculation.......................................... 211
7.6.3 Boundary and Initial Conditions................................ 211
7.6.4 Steady and Transient Solution Methods.......................... 213
7.7 Artificial Compressibility Scheme.................................... 214
CONTENTS
viii
7.8 Nusselt Number, Drag and Stream Function............................. 215
7.8.1 Nusselt Number............................................... 215
7.8.2 Drag Calculation............................................. 216
7.8.3 Stream Function.............................................. 217
7.9 Mesh Convergence..................................................... 218
7.10 Laminar Isothermal Flow.............................................. 219
7.11 Laminar Nonisothermal Flow........................................... 231
7.11.1 Forced Convection Heat Transfer.............................. 232
7.11.2 Buoyancy-driven Convection Heat Transfer..................... 238
7.11.3 Mixed Convection Heat Transfer............................... 240
7.12 Extension to Axisymmetric Problems................................... 243
7.13 Summary.............................................................. 246
7.14 Exercises............................................................ 247
References................................................................. 249
8 Turbulent Flow and Heat Transfer 253
8.1 Introduction........................................................ 253
8.1.1 Time Averaging............................................... 254
8.1.2 Relationship between k, e, vT and aT......................... 256
8.2 Treatment of Turbulent Flows......................................... 257
8.2.1 Reynolds Averaged Navier-Stokes (RANS)....................... 257
8.2.2 One-equation Models........................................ 258
8.2.3 Two-equation Models.......................................... 259
8.2.4 Nondimensional Form of the Governing Equations............... 260
8.3 Solution Procedure................................................... 262
8.4 Forced Convective Flow and Heat Transfer............................. 263
8.5 Buoyancy-driven Flow................................................. 272
8.6 Other Methods for Turbulence......................................... 275
8.6.1 Large Eddy Simulation (LES).................................. 275
8.7 Detached Eddy Simulation (DES) and Monotonically Integrated LES
(MILES).............................................................. 278
8.8 Direct Numerical Simulation (DNS).................................... 278
8.9 Summary ............................................................. 279
References................................................................. 279
9 Heat Exchangers 281
9.1 Introduction......................................................... 281
9.2 LMTD and Effectiveness-NTU Methods................................... 283
9.2.1 LMTD Method.................................................. 283
9.2.2 Effectiveness - NTU Method................................... 285
9.3 Computational Approaches............................................. 286
9.3.1 System Analysis.............................................. 286
9.3.2 Finite Element Solution to Differential Equations............ 289
9.4 Analysis of Heat Exchanger Passages.................................. 289
CONTENTS ix
9.5 Challenges............................................................ 297
9.6 Summary............................................................... 299
References................................................................... 299
10 Mass Transfer 301
10.1 Introduction.......................................................... 301
10.2 Conservation of Species............................................... 302
10.2.1 Nondimensional Form........................................... 304
10.2.2 Buoyancy-driven Mass Transfer................................. 305
10.2.3 Double-diffusive Natural Convection........................... 306
10.3 Numerical Solution.................................................... 307
10.4 Turbulent Mass Transport.............................................. 317
10.5 Summary............................................................. 319
References.................................................................. 319
11 Convection Heat and Mass Transfer in Porous Media 321
11.1 Introduction.......................................................... 321
11.2 Generalized Porous Medium Flow Approach .............................. 324
11.2.1 Nondimensional Scales......................................... 327
11.2.2 Limiting Cases.............................................. 329
1! .3 Discretization Procedure.............................................. 329
11.3.1 Temporal Discretization....................................... 330
11.3.2 Spatial Discretization........................................ 331
11.3.3 Semi- and Quasi-Implicit Forms................................ 332
11.4 Nonisothermal Flows................................................... 333
11.5 Porous Medium-Fluid Interface......................................... 342
11.6 Double-diffusive Convection........................................... 347
11.7 Summary............................................................. 349
References.................................................................. 349
12 Solidification 353
12.1 Introduction.......................................................... 353
12.2 Solidification via Heat Conduction.................................... 354
12.2.1 The Governing Equations....................................... 354
12.2.2 Enthalpy Formulation.......................................... 354
12.3 Convection During Solidification...................................... 356
12.3.1 Governing Equations and Discretization........................ 358
12.4 Summary............................................................... 363
References............................................................... 364
13 Heat and Mass Transfer in Fuel Cells 365
13.1 Introduction.......................................................... 365
13.1.1 Fuel Cell Types............................................... 367
13.2 Mathematical Model.................................................... 368
X
CONTENTS
13.2.1 Anodic and Cathodic Compartments............................. 371
13.2.2 Electrolyte Compartment...................................... 373
13.3 Numerical Solution Algorithms........................................ 373
13.3.1 Finite Element Modeling of SOFC ............................ 374
13.4 Summary.............................................................. 378
References................................................................ 378
14 An Introduction to Mesh Generation and Adaptive Finite Element Methods 379
14.1 Introduction..................................................... 379
14.2 Mesh Generation...................................................... 380
14.2.1 Advancing Front Technique (AFT).............................. 381
14.2.2 Delaunay Triangulation....................................... 382
14.2.3 Mesh Cosmetics............................................... 387
14.3 Boundary Grid Generation............................................. 390
14.3.1 Boundary Grid for a Planar Domain............................ 390
14.3.2 NURBS Patches.............................................. 391
14.4 Adaptive Refinement Methods.......................................... 392
14.5 Simple Error Estimation and Mesh Refinement.......................... 393
14.5.1 Heat Conduction.............................................. 394
14.6 Interpolation Error Based Refinement................................. 397
14.6.1 Anisotropic Adaptive Procedure............................... 398
14.6.2 Choice of Variables and Adaptivity........................... 399
14.7 Summary.............................................................. 401
References................................................................. 402
15 Implementation of Computer Code 405
15.1 Introduction......................................................... 405
15.2 Preprocessing........................................................ 406
15.2.1 Mesh Generation.............................................. 406
15.2.2 Linear Triangular Element Data............................. 408
15.2.3 Element Area Calculation..................................... 409
15.2.4 Shape Functions and Their Derivatives........................ 410
15.2.5 Boundary Normal Calculation.................................. 411
15.2.6 Mass Matrix and Mass Lumping................................. 412
15.2.7 Implicit Pressure or Heat Conduction Matrix.................. 414
15.3 Main Unit............................................................ 416
15.3.1 Time-step Calculation........................................ 416
15.3.2 Element Loop and Assembly.................................... 419
15.3.3 Updating Solution............................................ 420
15.3.4 Boundary Conditions.......................................... 421
15.3.5 Monitoring Steady State...................................... 422
15.4 Postprocessing....................................................... 423
15.4.1 Interpolation of Data........................................ 424
15.5 Summary............................................................ 424
References............................................................... 424
CONTENTS xi
A Gaussian Elimination 425
Reference.............................................................. 426
B Green’s Lemma 427
C Integration Formulae 429
C. 1 Linear Triangles.................................................. 429
C.2 Linear Tetrahedron................................................. 429
D Finite Element Assembly Procedure 431
E Simplified Form of the Navier-Stokes Equations 435
F Calculating Nodal Values of Second Derivatives 437
Index
439
Fundamentals of the Finite Element
Method for Heat and Mass Transfer
Second Edition
P. Nithiarasu and R. W. Lewis
Zienkiewicz Centre for Computational Engineering, College of Engineering, Swansea University, UK
K. N. Seetharamu
Department of Mechanical Engineering, PESIT, Bangalore, Karnataka, India
Fundamentals of the Finite Element Method for Heat and Mass Transfer, Second Edition, is a
comprehensively updated new edition and is a unique book on the application of the finite element
method to heat and mass transfer.
The early chapters are designed to teach beginners the basics of the finite element method and heat
transfer. The latter chapters then progressively take the reader through research and advanced
topics. The early part of the book provides a fundamental knowledge to tackle the applications
introduced at the latter stage of the book. Such applications include different heat transfer
mechanisms, heat and mass transfer in porous media, turbulent heat transfer, and transport in heat
exchangers and fuel cells. A beginner will be able to appreciate the detailed formulations of different
problems and demonstration of their use via numerical examples. Both students and lecturers will
benefit from the large number of numerical examples and exercises provided. Researchers who have
some knowledge of the finite element method and heat transfer will benefit from more advanced
topics such as turbulent heat transfer, porous media, fuel cells, heat exchangers, solidification, mesh
generation, and computer implementation.
Key features:
Addresses fundamentals, applications, and computer implementation
Includes a large number of worked examples and exercises
Fills the gap between learning and research
Fundamentals of the Finite Element Method for Heat and Mass Transfer, Second Edition,
is a comprehensive textbook for senior undergraduates, postgraduates, lecturers, and early career
researchers in the areas of the finite element method for heat and mass transfer.
Educational computer codes are also freely available to download, modify, and use at
www.zetacomp.com
ISBN 978-0-470-75625-6
|
| any_adam_object | 1 |
| author | Nithiarasu, Perumal Lewis, Roland W. Seetharamu, Kankanhalli N. |
| author_GND | (DE-588)1046207563 (DE-588)1055769390 |
| author_facet | Nithiarasu, Perumal Lewis, Roland W. Seetharamu, Kankanhalli N. |
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| building | Verbundindex |
| bvnumber | BV041294543 |
| classification_rvk | SK 910 UF 4000 UG 2500 |
| classification_tum | MTA 700f MTA 009f |
| ctrlnum | (OCoLC)939391947 (DE-599)HBZHT016415817 |
| dewey-full | 530.155353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.155353 |
| dewey-search | 530.155353 |
| dewey-sort | 3530.155353 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| edition | Second edition |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV041294543 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:53:35Z |
| institution | BVB |
| isbn | 9780470756256 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026743460 |
| oclc_num | 939391947 |
| open_access_boolean | |
| owner | DE-703 DE-91G DE-BY-TUM DE-29T |
| owner_facet | DE-703 DE-91G DE-BY-TUM DE-29T |
| physical | xiii, 450 Seiten Illustrationen |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in computational mechanics |
| spelling | Nithiarasu, Perumal Verfasser (DE-588)1046207563 aut Fundamentals of the finite element method for heat and mass transfer P. Nithiarasu (Zienkiewicz Centre for Comutational Engineering, College of Engineering, Swansea University, UK), R.W. Lewis (Zienkiewicz Centre for Comutational Engineering, College of Engineering, Swansea University, UK), K.N. Seetharamu (Department of Mechanical Engineering, PESIT, Bangalore, Karnataka, India) Second edition Chichester, West Sussex Wiley 2016 xiii, 450 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Wiley series in computational mechanics Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Wärmeübertragung (DE-588)4064211-2 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Wärmeübertragung (DE-588)4064211-2 s Finite-Elemente-Methode (DE-588)4017233-8 s DE-604 Strömungsmechanik (DE-588)4077970-1 s Lewis, Roland W. Verfasser (DE-588)1055769390 aut Seetharamu, Kankanhalli N. Verfasser aut Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026743460&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026743460&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Nithiarasu, Perumal Lewis, Roland W. Seetharamu, Kankanhalli N. Fundamentals of the finite element method for heat and mass transfer Strömungsmechanik (DE-588)4077970-1 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Wärmeübertragung (DE-588)4064211-2 gnd |
| subject_GND | (DE-588)4077970-1 (DE-588)4017233-8 (DE-588)4064211-2 (DE-588)4123623-3 |
| title | Fundamentals of the finite element method for heat and mass transfer |
| title_auth | Fundamentals of the finite element method for heat and mass transfer |
| title_exact_search | Fundamentals of the finite element method for heat and mass transfer |
| title_full | Fundamentals of the finite element method for heat and mass transfer P. Nithiarasu (Zienkiewicz Centre for Comutational Engineering, College of Engineering, Swansea University, UK), R.W. Lewis (Zienkiewicz Centre for Comutational Engineering, College of Engineering, Swansea University, UK), K.N. Seetharamu (Department of Mechanical Engineering, PESIT, Bangalore, Karnataka, India) |
| title_fullStr | Fundamentals of the finite element method for heat and mass transfer P. Nithiarasu (Zienkiewicz Centre for Comutational Engineering, College of Engineering, Swansea University, UK), R.W. Lewis (Zienkiewicz Centre for Comutational Engineering, College of Engineering, Swansea University, UK), K.N. Seetharamu (Department of Mechanical Engineering, PESIT, Bangalore, Karnataka, India) |
| title_full_unstemmed | Fundamentals of the finite element method for heat and mass transfer P. Nithiarasu (Zienkiewicz Centre for Comutational Engineering, College of Engineering, Swansea University, UK), R.W. Lewis (Zienkiewicz Centre for Comutational Engineering, College of Engineering, Swansea University, UK), K.N. Seetharamu (Department of Mechanical Engineering, PESIT, Bangalore, Karnataka, India) |
| title_short | Fundamentals of the finite element method for heat and mass transfer |
| title_sort | fundamentals of the finite element method for heat and mass transfer |
| topic | Strömungsmechanik (DE-588)4077970-1 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Wärmeübertragung (DE-588)4064211-2 gnd |
| topic_facet | Strömungsmechanik Finite-Elemente-Methode Wärmeübertragung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026743460&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026743460&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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