Fundamentals of the Finite Element Method for Heat and Mass Transfer

2. Auflage 2016
ISBN: 978-0-470-75625-6
Verlag: Wiley

Buch, Englisch, 464 Seiten, Format (B × H): 178 mm x 252 mm, Gewicht: 1048 g

Reihe: Wiley Series in Computational Mechanics

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.

• Addresses fundamentals, applications and computer implementation

• Educational computer codes are freely available to download, modify and use

• Includes a large number of worked examples and exercises

• Fills the gap between learning and research

Autoren/Hrsg.

Nithiarasu, Perumal

Lewis, Roland W.

Seetharamu, Kankanhalli N.

Fachgebiete

• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Technische Thermodynamik
• Technische Wissenschaften Technik Allgemein Ingenieurwissenschaftliches Knowhow
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Produktionstechnik

Inhaltsverzeichnis

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 Solution 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 The Finite Element Method 39

3.1 Introduction 39

3.2 Elements and Shape Functions 42

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

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

Über Autor(innen)

Perumal Nithiarasu, DSc, PhD, is currently the head of Zienkiewicz Centre for Computational Engineering at Swansea University. He has more than twenty years of teaching and research experience in the areas of finite element method, heat and mass transfer, fluid dynamics and biomedical engineering. He is a founding co-chair of the international conference series, Computational Methods for Thermal Problems (ThermaCOMP, www.thermacomp.com). Professor Nithiarasu is a winner of ECCOMAS young investigator award in 2004 and he was awarded the Zienkiewicz Silver Medal of the Institution of Civil Engineers, UK in 2002. Professor Nithiarasu has published more than 300 articles and two textbooks in the areas of heat and fluid flow.?Professor Nithiarasu is the founding editor of the International Journal for Numerical Methods in Biomedical Engineering, published by Wiley. He serves on the editorial boards of several international journals.

Roland Lewis, DSc, PhD, FREng, has more than forty years of experience in teaching, research and administration in the area of heat transfer. Previously, Professor Lewis served as the head of Mechanical Engineering department in Swansea University.?His contributions in the areas of solidification and porous media are very well known. Until recently, he was the editor in chief of the International Journal for Numerical Methods in Engineering and Communications in Numerical Methods in Engineering. Although retired, he is actively editing the International Journal of Numerical Methods for Heat & Fluid Flow. He has also been serving as the honorary chair of the international conference series, Computational Methods in Thermal Problems (ThermaCOMP, www.thermacomp.com).?Author of nearly 400 articles, Professor Lewis was honoured with IACM Computational Mechanics award and fellowship. He is also a fellow of the Royal Academy of Engineering, UK.

K.N. Seetharamu currently holds a prestigious chair professor position in the Mechanical Engineering department of the PES University, Bangalore. He has more than forty years of teaching and research experience in the areas of heat transfer and finite element method. Previously he was a professor of Thermal Engineering in Institute of Technology Madras.?Professor Seetharamu also has spent more than ten years in University of Sains Malaysia, carrying out research in the areas of heat transfer, energy and electronics packaging.?Author of more than 300 publications, Professor Seetharamu is one of the top heat transfer engineers in India. He is a fellow of the Indian National Academy. Recently, the Indian Society for Heat and Mass Transfer has established a biennial award in his name to honour Professor Seetharmau's achievements.