Perumal Nithiarasu, Roland W. Lewis

Fundamentals of the Finite Element Method for Heat and Mass Transfer

• Gebundenes Buch

Produktbeschreibung

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

Produktdetails

• Wiley Series in Computational Mechanics
• Verlag: Wiley & Sons
• 2. Aufl.
• Seitenzahl: 464
• Erscheinungstermin: März 2016
• Englisch
• Abmessung: 253mm x 179mm x 28mm
• Gewicht: 1038g
• ISBN-13: 9780470756256
• ISBN-10: 047075625X
• Artikelnr.: 30588975

Autorenporträt

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.

Inhaltsangabe

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 ElementMethod 86 3.4
Formulation for the Heat Conduction Equation 89 3.4.1 Variational Approach
90 3.4.2 The GalerkinMethod 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 PlaneWalls 105
4.2.1 Homogeneous Wall 105 4.2.2 CompositeWall 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 GalerkinMethod 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 ElementMethod (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 ofMomentum 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
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 kappa, epsilon, nyT and
alphaT 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
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 TurbulentMass
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 11.3 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 PorousMedium-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 13.2.1 Anodic and Cathodic
Compartments 371 13.2.2 Electrolyte Compartment 373 13.3 Numerical Solution
Algorithms 373 13.3.1 Finite ElementModeling 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 MassMatrix 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 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