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Fundamentals of the Finite Element Method for Heat and Mass Transferm, 2/Ed > 열역학

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Fundamentals of the Finite Element Method for Heat and Mass Transferm, 2/Ed
판매가격 59,000원
저자 Nithiarasu
도서종류 외국도서
출판사 Wiley
발행언어 영어
발행일 2016-03
페이지수 464
ISBN 9780470756256
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  • 도서 정보

    도서 상세설명

    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 κ, ε, νT and αT 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
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