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 |  موضوع: كتاب Analytical Methods in Conduction Heat Transfer - Daniel W. Mackowski الأحد 06 نوفمبر 2016, 7:34 pm | |
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Analytical Methods in Conduction Heat Transfer
Daniel W. Mackowski
ويتناول الموضوعات الأتية :
Analytical Methods in Conduction Heat Transfer
Daniel W. Mackowski
Mechanical Engineering Department
Auburn University
Contents
1 Preliminaries and Review 7
1.1 The Conduction Equation 7
1.1.1 Fourier’s Law and the thermal conductivity 9
1.1.2 The form of the conduction equation 10
1.1.3 Boundary conditions 11
1.2 One–Dimensional Steady Conduction 12
1.2.1 The Thermal Resistance 12
1.2.2 Heat generation 14
1.3 Extended Surfaces 20
1.3.1 The fin equation 20
1.3.2 Simple fins of uniform cross section 23
1.3.3 Measures of fin performance 24
1.3.4 Fins of non uniform cross section 27
1.3.5 Fin optimization 29
2 Advanced 1–D Analytical Methods 35
2.1 Introduction 35
2.2 Application of Mathematica to the annular fin 36
2.2.1 Formulation of the problem 36
2.2.2 Explanation of the Mathematica code 37
2.2.3 Heat transfer 39
2.3 Ordinary and modified Bessel functions 40
2.3.1 Definitions and Properties 40
2.3.2 The general Bessel equation 43
3 Transient and One Dimensional Conduction 47
3.1 Introduction 47
3.2 The transient impulse and 1–D cartesian problem 48
3.3 Orthogonal functions and orthogonality 57
34 CONTENTS
3.4 More on transient problems 62
3.4.1 Convection BCs 62
3.4.2 Heat transfer 66
3.4.3 Non–homogeneous BCs/DEs: Partial solutions 67
3.4.4 Problems with no steady state 72
3.4.5 Transient problems in radial systems 75
3.5 Computational Strategies in Mathematica 83
3.5.1 Evaluation of simple series 83
3.5.2 Eigencondition evaluation 84
3.5.3 Series terms that are expensive to computute: advanced summation methods 86
3.6 Summary 89
4 Two Dimensional Steady–State Conduction 93
4.1 Introduction 93
4.2 2–D Cartesian configurations 93
4.2.1 Specified temperature boundary conditions 93
4.2.2 Convection boundary conditions 98
4.3 Superposition 102
4.3.1 Superposition example #1 102
4.3.2 Superposition example #2 108
4.3.3 Superposition example #3 111
4.4 Two dimensional problems in cylindrical coordinates 115
4.4.1 2–D heat transfer in a circular fin 115
4.4.2 The long, annular cylinder: problems in r and φ 119
4.4.3 Math digression: 2–D in r and φ solutions 125
4.5 Convection–Diffusion Problems 127
4.6 Summary 130
5 General Multidimensional Conduction 135
5.1 Introduction 135
5.2 Transient and 2–D conduction 135
5.2.1 Reduction to 1–D 135
5.2.2 Separation of Variables 138
5.2.3 Inhomogeneous problems 140
5.2.4 Cylindrical geometry example 144
5.3 3–D steady conduction 149
5.3.1 Cartesian geometries 149
5.3.2 Cylindrical geometries 150
5.3.3 Spherical coordinates 151
5.4 Variation of Parameters 153CONTENTS 5
5.4.1 Transient problems 153
5.4.2 Steady problems 156
5.5 Application of Mathematica to multidimensional problems 160
5.6 Semi–Infinite Regions 165
5.6.1 SI problems in two directions: Fourier transform techniques 166
6 General Time–Dependent Conduction 173
6.1 Introduction 173
6.2 Initial value problems with time–dependent BCs and/or sources 173
6.2.1 Time–dependent superposition: Duhamel’s theorem 174
6.2.2 Discontinuous and piecewise continuous forcing functions 177
6.2.3 Solution by variation of parameters 185
6.3 Time–harmonic boundary conditions and sources 187
6.3.1 Periodic BCs/sources of arbitrary form 192
6.4 The semi–infinite medium 193
6.4.1 The step change in temperature: similarity solution 194
6.4.2 Laplace transform methods 196
6.4.3 Periodic BCs in semi–infinite media 199
7 Moving Interface Problems 203
7.1 Introduction 203
7.2 The Interface Continuity Conditions 203
7.3 The Neumann problem 205
7.4 Radial Coordinates 210
7.4.1 Moving interface from a line source 211
8 Hybrid Analytical/Numerical Methods in Conduction 215
8.1 Introduction 215
8.2 Mixed boundary conditions 216
8.2.1 The rectangular enclosure 216
8.2.2 The saw–tooth region 223
8.3 Nonorthogonal domains 230
8.3.1 Joined rectangular regions 230
8.3.2 Rectangular–cylindrical systems 2366 CONTENT
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