Page 2 - Fundamentals of The Finite Element Method for Heat and Fluid Flow
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Contents







                        Preface                                                                xiii

                        1 Introduction                                                          1
                           1.1  Importance of Heat Transfer .. ... .. .. .. .. .. .. ... .. .. ..  1
                           1.2  Heat Transfer Modes .. .. .. ... .. .. .. .. .. .. ... .. .. ..  2
                           1.3  The Laws of Heat Transfer . .. ... .. .. .. .. .. .. ... .. .. ..  3
                           1.4  Formulation of 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  Boundary and Initial Conditions . . . . . . . . . . . . . . . . . . . . . . . . 13
                           1.7  Solution Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
                           1.8  Summary .. .. .. .. .. .. ... .. .. .. .. .. .. ... .. .. .. 15
                           1.9  Exercise. .. .. .. .. .. .. ... .. .. .. .. .. .. ... .. .. .. 15
                           Bibliography . .. .. .. .. .. .. ... .. .. .. .. .. .. ... .. .. .. 17

                        2 Some Basic Discrete Systems                                          18
                           2.1  Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
                           2.2  Steady State Problems . .. .. ... .. .. .. .. .. .. ... .. .. .. 19
                               2.2.1  Heat flow in a composite slab .. .. .. .. .. .. ... .. .. .. 19
                               2.2.2  Fluid flow network . .. ... .. .. .. .. .. .. ... .. .. .. 22
                               2.2.3  Heat transfer in heat sinks (combined conduction–convection) . . . 25
                               2.2.4  Analysis of a heat exchanger . . . . . . . . . . . . . . . . . . . . . 27
                           2.3  Transient Heat Transfer Problem (Propagation Problem) . . . . . . . . . . . 29
                           2.4  Summary .. .. .. .. .. .. ... .. .. .. .. .. .. ... .. .. .. 31
                           2.5  Exercise. .. .. .. .. .. .. ... .. .. .. .. .. .. ... .. .. .. 31
                           Bibliography . .. .. .. .. .. .. ... .. .. .. .. .. .. ... .. .. .. 37
                        3 The Finite Element Method                                            38
                           3.1  Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
                           3.2  Elements and Shape Functions . ... .. .. .. .. .. .. ... .. .. .. 41
                               3.2.1  One-dimensional linear element. .. .. .. .. .. ... .. .. .. 42
                               3.2.2  One-dimensional quadratic element . .. .. .. .. ... .. .. .. 45
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