Constructal theory and multi-scale geometries
Theory and applications in energetics, chemical engineering and materials

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Table of contents INTRODUCTION Queiros-Cond?. and Feidt M. 11 CHAPTER 1 : CONSTRUCTAL DESIGN PRINCIPLES FOR VASCULAR SMART STRUCTURES Bejan A. and Lorente S. 15 1. The constructallaw 15 2. Why f10w structures must be compact (optimal size, fixed volume fraction) 15 3. The f10w of stresses, band-in-glove with the f10w of fluid and heat 16 4. When f10w structures must be vascular (multi-scale, tree-like) 17 5. Trees matched canopy to canopy 17 6. Trees, grids, orthogonal and diagonal channels 17 7. Line to line trees: upright trees altemating with upside down trees 18 8. The future belongs to the vascularized 22 References 22 Nomenclature 23 CHAPTER Il : CONDUCTION HEAT TRANSFER IN SUPER INSULATING MATERIALS, FROM SELF-SIMILAR NANOSCALE MEDIUM TO MACROSCOPIC GRANULAR PACKING Lartigue B. and Spagno/ S. Abstract 25 1. Introduction 25 2. Conduction heat transfer modelling at nanoscale 26 2.1 Geometrie representations 26 2.2 Heat transfer modeling 28 2.3 Results 30 3. Heat transfer at macroscopic scale 31 3.1 Geometrie representations 31 3.2 Heat transfer modeling 32 3.3 Results 33 4. Conclusion 34 Biography 34 References 34 CHAPTER III : CONSTRUCTAL DESIGN OF MICROEVAPORATORS FOR THERMAL MANAGEMENT OF ELECTRONIC COMPONENTS Revellin R. and Bonjour J. Abstract 37 1. Introduction 38 2. Critical heat tlux 40 3. Thermal resistance 42 4. Discussion 44 5. Conclusions 44 References 45 CHAPTER IV: HEAT-TRANSFER CHARASTERISTICS IN MULTI-SCALE FLOW NETWORKS WITH PARALLEL OR INTERLACED CHANNELS Commenge J.-M., Saber M., Genin G., Tondeur D. and Falk L. Abstract 47 Introduction 47 Flow networks with parallel channels 49 Modelling of tlow distribution and heat transfer through parallel-channels networks 50 Heat-transfer through two-scale networks with parallel channels 52 HeaHransfer through muiti-scaie networks with parallel channels 55 Flow networks with interlaced channels 57 Flow distribution through interlaced-channel networks 59 Heat-transfer characteristics of interlaced-channei networks 61 Conclusion 62 References 62 CHAPTER V: PLANETARY FLOWS AND GEOMORPHOLOGY IN THE LIGHT OFCONSTRUCTALTHEORY Hector Reis A. Abstract 65 1. Introduction 65 2. Global atmospheric circulations 66 3. Scaling laws of river basins 68 4. Scaling laws of street networks 70 5. Beachface slope and sand size 71 6. Conclusions 73 Bibliography 74 CHAPTER VI: QUASI-CONTINUOUS L1NEAR CHAINS WITH SELF-SIMILAR HARMONIC INTERACTIONS Michelitsch T.-M., Maugin G.-A., Nicol/eau F.C.G.A., Nowakowski A.-F. and Derogar S. Abstract 77 1. Introduction 77 2. Results 78 3. Conclusions 78 4. Acknowledgements 79 References 79 CHAPTER VII: MULTI-SCALE GEOMETRIES IN ATOMIZATION OF L1QUIDS Le Moyne L. Abstract 81 Introduction 81 Scale aspects of sprays 83 Entropic-skins geometry 86 Construction and constructal approach 89 Conclusion 91 Acknowledgement 91 References 91 CHAPTER VIII: OPTIMIZATION OF THE POROSITY OF CATALYSTS FOR MAXIMUM EFFECTIVENESS GaunandA. Summary 93 1. Introduction 93 2. Mass balances and efTectiveness 94 3. Optimum continuous porosity gradient in catalysts 96 3.1 Use of the Lagrange multiplier method 96 3.2 First-order kinetics 97 3.3 Second-order kinetics 100 3.4 Comparison to optimum uniform porosity media: case of first-order kinetics 102 4. How to approach optimum porosity gradient: efTectiveness of multi-layered slab of catalyst for first-order kinetics 103 Conclusion 105 Acknowledgements 105 References 106 Appendix 106 CHAPTER IX: CONSTRUCTAL CASCADE OF CARNOT ENGINE CYCLES Laheurte G., Feidt M., Boussehain R. and Queiros-Cond?. Abstract 109 Introduction 109 Model and optimization for a two cycles O.R.C. cascade 110 First law efficiency optimization 111 Useful mechanical power optimization 111 Consequence in term of first law efficiency optimization 112 Extension of the model and optimization for a N cycles O.R.C. cascades 112 Conclusions 114 References 115 CHAPTER X: A SCALE-ENTROPY DIFFUSION EQUATION FOR MULTI-SCALE SYSTEMS: THE PARABOLIC CASE Queiros-Cond?. and Feidt M. Abstract 117 ). Introduction 117 2. Scale-entropy diffusion equation: the general case 117 3. Equipartition of scale-entropy losses in scale-space: parabolic scaling 119 4. Turbulent combustion 120 5. Parabolic scaling of constructal networks 122 6. Multi-scale dynamics of the american power grid: outages statistics 122 7. DifTusion-limited aggregates 124 8. Scale-dependent structure and parabolic scaling of large-scale structure of galaxies 125 9. Parabolic scaling of petroleum fields 128 10. Conclusion 129 References 129