Shape and Structure, from Engineering to Nature Book

	List of Symbols
	Preface
1	Natural Form, Questioning, and Theory	1
1.1	The Great Puzzle: From What Principle can Geometric Form be Deduced?	1
1.2	The Hardest Questions	4
1.3	The Objective and Constraints Principle	6
2	Mechanical Structure	14
2.1	Cantilever Beam: Objective and Constraints	14
2.2	External Shape	16
2.3	Internal Structure	18
2.4	Shape and Structure, Together	20
2.5	Column in End Compression	22
2.6	The Concept of "Better"	24
3	Thermal Structure	29
3.1	Cooling Electronics: Objective and Constraints	29
3.2	Volume Cooled by Natural Convection	29
3.3	Volume Cooled by Forced Convection	35
3.4	The Method of Intersecting the Asymptotes	40
3.5	The Balance between Stream-Travel Time and Diffusion Time	41
3.6	Optimal Longitudinal Flow Pulsations	42
3.7	From Constructal Principle to Internal Structure	44
3.8	Cracks in Shrinking Solids	45
4	Heat Trees	52
4.1	The Volume-to-Point Flow Problem	52
4.2	Elemental Volume	53
4.3	First Construct and Growth	56
4.4	Second and Higher-Order Constructs	58
4.5	Constructal Law	60
4.6	Tapered Channels and Optimal Angles	62
4.7	Three-Dimensional Heat Trees	65
4.8	Time-Dependent Discharge from a Volume to One Point	67
4.9	Constructal Design: Increasing Complexity in a Volume of Fixed Size	69
4.10	Design with Unrestricted Elemental Features	74
4.11	Constructal Heat Trees Are Robust	77
5	Fluid Trees	82
5.1	Bathing a Volume: Objective and Constraints	82
5.2	Elemental Volume	84
5.3	First and Higher-Order Constructs	88
5.4	Channels with Hagen-Poiseuille Flow	91
5.5	Optimization of Void-Space Distribution	92
5.6	Constructal Design: Increasing Complexity in a Volume of Fixed Size	94
5.7	Three-Dimensional Fluid Trees	99
5.8	Scaling Laws of Living Trees	108
6	Ducts and Rivers	117
6.1	Geometric Puzzles	117
6.2	Optimal River Channel Cross Sections	122
6.3	Optimal Duct Cross Sections	127
6.4	Deterministic River Drainage Basins	128
6.5	River Basins with Randomly Distributed Resistance to Erosion	137
6.6	River Basins with Optimized External Shape	137
6.7	Constructal Fluid Trees are Robust	142
6.8	Rivers of People	144
7	Turbulent Structure	149
7.1	Two Flow Regimes: High Resistance and Low Resistance, Intertwined	149
7.2	Why Do Icebergs and Logs Drift Sideways?	150
7.3	The First and Smallest Eddy	151
7.4	The Stepwise Growth of Mixing Regions	157
7.5	The Onset of Rolls in Fluid Layers Heated from Below	158
7.6	Partitioned Fluid Layer Heated from the Side	161
7.7	Optimization of Flow Geometry in Layers Heated from Below	163
7.8	Porous Layer Saturated with Fluid and Heated from Below	169
7.9	Natural Structure in Multiphase Flow Systems	174
7.10	Dendritic Crystals	175
8	Convective Trees	181
8.1	Convection in the Interstices versus Convection in the Tree Branches	181
8.2	Two-Dimensional T-Shaped Plate Fins	182
8.3	Umbrellas of Cylindrical Fins	187
8.4	Fin Trees with Optimal Plate-to-Plate Spacings	189
8.5	Trees of Circular Fins	198
8.6	Conduction in Interstitial Spaces and Convection in Channels	202
8.7	Parallel-Plate Channels	203
8.8	Optimally Tapered Parallel-Plate Channels	208
8.9	Round Tubes	212
8.10	Two Fluid Trees in Counterflow are One Tree for Convection	215
9	Structure in Power Systems	219
9.1	Allocation of Heat Exchange Inventory	220
9.2	Distribution of Insulation	223
9.3	Structure in Low-Temperature Machines	226
9.4	Streams in Counterflow	230
9.5	Flying Machines and Animals	234
9.6	Flying Carpets and Processions	240
10	Structure in Time: Rhythm	246
10.1	Intermittent Heat Transfer	247
10.2	Defrosting Refrigerators	249
10.3	Cleaning Power Plants	252
10.4	Breathing	254
10.5	Heart Beating	257
10.6	The Effect of Animal Body Size	260
11	Transportation and Economics Structure	270
11.1	Minimum Travel Time	271
11.2	Minimum Cost	278
11.3	Maximum Revenue	283
11.4	Development of Economics Structure in Time	287
11.5	Optimally Shaped Triangular Areas	288
11.6	Older Methods in Spatial Economics	293
11.7	The Law of Refraction	295
11.8	The Law of Parsimony	296
12	Shapes with Constant Resistance	300
12.1	How, Not What	300
12.2	More Degrees of Freedom	301
12.3	More Efficient Structures Look More "Natural"	308
12.4	More Material Where the Need is Greater	311
12.5	An Old and Prevalent Natural Phenomenon	312
	About the Author	315
	Author Index	317
	Subject Index	320