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Constructal theory of generation of configuration in nature and engineering
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Image of FIG. 1.
FIG. 1.

(Color) Constructal theory proceeds in time against empiricism or copying from nature (Ref. 6). Bottom: the Lena delta and dendritic architecture derived from the constructal law.

Image of FIG. 2.
FIG. 2.

The evolution of the cross-sectional configuration of a stream composed of two liquids, low viscosity, and high viscosity. In time, the low viscosity liquid coats all the walls, and the high viscosity liquid migrates toward the center. This tendency of “self-lubrication” is the action of the constructal law of the generation of flow configuration in geophysics (e.g., volcanic discharges, drawn after Ref. 16) and in many biological systems.

Image of FIG. 3.
FIG. 3.

Elemental area of a river basin viewed from above: seepage with high resistivity (Darcy flow) proceeds vertically, and channel flow with low resistivity proceeds horizontally. Rain falls uniformly over the rectangular area . The flow from the area to the point (sink) encounters minimum global resistance when the external shape is optimized. The generation of geometry is the mechanism by which the area-point flow system assures its persistence in time, its survival.

Image of FIG. 4.
FIG. 4.

Constructal sequence of assembly and optimization, from the optimized elemental area (, Fig. 3) to progressively larger area-point flows (Ref. 23).

Image of FIG. 5.
FIG. 5.

Area-point flow in a porous medium with Darcy flow and grains that can be dislodged and swept downstream (Ref. 22).

Image of FIG. 6.
FIG. 6.

The evolution (persistence, survival) of the tree structure when(, the flow rate is increased in steps ) (Ref. 22).

Image of FIG. 7.
FIG. 7.

The evolution (persistence, survival) of the tree structure in a random-resistance erodable domain ( and increases in steps of ) (Ref. 22).

Image of FIG. 8.
FIG. 8.

Floating object at the interface between two fluid masses with relative motion (Ref. 6).

Image of FIG. 9.
FIG. 9.

The two momentum-transfer mechanisms that compete at the interface between two flow regions of the same fluid (Ref. 6).

Image of FIG. 10.
FIG. 10.

The universal proportionality between the length of the laminar section and the buckling wavelength in a large number of flows (Ref. 17).

Image of FIG. 11.
FIG. 11.

Bénard convection as a constructal design: the intersection of the many-cell and few-cell asymptotes.

Image of FIG. 12.
FIG. 12.

Earth model (Refs. 30 and 31) with equatorial and polar zones, and convective heat current carried by natural convection loops that constitute the brake to which the Sun-Earth-Universe engine is connected (see also Fig. 33).

Image of FIG. 13.
FIG. 13.

The construction of the tree of convective heat currents: (A) the constrained optimization of the geometry of a T-shaped construct; (B) the stretched tree of optimized constructs; (C) the superposition of two identical trees oriented in counterflow; and (D) the convective heat flow along a pair of tubes in counterflow (Ref. 6).

Image of FIG. 14.
FIG. 14.

The allometric law for animal hair strand diameter and body length scale.

Image of FIG. 15.
FIG. 15.

(Color online) The distributed destruction of food or fuel exergy during flight.

Image of FIG. 16.
FIG. 16.

(A) The periodic trajectory of a flying animal and (B) the cyclical progress of a swimming animal.

Image of FIG. 17.
FIG. 17.

The flying speeds of insects, birds and airplanes, and their theoretical constructal speed (Ref. 6).

Image of FIG. 18.
FIG. 18.

(Color) Comparison of theoretical predictions with the speeds, stroke frequencies, and force outputs of a wide variety of animals (from Ref. 52 and references therein). The theoretical predictions are based on scale analysis, which neglects factors of order 1 and therefore should be accurate in an order of magnitude sense. Note, however, that in nearly all cases the theory comes closer than order of magnitude agreement with empirical data.

Image of FIG. 19.
FIG. 19.

The origin of the “characteristic size” of the flow component (organ) of a larger flow system (animal) that moves.

Image of FIG. 20.
FIG. 20.

Optimal construct of parallel plates with laminar forced convection.

Image of FIG. 21.
FIG. 21.

Multiscale construct of parallel plates (Ref. 78).

Image of FIG. 22.
FIG. 22.

Multiscale construct of parallel cylinders in cross flow (Ref. 79).

Image of FIG. 23.
FIG. 23.

Multiple length scales on a wall with concentrated heat sources and maximum heat transfer density in laminar forced convection (Ref. 84).

Image of FIG. 24.
FIG. 24.

Elemental conduction volume with progressively greater freedom to morph and progressively higher performance (Ref. 87).

Image of FIG. 25.
FIG. 25.

Second construct optimized numerically, and the effect of changing the number of high-conductivity inserts of intermediate size (Ref. 21).

Image of FIG. 26.
FIG. 26.

The performance vs freedom domain of flows that connect the center with equidistant points on a circle (Ref. 74).

Image of FIG. 27.
FIG. 27.

The time evolution of convective architectures with small thermal resistance and small fluid flow resistance (Ref. 120).

Image of FIG. 28.
FIG. 28.

The evolution of thermofluid performance of architectures for two-stream counterflow heat exchangers (Ref. 123): from right to left, two adjacent tubes, two radial flow sheets, and two trees (Fig. 29).

Image of FIG. 29.
FIG. 29.

Counterflow heat exchanger with two point-circle flow trees (Ref. 123) of the types (b)–(d) shown in Fig. 26.

Image of FIG. 30.
FIG. 30.

(Color) Performance vs freedom to change configuration, at fixed global external size (Refs. 7 and 8).

Image of FIG. 31.
FIG. 31.

(Color) Performance vs freedom to change configuration, at fixed global internal size (Refs. 7 and 8).

Image of FIG. 32.
FIG. 32.

More freedom “to morph” leads to higher performance and asymmetry in the circle-point tree networks of Fig. 26 (after Ref. 109).

Image of FIG. 33.
FIG. 33.

Every nonequilibrium (flow) component of the earth functions as an engine that drives a brake (Refs. 13 and 31). The constructal law governs “how” the system functions: by generating a flow architecture that distributes imperfections optimally to fill the flow space (e.g., Table V). As a consequence, the “engine” part evolves in time toward generating maximum power (or minimum dissipation), and the “brake” part does the rest: maximum dissipation. Evolution means that each flow system assures its persistence (survival) in time by freely morphing into easier and easier flow structures under global finiteness constraints. The arrows proceed from left to right because this is the general drawing for a flow (nonequilibrium) system, in steady or unsteady state. When equilibrium is reached, all the flows cease, and the arrows disappear.

Image of FIG. 34.
FIG. 34.

Splat vs splash configuration, after a liquid droplet impacts a wall. If the droplet is small and slow enough, it comes to rest viscously as a disk. If the droplet is large and fast enough, it splashes into needles that grow radially until they are arrested by viscous effects.


Generic image for table
Table I.

The laminar flow resistances of ducts with regular polygonal cross sections with sides (Ref. 1).

Generic image for table
Table II.

Optimized cross-sectional shapes of open channels (Ref. 1).

Generic image for table
Table III.

The theoretical structure of constructal river basins (Ref. 23).

Generic image for table
Table IV.

Traditional critical numbers for transitions in several key flows and the corresponding local Reynolds number (Ref. 17).

Generic image for table
Table V.

How the balancing of high resistivity flow with low resistivity flow in a wide diversity of flow systems (courtesy of Stéphen Périn).


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Constructal theory of generation of configuration in nature and engineering