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TECHNICAL PAPERS: 1999 Max Jakob Memorial Award Lecture

From Heat Transfer Principles to Shape and Structure in Nature: Constructal Theory

[+] Author and Article Information
Adrian Bejan

Duke University, Durham, NC 27708-0300e-mail: abejan@duke.edu

J. Heat Transfer 122(3), 430-449 (Mar 20, 2000) (20 pages) doi:10.1115/1.1288406 History: Accepted March 20, 2000; Received March 20, 2000
Copyright © 2000 by ASME
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References

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Stanescu,  G., Fowler,  A. J., and Bejan,  A., 1996, “The Optimal Spacing of Cylinders in Free-Stream Cross-Flow Forced Convection,” Int. J. Heat Mass Transf., 39, pp. 311–317.
Ledezma,  G. A., Morega,  A. M., and Bejan,  A., 1996, “Optimal Spacing Between Fins With Impinging Flow,” ASME J. Heat Transfer, 118, pp. 570–577.
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Basak,  T., Rao,  K. K., and Bejan,  A., 1996, “A Model for Heat Transfer in a Honey Bee Swarm,” Chem. Eng. Sci., 51, pp. 387–400.
Bejan,  A., Ikegami,  Y., and Ledezma,  G. A., 1998, “Constructal Theory of Natural Crack Pattern Formation for Fastest Cooling,” Int. J. Heat Mass Transf., 41, pp. 1945–1954.
Bejan,  A., 1997, “Constructal-Theory Network of Conducting Paths for Cooling a Heat Generating Volume,” Int. J. Heat Mass Transf., 40, pp. 799–816.
Ledezma,  G., Bejan,  A., and Errera,  M. R., 1997, “Constructal Tree Networks for Heat Transfer,” J. Appl. Phys., 82, pp. 89–100.
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Almogbel,  M., and Bejan,  A., 1999, “Conduction Trees With Spacings at the Tips,” Int. J. Heat Mass Transf., 42, pp. 3739–3756.
Dan,  N., and Bejan,  A., 1998, “Constructal Tree Networks for the Time-Dependent Discharge of a Finite-Size Volume to One Point,” J. Appl. Phys., 84, pp. 3042–3050.
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Neagu,  M., and Bejan,  A., 1999, “Three-Dimensional Tree Constructs of ‘Constant’ Thermal Resistance,” J. Appl. Phys., 86, pp. 7107–7115.
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Bejan,  A., and Errera,  M. R., 1997, “Deterministic Tree Networks for Fluid Flow: Geometry for Minimal Flow Resistance between a Volume and One Point,” Fractals, 5, pp. 685–695.
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Figures

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Model of power plant with two heat transfer surfaces, and the maximization of power output subject to fixed heat input (QH) and fixed total heat transfer surface (C)
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Three designs for the internal structure of a fixed volume with fixed total heat generating rate and stream of coolant flowing vertically. The objective is to maximize the global thermal conductance between the volume and the stream, which is equivalent to minimizing the area with hot-spot temperatures (red).
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The regulation of temperature in a swarm of honeybees (39). The left side shows the structure of the swarm cluster at a low ambient temperature. The right side is for a high ambient temperature, and shows the construction of almost equidistant ventilation channels with a characteristic spacing. Indicated are also the heat transfer from the swarm (arrows), areas of active metabolism (crosses), areas of resting metabolism (dots), and local approximate temperature.
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Patterns of cracks on the ground
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Elemental volume with uniform volumetric heat generation rate and high-conductivity insert along its axis of symmetry (42)
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How optimal shape is derived from the minimization of global resistance between a volume and one point. Three competing designs are shown. The volume and the heat generation rate are fixed. Variable is the aspect ratio of the rectangular domain. The resistance is proportional to the peak temperature difference, which is measured between the hot spots (red) and the heat sink (blue). The middle shape minimizes the areas covered by red, and has the smallest volume-point resistance.
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The first construct: a large number of elemental volumes connected to a central high-conductivity path (42)
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The internal and external geometry of a second construct optimized numerically (ϕ2=0.1,kp/k0=300,n1=8; left side, n2=2; right side, n2=4) (49)
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The optimized fourth construct (42)
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The optimized eighth construct (42)
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Optimal shapes of elemental volumes with spacings at the tips of the high-conductivity channels: the effect of varying k̃=kp/k0 and ϕ0=D0/H0 (49)
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The optimization of the angle of confluence between tributaries and their common stem in a first construct (ϕ1=0.1,k̃=50,n1=4) (43)
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The second construct optimized for minimum resistance in steady volume-point flow, and the effect of changing the number of first constructs, n2; see also Table 1 (43)
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The second construct optimized for minimum time of discharge from a volume to one point, and the effect of changing the number of first constructs, n22=0.1,k̃=300,D1/D0=5,D2/D0=10) (50)
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Evolution of the optimized elemental-volume design for minimum flow resistance between a volume and one point (52). The numbers in the right column indicate the global volume-point resistance as a multiple of the resistance of design (d).
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Optimal external and internal features of the first construct with constant thermal resistance (51)
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The top drawing shows the third construct containing four constant-resistance second constructs or eight first constructs, cf. Fig. 16 (51). The bottom figure is the river drainage basin generated by a deterministic erosion model based on global flow resistance minimization (59).
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(a) The volume AW that serves as convective heat sink for the concentrated heat current q, and (b) the smallest volume element defined by a single plate fin (64)
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First construct consisting of a large number of elemental one-fin volumes (64)
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The evolution of the optimized first construct of plate fins as the total volume increases (64)
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Three-dimensional constructs for flow between a volume and one point: the doubling of the outer dimension in going from the optimized third construct (a) to the optimized sixth construct (b) (270)
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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 (81)

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