Adrian Bejan

Duke University, Mechanical Engineering and Materials Science, Faculty Member

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Thermodynamics
Phone: 1 919 660 5309
Address: Duke University
Department of Mechanical Engineering
Box 90300
Durham, NC 27708-0300, USA

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Papers by Adrian Bejan

Numerical Analysis of a Tree-Shaped Cooling Structure for a 2-D Slab: A Validation of a “Constructally Optimal” Configuration

by Mauro Robbe and Adrian Bejan

Volume 4: Fatigue and Fracture, Heat Transfer, Internal Combustion Engines, Manufacturing, and Technology and Society, 2006

A 2-d rectangular slab, internally cooled by circular tubes of different diameters, is used as a ... more A 2-d rectangular slab, internally cooled by circular tubes of different diameters, is used as a benchmark to perform a numerical thermal optimization procedure on a heat transfer configuration obtained by “constructal” considerations. Three different geometric arrangements are investigated: in the first one, all cooling holes have the same diameter; in the second, there are two hierarchies of holes with two different diameters; in the third, yet another series of smaller holes is added. To assist the user in systematically assembling multiple configurations, a custom user interface utility for generating constructal geometries has been developed. Thermal boundary conditions are assigned as if the slab were the axial cross-section of an elongated prismatic body, and as if the ducts were internally cooled by forced convection. For each case (single diameter of the cooling holes, 2 and 3 different diameters) a series of numerical simulations has been run to assess and compare the perf...

Thermodynamic optimization of flow architecture: dendritic structures and optimal sizes of components

ABSTRACT

Compact Heat Transfer Flow Structures

Porous and Complex Flow Structures in Modern Technologies, 2004

Mechanical and Flow Structures Combined

Drying of Porous Materials

Porous and Complex Flow Structures in Modern Technologies, 2004

Quo Vadis Constructal Theory?

... 467 Design with Constructal Theory Adrian Bejan, Sylvie Lorente Copyright 0 2008 by John Wile... more

Quo Vadis Constructal Theory?

... 467 Design with Constructal Theory Adrian Bejan, Sylvie Lorente Copyright 0 2008 by John Wile... more

Tree-shaped flow structures: are both thermal-resistance and flow-resistance minimisations necessary?

ABSTRACT

Tree-shaped flow structures: are both thermal-resistance and flow-resistance minimisations necessary?

ABSTRACT

Constructal theory of energy-system and environment flow configurations

Configuration of air filters based on the constructal theory

Constructal flow orientation in conjugate cooling channels with internal heat generation

International Journal of Heat and Mass Transfer, 2013

ABSTRACT This paper presents the development of the three-dimensional flow architecture of conjug... more ABSTRACT This paper presents the development of the three-dimensional flow architecture of conjugate cooling channels in forced convection with internal heat generation within the solid for an array of circular cooling channels with different flow orientation. Three flow orientations were studied: array of channels with parallel flow; array of channels in which the flow in every second row is in a counter direction with its neighbours, and flows in all the arrays of channels are in counter flow relative to each other. The geometric configurations were determined in such a way that the peak temperature was minimised subject to the constraint of fixed global volume of solid material. The degrees of freedom of the design were hydraulic diameter and channel to channel spacing. A gradient-based optimisation algorithm was applied to search for the best optimal geometric configurations that improve thermal performance by minimising thermal resistance for a wide range of dimensionless pressure differences. The effect of porosities, applied pressure difference, flow orientation and heat generation rate on the optimal hydraulic diameter and channel to channel spacing is reported. The results show that the effects of dimensionless pressure drop on minimum thermal resistance were consistent with those obtained in the open literature.

Heat tubes: Conduction and convection

International Journal of Heat and Mass Transfer, 2019

This note offers a clear view of heat transfer fundamentals in terms of 'heat tubes', which are m... more This note offers a clear view of heat transfer fundamentals in terms of 'heat tubes', which are macroscopic architectures for the flow of energy through complex energy systems. The note focuses on heat tubes with conduction and convection, although heat tubes with radiation through stacks of radiation shields have also been treated in the literature. It is shown how to shape a heat tube and how to cool it along its length so that its thermodynamic performance evolves. Several instances of confusion are clarified along the way.

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Thermodynamics of heating

Proc. Roy. Soc. A, 2019

Heat transfer is a mature science, and so is thermodynamics. They are almost 200 years old having... more Heat transfer is a mature science, and so is thermodynamics. They are almost 200 years old having developed largely independently until the 1980s. Maturity comes from the usefulness and success of the thermal sciences. This review uses the thermodynamics of heat transfer to focus on aspects that are usually not discussed in physics: performance, purpose, function, objective and direction of evolutionary design. The article illustrates the unity of the thermal sciences discipline (heat transfer + thermodynamics + constructal law), and uses the opportunity to correct a few recent interpretations of the thermodynamics of heat transfer regarding dissipative engines and energy storage.

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The fastest animals and vehicles are neither the biggest nor the fastest over lifetime

by Adrian Bejan and Umit Gunes

Here we show how the size of a body affects its maximum average speed of movement through its env... more Here we show how the size of a body affects its maximum average speed of movement through its environment. The theoretical challenge was to predict that 'outliers' must exist, such as the cheetah for terrestrial animals and the jet fighter for airplanes. We show that during a travel that starts from rest and continues at cruising speed, the body size for minimum travel time, or maximum average speed, is not the biggest. The results are compared with extensive data for military aircraft for chase, attack and reconnaissance, in addition to data for commercial aircraft. The paper also explains why in earlier studies of flying (animals, airplanes) the airplane data deviated upward (toward greater speeds) relative to the theoretical trend followed by flying animals, and why the fastest animal flyers are one thousand times smaller than the fastest swimmers. Unlike the biggest animals and airplanes (elephant, whale, commercial jet), which move constantly, the fastest animals and airplanes spend most of their lives at rest. When judged for speed averaged over lifetime, the fastest 'sprinters' are in fact the slowest movers (as in Aesop's fable 'The Tortoise and the Hare'). Bigger bodies tend to move faster on land, in water, and in the air. This broad trend is supported by the speed-size data collected from many sources for flying, running and swimming (Fig. 1) 1. On this unifying background, out-liers exist. The burst speed of the cheetah is greater than the steady speed of the elephant. The tuna can swim faster than the steady whale. There are outliers that are even more distant from the general trend, but they should not be confused with the fastest runners, swimmers and fliers. For example, there are insects (e.g., the flea) that snap and jump at speeds much greater than what their speed-mass scaling law would predict. The ant odontomachus holds this kind of speed record (of order 200 km/h) by snapping its jaws shut, in order to jump to the side, to get out of the way of danger. This is a one-shot event, not cyclical locomotion. Most of her life, this ant walks on land at ant speed, in accord with the speed-mass scaling law for animal locomotion 1. Hirt et al. 2 addressed this aspect of animal locomotion with a model chosen to account for the starting (accelerating) period in the movement of the fastest animals. The model consisting of elastic fast-twitch fibers was constructed such that the speed emerges as a concave function of body size, with its peak at a body size that is not the largest size (Fig. 2). Bejan 3 observed that the existence of body size for peak speed also rules the evolutionary design of jet fighter aircraft, which is the human made counterpart of the animal of prey, with a high burst speed followed by a long period of inactivity on the ground. The following analysis is a theoretical treatment of this physics aspect of locomotion. It is a generalization of the unifying theory of animate, inanimate and vehicle movement, which includes the lifetime and life travel of animate and inanimate movement 4. Additionally, the following theory accounts for several features of the alignment of locomotion data that have not been questioned. One is the fact that the data for airplanes in Fig. 1 are not aligned with the data for animal fliers. Why are the airplane data trending above the animal speed-mass correlation? Why do the airplane data fall on a steeper line than the data for animal fliers? Moving over to Fig. 2, why does the body size for peak speed decrease in the direction from swimming to running and flying? Published: xx xx xxxx OPEN

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J. Bonjour, L.A.O. Rocha, A. Bejan, F. Meunier, Dendritic fins optimization for a coaxial two-stream heat exchanger. Int. J. Heat Mass Transfer, 2004, Vol. 47, N° 1, p. 111-124

by Jocelyn Bonjour and Adrian Bejan

International Journal of Heat and Mass Transfer

This paper documents the fundamental relation between the maximization of global performance and ... more This paper documents the fundamental relation between the maximization of global performance and the maleable (morphing) architecture of a flow system with global constraints. The example is the coaxial two-stream heat exchanger with flow through a porous bed in the annular space. It is shown that the constraints force the design toward heat exchangers with finite axial length, where additional improvements are derived from installing high-conductivity fins across the porous bed. The maximization of global performance is achieved through the optimization of the configuration of plate fins. Configurations with radial fins are optimized analytically and numerically. Configurations with branched fins are optimized numerically. It is shown that the best configuration (radial vs. branched) depends on the size of the heat exchanger cross-section. When the size is small, the best is the radial pattern. When the size exceeds a certain threshold, the best configuration is the optimized branched tree of fins.

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Optimal Spacing of Parallel Boards with Discrete Heat Sources Cooled by Laminar Forced Convection

by A. Morega and Adrian Bejan

Numerical Heat Transfer, Part A: Applications, 1994

Page 1. OPTIMAL SPACING OF PARALLEL BOARDS WITH DISCRETE HEAT SOURCES COOLED BY LAMINAR FORCED CO... more

Thermodynamics today

In this paper I use the example set by Prof. Jan Szargut as point of reference for a brief look a... more In this paper I use the example set by Prof. Jan Szargut as point of reference for a brief look at the current state of thermodynamicsdthe doctrine, its reach and importance. I start with my first encounter with Prof. Jan Szargut in 1979, and I show how his work influenced mine. Next, I review the structure that underpins thermodynamics as a discipline: the laws and the self-standing phenomena that they underpin , and graphic methods that convey these principles. Along the way, I draw attention to a recent trend that is caused by the inflation in scientific publishing due to the internet: the most common mistakes and misconceptions in thermodynamics, and how they are being spread. In sum, this paper is a call to action, to value, improve and defend the science of thermodynamics.

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Numerical Analysis of a Tree-Shaped Cooling Structure for a 2-D Slab: A Validation of a “Constructally Optimal” Configuration

by Mauro Robbe and Adrian Bejan

Volume 4: Fatigue and Fracture, Heat Transfer, Internal Combustion Engines, Manufacturing, and Technology and Society, 2006

Thermodynamic optimization of flow architecture: dendritic structures and optimal sizes of components

ABSTRACT

Compact Heat Transfer Flow Structures

Porous and Complex Flow Structures in Modern Technologies, 2004

Mechanical and Flow Structures Combined

Drying of Porous Materials

Porous and Complex Flow Structures in Modern Technologies, 2004

Quo Vadis Constructal Theory?

... 467 Design with Constructal Theory Adrian Bejan, Sylvie Lorente Copyright 0 2008 by John Wile... more

Quo Vadis Constructal Theory?

... 467 Design with Constructal Theory Adrian Bejan, Sylvie Lorente Copyright 0 2008 by John Wile... more

Tree-shaped flow structures: are both thermal-resistance and flow-resistance minimisations necessary?

ABSTRACT

Tree-shaped flow structures: are both thermal-resistance and flow-resistance minimisations necessary?

ABSTRACT

Constructal theory of energy-system and environment flow configurations

Configuration of air filters based on the constructal theory

Constructal flow orientation in conjugate cooling channels with internal heat generation

International Journal of Heat and Mass Transfer, 2013

Heat tubes: Conduction and convection

International Journal of Heat and Mass Transfer, 2019

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Thermodynamics of heating

Proc. Roy. Soc. A, 2019

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The fastest animals and vehicles are neither the biggest nor the fastest over lifetime

by Adrian Bejan and Umit Gunes

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J. Bonjour, L.A.O. Rocha, A. Bejan, F. Meunier, Dendritic fins optimization for a coaxial two-stream heat exchanger. Int. J. Heat Mass Transfer, 2004, Vol. 47, N° 1, p. 111-124

by Jocelyn Bonjour and Adrian Bejan

International Journal of Heat and Mass Transfer

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Optimal Spacing of Parallel Boards with Discrete Heat Sources Cooled by Laminar Forced Convection

by A. Morega and Adrian Bejan

Numerical Heat Transfer, Part A: Applications, 1994

Page 1. OPTIMAL SPACING OF PARALLEL BOARDS WITH DISCRETE HEAT SOURCES COOLED BY LAMINAR FORCED CO... more

Thermodynamics today

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Maximum heat transfer from multi-scale fins arranged in a row with non-uniform geometry.

by Josua P Meyer and Adrian Bejan

This paper described numerical the procedure used to determine the optimum configuration of two r... more This paper described numerical the procedure used to determine the optimum configuration of two rows of pin fins so that the total heat transfer rate is maximized. The heat transfer across the fins is by laminar forced convection bathed by a free-stream that is uniform and isothermal. The optimization is subjected to fixed volume of fin materials. The dimensions of the optimized configuration are the result of balancing conduction along the fins with convection transversal to the fins. Numerical results on the effect of dimensionless pressure drop and the thermal conductivity ratio on the optimal configuration are reported. Results obtained from numerical analyses are comparable to those in the open literature. The results also show that the flow structure performs best when the fin diameters and heights are non-uniform. INTRODUCTION Recent advances in the computational power of microprocessors have led to a significant increase in power densities in electronic devices and appliances. Under the conditions of high clock speeds and shrinking package size, the heat discharge per unit volume from these devices has increased dramatically over the past decade. Therefore, various types of cooling systems and techniques [1-10] have been proposed and developed. One of the most recent techniques is constructal design [1, 2] which is now a growing field in thermal sciences. It is used as a method of discovering effective flow configurations for thermal and fluid systems. This method is guided by the Constructal law: the progress made with this law to predict design in nature has been documented in physics and

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Maximum heat transfer rate density from ducts with wrinkled entrances.

by Josua P Meyer and Adrian Bejan

This paper reports an increase in the heat transfer rate density by using wrinkled entrance regio... more This paper reports an increase in the heat transfer rate density by using wrinkled entrance regions in ducts with laminar flow. The heat transfer rate density is increased by taking advantage of the presence of relatively isothermal fluid in the entrance regions. In order to stimulate a more complete thermal interaction between walls and fluid, the square entrances are wrinkled on the perimeter, at the one-third and the two-third positions. The new structure has two degrees of freedom. The fluid flow through the ducts is forced by the imposed pressure difference across the duct. Numerical simulations document the effects of the dimensionless pressure drop on the optimized configurations and show a fifteen percent enhancement in heat transfer rate density.

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Optimal geometry for conjugate heat transfer in a cooling channel.

by Josua P Meyer and Adrian Bejan

This paper reports on the geometric optimization of a heat-sink cooling channel where the objecti... more This paper reports on the geometric optimization of a heat-sink cooling channel where the objective is to maximize the global thermal conductance of the heat-sink and the coolant channel, subject to two global constraints: fixed total volume and solid material (heat-sink). This is a conjugate problem with conduction in the solid and forced convective flow in the cooling channel. The geometric optimization was carried out at three levels: (i) the internal structure which represents the relative thickness of the solid substrate, the vertical thickness and the base, and the external structure which accounts for (ii) the rectangular cross-section, and (iii) the axial flow length of the heat sink. Numerical results show that optimized flow length and global thermal conductance increase with increase in the dimensionless pressure drop number, similarly the global thermal conductance increases as the volume fraction for the conducting solid increases. The optimized longitudinal length decreases with increase in the solid volume fraction and dimensionless thermal conductivity. The available volume is distributed optimally through the system so that the global thermal conductance is maximized. Nomenclature Be Bejan number based on volume Be L Bejan number based on L B channels width, m C global conductance C p specific heat at constant pressure, J/kg.K G computational width (B/2 + t 1), m

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Along with Constructal Theory

University of Lausanne, Faculty of Geosciences and the Environment, 2006

Design in Nature, How the Constructal Law Governs Evolution in Biology, Physics, Technology, and Social Organization

Doubleday, 2012

Convection in Porous Media, Fifth Edition

Springer, 2017

Advanced Engineering Thermodynamics, Forth Edition

Wiley, 2016

The Physics of Life: The Evolution of Everything

St. Martin’s Press, 2016

Convection Heat Transfer, Forth Edition

Wiley, 2013

Constructal Law and the Unifying Principle of Design

Springer, 2013

Convection in Porous Media, Fourth Edition

Springer, 2013

Design with Constructal Theory

Wiley, 2008

Constructal Human Dynamics, Security and Sustainability

Springer, 2007

Advanced Engineering Thermodynamics, Third Edition

John Wiley & Sons, 2006

Convection in Porous Media, Third Edition

Springer-Verlag, 2006

La Loi Constructale

L’Harmattan, 2005

Convection Heat Transfer, Third Edition

John Wiley & Sons, 2004

Porous and Complex Flow Structures in Modern Technologies

Springer-Verlag, 2004

Emerging Technologies and Techniques in Porous Media

Kluwer Academic Publishers, 2004

Heat Transfer Handbook

Wiley, 2003

Shape and Structure, from Engineering to Nature

Cambridge University Press, 2000

Thermodynamic Optimization of Complex Energy Systems

Kluwer Academic Publishers, 1999

Energy and the Environment

Kluwer Academic Publishers, 1999

Technology Evolution, from the Constructal Law

Geometric optimization of cooling techniques

Tree Flow Networks in Urban Design

by Sylvie Lorente and Adrian Bejan

Constructal Theory of Social Dynamics, 2007

Mechanics of Fluid Flow Through a Porous Medium

Convection in Porous Media, 2012

ABSTRACT By a porous medium, we mean a material consisting of a solid matrix with an interconnect... more ABSTRACT By a porous medium, we mean a material consisting of a solid matrix with an interconnected void. We suppose that the solid matrix is either rigid (the usual situation) or it undergoes small deformation. The interconnectedness of the void (the pores) allows the flow of one or more fluids through the material. In the simplest situation (“single-phase flow”), the void is saturated by a single fluid. In “two-phase flow,” a liquid and a gas share the void space.

Fundamentals of Scale Analysis, Heatline Visualization, and The Intersection of Asymptotes

ABSTRACT The main objective of this chapter is to review the fundamentals of three simple methods... more ABSTRACT The main objective of this chapter is to review the fundamentals of three simple methods of problem solving and presentation of convection in porous media: scale analysis, heat lines, and the intersection of asymptotes method. Another objective is to draw attention to the growing literature that is devoted to the development and application of these methods, see Bejan et al. [5].

External Natural Convection

Convection in Porous Media, 2012

ABSTRACT Numerical calculation from the full differential equations for convection in an unbounde... more ABSTRACT Numerical calculation from the full differential equations for convection in an unbounded region is expensive, and hence approximate solutions are important. For small values of the Rayleigh number Ra, perturbation methods are appropriate. At large values of Ra thermal boundary layers are formed, and boundary-layer theory is the obvious method of investigation. This approach forms the subject of much of this chapter. We follow to a large extent the discussion by Cheng (1985a), supplemented by recent surveys by Pop and Ingham (2000, 2001) and Pop (2004).

Double-Diffusive Convection

Convection in Porous Media, 2012

Convection with Change of Phase

Bejan/Convection Heat Transfer 4e, 2013

Constructal Theory of Written Language

Constructal Theory of Social Dynamics, 2007

Improved thermal design of the cryogenic cooling system for a superconducting synchronous generator

Thesis. 1975. Ph.D.--Massachusetts Institute of Technology. Dept. of Mechanical Engineering. Vita... more

Energy theory of periodic economic growth

by Adrian Bejan and Umit Gunes

International Journal of Energy Research, 2020

This article shows that the sudden end of economic expansion (movement, wealth) emerges as a natu... more This article shows that the sudden end of economic expansion (movement, wealth) emerges as a natural, physical feature of the spreading movement, which has access to power (money), freedom to morph, and power storage (savings) for future movement on even greater areas. The movement is driven by power generation, which is interspaced with power savings on the same area. The theory is constructed systematically from the physical basis of economics concepts (money, savings, time, and bubbles) to a physics model that accounts for the time‐dependent spreading of movement on an area. Previous study has shown that physics accounts for the proportionality between the annual wealth (GDP) of a population and the annual consumption of fuel to generate power for that population. The present theory extends this view to the more realistic situation where every movement in society (wealth and fuel consumption) is time dependent.

University rankings: Quality, size and permanence

by Umit Gunes and Adrian Bejan

European Review, 2020

Why are the rankings of universities not changing? Why is the demographic composition of top univ... more Why are the rankings of universities not changing? Why is the demographic composition of top universities the same? In this review, these questions are addressed based on physics. Although size matters, higher ranks do not correlate with bigger sizes. The higher ranks belong to universities that have more authors who receive more citations. Citations are a record of how ideas spread from the source to the whole globe, in accordance with the physics of the logistics S-curve phenomenon. The spreading occurs in three periods – slow, fast, slow – and the population served by each idea during its lifetime depends on the size of the first big channel that carries the idea. An idea from a famous university has a larger spreading territory around it than an idea from a lesser-known university. Creativity is key: rankings come from visibility through citations, and, in turn, visibility for an author is aided by the higher visibility of the university. The demographic composition of the top universities is the same: for instance, the percentage of female authors and authors of East Asian origin among the 200 most cited authors does not vary significantly over the 20 highest ranked universities.

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