Adrian Bejan's Blog, page 2

Adrian Bejan | Serpentines, Galilei, & the fish, from Design in Nature

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In this video, Adrian Bejan begins with the familiar model of animal motion, where effort is split into two parts: vertical and horizontal. He revisits the freedom to change as a way for animals to minimize total effort, linking movement to hunger, food search, and the environments that shape behavior. Bejan introduces R as the resistance factor that differentiates movement in air, water, and on land. He then presents a new challenge, the observation that fish do not seem to fight gravity the same way flyers and runners do. Along the way, Bejan dives into history, revisiting Galilei and his experimental proof of acceleration, not through high technology, but with wet boards and dripping water.

Bejan discusses how animals balance W1 (vertical effort) and W2 (horizontal effort), emphasizing that the trade-off determines optimal speed and rhythm.

He explains how R varies across media, lowest in air, highest in water, intermediate on land, and how terrain complexity affects movement, making serpentine paths preferable on steep or bushy landscapes.

Bejan draws parallels between optimal animal speed and free-fall velocity, showing how larger animals reach greater speeds due to body mass and density.​

He introduces Galilei’s method of observing acceleration using dripping water and wooden boards, highlighting early experimental design and the scientific method.

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Umit Gunes, Ph.D.
Assoc. Prof.​ |​ Yildiz Technical University
Editor​ | International Communications in Heat and Mass Transfer
Guest Editor​ |​ Philosophical Transactions of the Royal Society A
Guest Editor​ |​ BioSystems
​Web | umitgunes.com

Adrian Bejan | Running, from Design in Nature

In this video, Adrian Bejan extends his analysis of animal locomotion to running, showing how flow architecture and resistance shape the evolution of movement on land. He introduces the factor R, a measure of environmental resistance, which varies between air, water, and land, influencing how animals move and how much effort they expend. Bejan connects these insights to frequency of undulation, size effects, and the food chain, explaining how physics predicts not only speed but also the natural hierarchy of who catches whom.

Bejan defines R with three memorable values: around 10 for flying in air, 1 for swimming in water, and an intermediate value for running on land, dependent on terrain quality.

He uses examples like the hippo on muddy ground and the ostrich or impala on flat land, showing how surface conditions change R and, therefore, running speed.

The frequency of undulation, leg stride, wing flapping, and tail movement decreases with animal size, predicting that bigger animals should move their limbs less frequently but still run faster than smaller ones.

Bejan illustrates how this prediction explains why elephants and hippos can outrun humans despite appearing sluggish, making them dangerous to overconfident observers in the wild.

He extends the food chain prediction: runners catch fish, birds catch runners, following the order of R values and showing how movement evolved toward easier access, from slow and burdensome to fast and economical.

Bejan concludes by linking this to the evolution of terrestrial locomotion, showing that life spread toward environments that offered greater access and lower effort per distance traveled.

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Umit Gunes, Ph.D.
Assoc. Prof. | Yildiz Technical University
Editor | International Communications in Heat and Mass Transfer
Guest Editor | Philosophical Transactions of the Royal Society A
Guest Editor | BioSystems
Web | umitgunes.com

Adrian Bejan | Flying, from Design in Nature

In this video, Adrian Bejan explores animal locomotion through the lens of configuration, freedom to change, and effort. He begins by connecting design in space with design in time, describing rhythm as an essential expression of flow. Using the flight of the condor as a case study, Bejan breaks down the movement of animals into cycles of vertical and horizontal motion, each with distinct effort. He emphasizes how freedom allows animals to adjust their movement, especially speed, to minimize total effort, revealing a natural tendency toward economical flow. From muddy roads to penguins in Antarctica, Bejan shows that all creatures, like fluids, flow through resistance, and their shapes and speeds are optimized by nature for persistence.

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Bejan presents flight as a cyclical process, involving two efforts: one vertical (lifting against gravity) and one horizontal (overcoming drag).

He introduces design in time as rhythm, using analogies from cars on snowy roads, string instruments, and cruising birds, to illustrate how flow systems pulse and repeat.

Using scale analysis, he shows how birds choose their cruising speed by balancing these efforts, highlighting speed as a key degree of freedom that birds can design.

Bejan connects the density of the body and the density of the environment to a resistivity factor, explaining why birds catch fish and not the reverse; resistance to flow determines directionality in the food chain.

He emphasizes that economic speed depends on mass, gravity, and the density difference between the animal and its surroundings, deriving a prediction that bigger animals are faster movers.

Bejan reframes flying as a flow architecture, where movement, like all flow in nature, is governed by the freedom to morph, interaction with the environment, and the minimization of effort over distance.

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Umit Gunes, Ph.D.
Assoc. Prof.​ |​ Yildiz Technical University
Editor​ | International Communications in Heat and Mass Transfer
Guest Editor​ |​ Philosophical Transactions of the Royal Society A
Guest Editor​ |​ BioSystems
​Web | umitgunes.com

Adrian Bejan | Constructal Law & Thermodynamics

In this video, Adrian Bejan explains how the Constructal Law expands the view of thermodynamics by showing that design is not just a human act but a natural phenomenon. He begins by revisiting the second law of thermodynamics, which was historically framed in the age of steam, with notable figures such as Carnot, Clausius, and Kelvin. Bejan defines the Constructal Law as a law of physics that accounts for the evolution of flow architecture in both animate and inanimate systems. Its central message is that flow systems persist by changing their configuration to provide greater access to their currents. Life, in this view, is a phenomenon of movement, and evolution is freedom to change.

Bejan presents the Constructal Law as: "For a finite size flow system (not infinitesimal) to persist in time (to live), it must evolve with freedom such that it provides easier and greater access to what flows."

He connects this to animate and inanimate systems, including human movement, animal locomotion, airplane design, and urban traffic, all of which show the same tendency to morph for easier flow.

Bejan contrasts the second law (movement from high to low temperature) with the Constructal Law (movement toward better configuration), stating that the former is about what happens, while the latter is about what comes next.

He emphasizes that design is a natural occurrence; it arises from physics, not imposed by intelligence or invention.

Bejan identifies freedom as the enabler of change, explaining that without the freedom to morph, systems cannot evolve or perform better over time.

He concludes that the Constructal Law is about life as movement, and its emergence in nature reveals how everything flows, everything morphs, and everything is connected through design.

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Umit Gunes, Ph.D.
Assoc. Prof.​ |​ Yildiz Technical University
Editor​ | International Communications in Heat and Mass Transfer
Guest Editor​ |​ Philosophical Transactions of the Royal Society A
Guest Editor​ |​ BioSystems
​Web | umitgunes.com

Adrian Bejan | The easy and the difficult, from Design in Nature

In this video, Adrian Bejan reflects on teaching and learning as an active, in-person exchange rather than a top-down process. He likens it to a boxing match. He encourages his students to participate, as he comes alive when they speak up. Moving beyond textbooks, he shifts his focus from cooling design to the deeper lessons of technological evolution. Bejan explains that although life becomes easier with new technologies, difficulties never disappear. While the easy may be seductive and widespread, the old and difficult remain essential and are practised by fewer people. They are also often more valuable over time. The lecture becomes a meditation on diversity in design, serendipity, and the power of historical understanding.

Bejan defines the evolution of technology as progressing from natural convection to forced convection and ultimately to conduction cooling, with each stage offering improved performance per unit volume.

He argues that progress in life and science requires changing direction when the current path becomes dull, even if only temporarily.

Easy things, such as communication, movement, and computing, improve our lives, but difficult things stay alive in the hands of the few, forming a lasting diversity of approaches.

He illustrates this with examples: photography did not eliminate portrait painting, steam locomotives did not replace horse-drawn carriages, and software has not replaced those who can still do maths by hand.

Bejan highlights email as a modern example of the easy, but reminds students of mailing's layered history: from handwritten letters sent to Cape Town, which served as a relay hub for ships exchanging mail, to the linking of navigation and Protestant history.

He concludes by saying that technology is a flow and that innovation often comes not from the obvious but from unexpected turns where the difficult is preserved and the easy is multiplied.

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Umit Gunes, Ph.D.
Assoc. Prof.​ |​ Yildiz Technical University
Editor​ | International Communications in Heat and Mass Transfer
Guest Editor​ |​ Philosophical Transactions of the Royal Society A
Guest Editor​ |​ BioSystems
Web | umitgunes.com

Adrian Bejan | Radial conduction cooling, innovation, from Design in Nature

In this video, Adrian Bejan reimagines a round slab of electronics, a disc, like a pizza, that generates heat uniformly and is cooled from the center. To prevent the system from overheating, Bejan introduces high-conductivity blades extending radially from the center, dividing the disc into equidistant sectors. Each sector becomes a pizza slice, a fundamental unit of analysis. He shows how the geometry, the material contrast, and the arrangement of slices determine the effectiveness of the design. This model of radial conduction leads to a deeper understanding of architecture, elemental systems, and the way design grows from the shape of the smallest feature.

Bejan divides the disc into triangular sectors, each with a cold center and hot corners, where the temperature difference drives the flow of heat toward the center.

Each sector includes a high-conductivity blade along its centerline, and Bejan defines the key dimensions as the horizontal length (radius) and the vertical span along the perimeter.

He applies the same logic as in earlier designs, with two components of temperature difference, vertical and radial, linked to the amount and quality of high-conductivity material.

The shape of the sector depends on the product of two quantities: the conductivity ratio and the volume fraction of expensive material. This determines both the thermal resistance and the optimal geometry.

Bejan calculates how many slices fit on the disc based on the size of one sector, showing that the elemental system defines the whole. “If you know the slice, you know the pizza.”

He concludes with the idea that radial design enables scaling. By adjusting the properties of the sector, the disc can grow, accommodate more cooling elements, and evolve as a system built from repeatable, efficient parts.

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Umit Gunes, Ph.D.
Assoc. Prof.​ |​ Yildiz Technical University
Editor​ | International Communications in Heat and Mass Transfer
Guest Editor​ |​ Philosophical Transactions of the Royal Society A
Guest Editor​ |​ BioSystems
​Web | umitgunes.com

Adrian Bejan | Rivers of heat, serendipity, innovation, from Design in Nature

In this video, Adrian Bejan introduces the concept of rivers of heat, a continuation of earlier flow models involving pedestrian flow and rivers of water. Now, the focus shifts to heat flowing through a rectangular slab, a system driven by heat generation per unit volume and shaped by a high-conductivity blade. Bejan presents the architecture as a sequence of cooling elements, each contributing to a larger system. Through this model, he explains how innovations emerge from understanding invisible flows and making decisions based on architecture, conductivity, and volume. Along the way, Bejan introduces the idea of serendipity, revealing how discovery happens unexpectedly through attention to design and flow.

Bejan presents a rectangular slab with a high-conductivity blade and internal heat generation, illustrating how heat escapes through the blade, much like water flows downhill from hillsides into a river.

The system evolves into multiple cooling elements, stacked and configured to create a larger structure, each delivering its heat current and contributing to the total flow.

The heat flow per unit area increases as the system size decreases, showing that miniaturization leads to more effective designs and more performance packed into a smaller space.

Bejan compares heat flow to knowledge, explaining that both transfer from high to low temperatures. This is a natural tendency linked to the second law of thermodynamics and irreversibility.

Bejan concludes with the idea that innovation is not a one-time event but a continuous process, driven by the architecture of flow and supported by the investments, both mental and material, made along the way.

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Umit Gunes, Ph.D.
Assoc. Prof.​ |​ Yildiz Technical University
Editor​ | International Communications in Heat and Mass Transfer
Guest Editor​ |​ Philosophical Transactions of the Royal Society A
Guest Editor​ |​ BioSystems
​Web | umitgunes.com

Adrian Bejan | Conduction in two materials, from Design in Nature

Adrian Bejan presents a flow system where heat is generated uniformly inside a rectangular slab. The heat flows out through a small exit made of a much better conductor, a blade with very high conductivity compared to the base material. The question is how to shape the architecture to minimize the temperature difference between the hottest and coldest points. Bejan uses scale analysis to show how the flow architecture, the placement of the blade, and the material contrast affect performance. This setup reflects real-world design trade-offs: what you pay for and get in return.

The slab is heated internally, and heat escapes only through one point, a highly conductive blade. The blade's conductivity is much greater than that of the rest of the slab.

The temperature difference inside the slab has two directions: vertical and horizontal. The slopes are shaped by the object's size, the materials' properties, and the flow path.

The better the conductor and the more of it you use, the easier the flow becomes. But both the conductivity ratio and the volume fraction cost money.

Bejan finds the shape that leads to the smallest temperature difference for a given amount of heat.

The final insight is that this is not just about conduction but about architecture. Architecture, in this case, means living longer and traveling farther.

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Umit Gunes, Ph.D.
Assoc. Prof.​ |​ Yildiz Technical University
Editor​ | International Communications in Heat and Mass Transfer
Guest Editor​ |​ Philosophical Transactions of the Royal Society A
Guest Editor​ |​ BioSystems

Adrian Bejan | Y shaped Conduction, from Design in Nature

Adrian Bejan investigates how to configure a Y-shaped structure so that the heat current entering a hot surface proceeds with the smallest possible temperature difference to the cold end. The focus is on thermal resistance, expressed as ΔT/Q. Bejan explains that minimizing this quantity requires morphing the flow architecture, using a given solid volume with fixed thermal conductivity (K). The analysis is grounded in solid body conduction, the simplest flow configuration. Drawing comparisons with the flow of water in a branching stream, Bejan connects the invisible movement of heat to the geometry of the structure and its historical foundation in caloric theory.

The objective is to reduce thermal resistance (ΔT/Q) by optimizing the configuration while using a fixed amount of material, defined by L₁, D₁, L₂, D₂, and W, and fixed thermal conductivity.

Bejan applies Fourier’s law, emphasizing that it is not a law but a definition of thermal conductivity. It links the heat current (Q) to the temperature difference and cross-sectional area divided by the path length.

He explains that the theory of heat transfer emerged from caloric theory, where quantities like heat and temperature difference were measured using thermometers and melted wax.

Bejan references Dainci, who observed that in trees the cross-section of the trunk appears equal to the sum of the cross-sections of the branches, but notes that living trees are not just flow systems, they also resist bending from wind, which alters the geometry.

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Umit Gunes, Ph.D.
Assoc. Prof.​ |​ Yildiz Technical University
Editor​ | International Communications in Heat and Mass Transfer
Guest Editor​ |​ Philosophical Transactions of the Royal Society A
Guest Editor​ |​ BioSystems

Submit your abstract to Constructal Law Conference 2025

From selected papers presented at the Constructal Law Conference 2025, authors will be recommended to submit new and original work for consideration to be published in the journals:

Philosophical Transactions of the Royal Society A

International Communications in Heat and Mass Transfer

BioSystems

Abstract Submission Deadline: July 15, 2025

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