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