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