Title: A constructal view of prefractal dendritic flow networks using an exergy analysis

Authors: Antonio F. Miguel

Addresses: Department of Physics, School of Science and Technology, University of Evora, Evora, Portugal; Institute of Earth Sciences – ICT, Pole of Evora, Evora, Portugal

Abstract: Evidence supports the interpretation that natural dendritic networks are described by fractal theory. It is recognised that the fractal description alone is not a complete description of nature of space filling. This study addresses the fundamental question of what the size of dendritic flow networks should be, in order to perform with the least irreversibilities, in addition to what fractal features-based pattern should have. Optimal shapes of symmetric and asymmetric networks for viscous flow and diffusion with junction loss effects are analysed based on exergy minimisation rate. Global size constraints included in the analysis are the volume and surface area. The optimal sizes of the flow networks are obtained, and prefractal dimensions that characterise these networks are computed. It is shown that the prefractal dimensions depend on both fluid transport mechanisms and space constraints. The physics link between prefractal regularity and optimal flow performance is clear presented.

Keywords: exergy analysis; prefractal dimension; constructal law; dendritic flow networks; scale factor; homothety ratio.

DOI: 10.1504/IJEX.2021.117604

International Journal of Exergy, 2021 Vol.36 No.1, pp.56 - 75

Received: 16 Dec 2020
Accepted: 28 Jan 2021

Published online: 07 Sep 2021 *

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