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Tree-Shaped Flow Networks Fundamentals

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Tree-Shaped Fluid Flow and Heat Transfer

Part of the book series: SpringerBriefs in Applied Sciences and Technology ((BRIEFSAPPLSCIENCES))

Abstract

The size of the offspring vessels and airways in circulatory and respiratory trees can be predicted by theory. We first review the relationship connecting a parent tube to daughter tubes based on the application of optimization principles, such as minimizing energy expenditure, minimizing the total flow resistance.

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Notes

  1. 1.

    “Maximum flow access” corresponds to minimum travel time or minimum transfer time (Bejan and Ledezma 1998). Thus, it is equivalent to state that “for a finite-size flow system to persist in time, it must evolve such that it provides a minimum travel time to currents that flow through it.”

  2. 2.

    Wechsatol et al. (2006) studied the effect of junction losses on the optimal connection of large vessels to small. They concluded that the junction losses have a sizeable effect on optimized geometry when a dimensionless parameter called svelteness, defined by the ratio between the external and internal length scales, is lower than the square root of 10.

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Authors and Affiliations

  1. Department of Physics, University of Évora, Évora, Portugal

    António F. Miguel

  2. Graduate Program in Mechanical Engineering, University of Vale do Rio dos Sinos, UNISINOS, São Leopoldo, Rio Grande do Sul, Brazil

    Luiz A. O. Rocha

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  1. António F. Miguel
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  2. Luiz A. O. Rocha
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Miguel, A.F., Rocha, L.A.O. (2018). Tree-Shaped Flow Networks Fundamentals. In: Tree-Shaped Fluid Flow and Heat Transfer. SpringerBriefs in Applied Sciences and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-73260-2_2

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  • DOI: https://doi.org/10.1007/978-3-319-73260-2_2

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