Abstract
Diverse tree structures such as blood vessels, branches of a tree and river basins exist in nature. The constructal law states that the evolution of flow structures in nature has a tendency to facilitate flow. This study suggests a theoretical basis for evaluation of flow facilitation within vascular structure from the perspective of evolution. A novel evolution parameter (Ev) is proposed to quantify the flow capacity of vascular structures. Ev is defined as the ratio of the flow conductance of an evolving structure (configuration with imperfection) to the flow conductance of structure with least imperfection. Attaining higher Ev enables the structure to expedite flow circulation with less energy dissipation. For both Newtonian and non-Newtonian fluids, the evolution parameter was developed as a function of geometrical shape factors in laminar and turbulent fully developed flows. It was found that the non-Newtonian or Newtonian behavior of fluid as well as flow behavior such as laminar or turbulent behavior affects the evolution parameter. Using measured vascular morphometric data of various organs and species, the evolution parameter was calculated. The evolution parameter of the tree structures in biological systems was found to be in the range of 0.95 to 1. The conclusion is that various organs in various species have high capacity to facilitate flow within their respective vascular structures.
Highlights
Constructal law is a theory that stipulates the generation of design evolve structures that increase flow [1,2,3]
The constructal law hypothesizes the evolution of design [5], and a mathematical formulation of constructal law based on thermodynamics is presented in Bejan and Lorente [6]
In order to compare the effect of shape factors on the value of evolution parameter for Newtonian, power law, and turbulent models, Ev is plotted as function of a and b
Summary
Constructal law is a theory that stipulates the generation of design evolve structures that increase flow [1,2,3]. In 1996, Bejan stated the constructal theory as ‘‘for a finite-size flow system to persist in time (to live) its configuration must evolve in such a way that provides greater and greater access to the currents that flow through it’’ [4]. According to the constructal law, a living system is a nonequilibrium system in thermodynamics with a structure that morphs towards configurations that provide easier flow through the system. According to the constructal law, the configuration of a flow system evolves to acquire more global performance (minimization of imperfection) over time. A diversity of designs with tree structures exists in nature such as blood vessels, river basins, bronchial and botanical trees. The well-known Murray’s law states that the flow through a branch is proportional to the diameter cube of the branch
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
