Please use this identifier to cite or link to this item:
Title: The natural emergence of asymmetric tree-shaped pathways for cooling of a non-uniformly heated domain
Authors: Çetkin, Erdal
Oliani, Alessandro
Keywords: Boundary conditions
Confined flow
Heat generation
Thermal conductance
Issue Date: 14-Jul-2015
Publisher: American Institute of Physics
Source: Çetkin, E., and Oliani, A. (2015). The natural emergence of asymmetric tree-shaped pathways for cooling of a non-uniformly heated domain. Journal of Applied Physics, 118(2). doi:10.1063/1.4926620
Abstract: Here, we show that the peak temperature on a non-uniformly heated domain can be decreased by embedding a high-conductivity insert in it. The trunk of the high-conductivity insert is in contact with a heat sink. The heat is generated non-uniformly throughout the domain or concentrated in a square spot of length scale 0.1 L0, where L0 is the length scale of the non-uniformly heated domain. Peak and average temperatures are affected by the volume fraction of the high-conductivity material and by the shape of the high-conductivity pathways. This paper uncovers how varying the shape of the symmetric and asymmetric high-conductivity trees affects the overall thermal conductance of the heat generating domain. The tree-shaped high-conductivity inserts tend to grow toward where the heat generation is concentrated in order to minimize the peak temperature, i.e., in order to minimize the resistances to the heat flow. This behaviour of high-conductivity trees is alike with the root growth of the plants and trees. They also tend to grow towards sunlight, and their roots tend to grow towards water and nutrients. This paper uncovers the similarity between biological trees and high-conductivity trees, which is that trees should grow asymmetrically when the boundary conditions are non-uniform. We show here even though all the trees have the same objectives (minimum flow resistance), their shape should not be the same because of the variation in boundary conditions. To sum up, this paper shows that there is a high-conductivity tree design corresponding to minimum peak temperature with fixed constraints and conditions. This result is in accord with the constructal law which states that there should be an optimal design for a given set of conditions and constraints, and this design should be morphed in order to ensure minimum flow resistances as conditions and constraints change.
ISSN: 0021-8979
Appears in Collections:Mechanical Engineering / Makina Mühendisliği
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

Files in This Item:
File Description SizeFormat 
5878.pdfMakale1.56 MBAdobe PDFThumbnail
Show full item record

CORE Recommender


checked on Feb 16, 2024


checked on Feb 26, 2024

Page view(s)

checked on Feb 26, 2024


checked on Feb 26, 2024

Google ScholarTM



Items in GCRIS Repository are protected by copyright, with all rights reserved, unless otherwise indicated.