Constructal optimization of tree-shaped assemblies for conduction.

摘要

This dissertation explores the geometric optimization of tree-shaped conduction assemblies using the Constructal theory. The objective is to maximize the global thermal conductance of the assembly subject to volume and material constraints.;The subject of this study is investigated with the wising need of an efficient electronics thermal management in mind. Hence, this study optimize both internal assemblies (chapters 1 and 2) where conduction trees channel out the heat from a heat generating volume (e.g. electronic packages), and external assemblies (extended surfaces, chapters 3 and 4) that dispose of the extracted heat to the outside. Although electronics thermal management is the stimulant of this research, the ideas explored have a range of applications. For example the compact fin designs investigated in chapters 3 and 4 can serve as a compact heat sink in a portable computer or in a compact heat exchanger in a jet engine or a satellite system. In general, the optimized assemblies of this study could be the choice whenever less volume, less weight and efficient cooling are of high priority.;Chapters 1 and 2 optimize the internal assemblies. In chapter 1, two methods of improving the performance of volume-to-point tree networks for two-dimensional heat conduction are presented. First, each construct is optimized with respect to all its degrees of freedom and second, spacings an allowed at the tips of the high-conductivity inserts. Chapter 2 explores the bounty of distributing the conduction tree nonuniformly,;Chapters 3 and 4 optimize the external conduction trees. In chapter 3 the constructal optimization method is used to produce compact fin designs, Assemblies of T-shaped plate fins, cylindrical fins, Tau-shaped fins, Narrow Tau-shaped fins, and the umbrella-shaped construct containing cylindrical fins are all considered, Chapter 4 extends the constructal optimization method to cylindrical assemblies of pin fins and cylindrical assemblies of tapered fins.;In all, this dissertation shows flat the optimization principle and the constraints deliver every geometric feature of the tree-shaped conduction assembly. These optimal features are reported in dimensionless terms for the different types of tree-shaped assemblies. The designs optimized numerically in this study lower the volume-to-point resistance of the Investigated conduction assemblies beyond the levels achieved in prior studies, and bring the shape of the conduction tree closer to the shapes seen in nature (e.g. natural trees and rivers). It was also shown that the optimized assemblies are relatively robust.