| This thesis explores the application of Constructal Theory and dendritic flow networks to heating and cooling. Chapter 1 is an introduction to Constructal Theory and the optimization of dendritic trees. In Chapter 2 we study the optimal geometric layout of schemes for distributing hot water uniformly over an area. Three configurations are optimized: (a) an area covered by a coiled stream, where all the users are aligned on the same stream, (b) a sequence of tree-shaped flows on square areas in which each area construct is made up of four smaller area constructs, and (c) a sequence of tree-shaped flows where each area construct is made up of two smaller area constructs.; In Chapter 3 the network of pipes is developed in steps, where each step consists of attaching to an existing network a new user that is placed in the position that allows the user to receive hot water at the highest temperature. In Chapter 4 we consider the fundamental problem of how to design a flow path with minimum overall resistance between one point (O) and many points situated equidistantly on a circle centered at O. In Chapter 5 we develop tree-shaped flow structures between one point and a straight line, one point and a plane, a circle and its center, and a point and many points distributed uniformly over an area.; In Chapter 6 we study the combination of trees with closed-loop structures, as in the leaf venation. The loops provide robustness to the design: the network continues to serve its assigned area even if one or more ducts are damaged. In Chapter 7 we develop the optimal tree-shaped flow paths for cooling a uniform heat-generating disc. The ultimate goal is to determine flow architectures that reach simultaneously two objectives: (i) minimal global fluid flow resistance (or pumping power), and (ii) minimal global thermal resistance. When the architecture is optimized for (i), the result is a dendritic structure, but when the objective is (ii) the optimal architecture has radial ducts. The dendrites produced by method (i) perform progressively better as the length scales become smaller. Optimized increasing complexity is the route to high thermal and fluid-flow performance in the limit of decreasing scales. (Abstract shortened by UMI.)... |
