Geometric optimization of flow systems with irreversibilities

This dissertation is based on several studies of the geometric optimization of flow systems.; Chapter 1 reports the solution to the fundamental problem of how to maximize the mechanical power extracted from a hot single-phase stream when the total heat transfer area bathed by the stream is constrained. The optimal stream temperature distribution is exponential in x, and so is the temperature distribution along the hot end of the system that converts the heat transfer into mechanical power. Similar conclusions are reached for the cold end heat exchanger, when the power system rejects heat to a cold single-phase stream.; Chapter 2 outlines a strategy for constructing the architecture of the volume-to-point path such that the flow resistance is minimal (constructal theory1). The given volume is viewed as an assembly of volume elements of various sizes. The main discovery is that the shape of each element can be optimized subject to fixed volume, such that the elemental volume-to-point flow resistance is minimal. The flow integrated over each new assembly is channeled through a high-permeability path to a point on the side of the assembly. Most of the main hypotheses are relaxed in the next chapter.; Chapter 3 describes an analytical and numerical study of the geometric minimization of the resistance to Darcy flow between a finite-size volume and one point. The volume is two-dimensional and contains materials with several permeabilities. At the end it yields the same conclusions reached in chapter 2 regarding the methodology and the results.; Chapter 4 shows that the dendritic patterns formed by low-resistance channels in a river drainage basin are reproducible and can be deduced from a single principle that acts at every step in the development of the pattern: the constrained minimization of global resistance in area-to-point flow.; Chapter 5 describes the geometric optimization of the internal structure of a volume that generates heat at every point and is cooled by a single stream. It is shown that in the end the fluid channels form a tree network that cools every point of the given volume.