Please use this identifier to cite or link to this item:
http://hdl.handle.net/11375/10153
Title: | OPTIMAL GEOMETRY IN A SIMPLE MODEL OF TWO-DIMENSIONAL HEAT TRANSFER |
Authors: | Peng, Xiaohui |
Advisor: | Protas, Bartosz David Lozinski and Nicholas Kevlahan David Lozinski and Nicholas Kevlahan |
Department: | Mathematics and Statistics |
Keywords: | Shape Differentiation;Cost Functional;Adjoint System;Spectral Method;Boundary Integral Equation;Shape Gradient;Numerical Analysis and Computation;Numerical Analysis and Computation |
Publication Date: | Oct-2011 |
Abstract: | <p>This investigation is motivated by the problem of optimal design of cooling elements in modern battery systems used in hybrid/electric vehicles. We consider a simple model of two-dimensional steady-state heat conduction generated by a prescribed distribution of heat sources and involving a one-dimensional cooling element represented by a closed contour. The problem consists in finding an optimal shape of the cooling element which will ensure that the temperature in a given region is close (in the least squares sense) to some prescribed distribution. We formulate this problem as PDE-constrained optimization and use methods of the shape-differential calculus to obtain the first-order optimality conditions characterizing the locally optimal shapes of the contour. These optimal shapes are then found numerically using the conjugate gradient method where the shape gradients are conveniently computed based on adjoint equations. A number of computational aspects of the proposed approach is discussed and optimization results obtained in several test problems are presented.</p> |
URI: | http://hdl.handle.net/11375/10153 |
Identifier: | opendissertations/5212 6176 2089606 |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Size | Format | |
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fulltext.pdf | 1.66 MB | Adobe PDF | View/Open |
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