Research Papers: Conduction

Optimal Thin-Film Topology Design for Specified Temperature Profiles in Resistive Heaters

[+] Author and Article Information
François Mathieu-Potvin

Département de Génie Mécanique, Université Laval, Québec City, QC, G1V 0A6, Canada

Louis Gosselin1

Département de Génie Mécanique, Université Laval, Québec City, QC, G1V 0A6, Canadalouis.gosselin@gmc.ulaval.ca


Corresponding author.

J. Heat Transfer 132(10), 101302 (Aug 18, 2010) (9 pages) doi:10.1115/1.4001935 History: Received October 02, 2008; Revised November 11, 2009; Published August 18, 2010; Online August 18, 2010

In this paper, we optimized the topology of a thin-film resistive heater as well as the electrical potential of the electrodes on the boundaries. The objective was to minimize the difference between the actual and prescribed temperature profiles. The thin-film thickness was represented by 100 design variables, and the electrical potential at each electrode were also design variables. The topology optimization problem (inverse problem) has been solved with two methods, i.e., with a genetic algorithm (GA) and with a conjugate gradient method using adjoint and sensitivity problems (CGA). The genetic algorithm used here was modified in order to prevent nonconvergence due to the nonuniqueness of topology representation. The conjugate gradient method used in inverse conduction was extended to cope with our electrothermal problem. The GA and CGA methods started with random topologies and random electrical potential values at electrodes. Both the CGA and GA succeeded in finding optimal thin-film thickness distributions and electrode potential values, even with 100 topology design variables. For most cases, the maximum discrepancy between the optimized and prescribed temperature profiles was under 0.5°C, relative to temperature profiles of the order of 70°C. The CGA method was faster to converge, but was more complex to implement and sometimes led to local minima. The GA was easier to implement and was more unlikely to lead to a local minimum, but was much slower to converge.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

The geometrical features of the resistive heating system

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Figure 2

Example of topology mesh and finite volume mesh

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Figure 3

The main steps of the genetic algorithm method

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Figure 4

The main steps of the conjugate gradient method with adjoint problem

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Figure 5

Prescribed temperature profiles and their known topologies with one free electrode

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Figure 6

Optimized topologies with the CGA method for one free electrode

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Figure 7

Optimized topologies with the GA method for one free electrode

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Figure 8

Optimized topology and potentials with the CGA method for four electrodes




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