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Research Papers: Conduction

An Algorithm Study on Inverse Identification of Interfacial Configuration in a Multiple Region Domain

[+] Author and Article Information
Chunli Fan

Department of Power Engineering, Naval University of Engineering, Wuhan 430033, P.R.C.c.fan@hotmail.com

Fengrui Sun, Li Yang

Department of Power Engineering, Naval University of Engineering, Wuhan 430033, P.R.C.

J. Heat Transfer 131(2), 021301 (Dec 15, 2008) (10 pages) doi:10.1115/1.2994765 History: Received December 19, 2007; Revised June 17, 2008; Published December 15, 2008

A two-dimensional inverse heat conduction problem to determine the interfacial configuration of a multiple region domain is solved by utilizing temperature readings on the outer surface of the whole domain. The method used is the modified one-dimensional correction method (MODCM) along with the finite element method. The MODCM is a simple but very accurate method, which first solves the multidimensional inverse heat conduction problem based on the simplified one-dimensional model, and the discrepancy in the result caused by this one-dimensional simplification is corrected afterward by an iterative process. A series of numerical experiments is conducted in order to verify the effectiveness of the algorithm. The method can identify the interfacial configuration of the multiple region domain with high accuracy. The average relative error of the identification result is not more than 10.4% when the standard deviation of the temperature measurement is less than 2.0% of the average measured temperature for the cases tested. The number of the measurement points of the inspection surface can be reduced with no obvious effect on the estimation results as long as it is still sufficient to describe the exact interfacial configuration. The method is proved to be a simple, fast, and accurate one that can solve successfully this interfacial configuration identification problem.

Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Geometry of the multiple region domain

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Figure 2

Schematics of the finite element mesh for one part of the whole domain (Nl: number of the node layers of the whole domain; Nli: number of the node layers of domain Ω1; and ● and ○ are the discrete points used for the inverse calculation on the interface and outer surface, respectively)

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Figure 3

Simplified one-dimensional heat transfer model of the multiple region domain

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Figure 4

Initial interfacial configurations calculated based on the one-dimensional inverse function 11 or 12 for the two conductivity distribution cases

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Figure 5

Effect of coefficient e on the initial interfacial configurations of the iteration (λ1=5, λ2=2)

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Figure 6

Interfacial configuration identification results when no measurement error is considered (ε=0.01)

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Figure 7

Temperature distributions on the outer surface of the whole domain for different conductivity distributions

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Figure 8

Effect of measurement error on the identification results: (a) λ1=2, λ2=5 and (b) λ1=5, λ2=2

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Figure 9

Effect of measurement error on the identification results: (a) λ1=2, λ2=20 and (b) λ1=20, λ2=2

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Figure 10

Identification results of the interfacial configuration when the number of measurement points is reduced to 12: (a) λ1=2, λ2=5 and (b) λ1=5, λ2=2

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Figure 11

Identification results of the interfacial configuration with 24 measurement points for test case II: (a) λ1=2, λ2=5 and (b) λ1=5, λ2=2

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Figure 12

Identification results of the interfacial configuration with 24 measurement points for test case II: (a) λ1=2, λ2=20 and (b) λ1=20, λ2=2

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Figure 13

Identification results of the interfacial configuration when the number of measurement points is reduced to 6: (a) λ1=2, λ2=5 and (b) λ1=5, λ2=2

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Figure 14

Identification results of the interfacial configuration with 24 measurement points for test case III: (a) λ1=2, λ2=5 and (b) λ1=5, λ2=2

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Figure 15

Identification results of the interfacial configuration with 24 measurement points for test case III: (a) λ1=2, λ2=20 and (b) λ1=20, λ2=2

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