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Research Papers: Conduction

A Thermal Stability Criterion for Heat Conduction in Multilayer Composite Solids

[+] Author and Article Information
Bingen Yang1

Department of Aerospace and Mechanical Engineering, University of Southern California, 3650 McClintock Avenue, Room 430, Los Angeles, CA 90089-1453bingen@usc.edu

Hang Shi

Department of Aerospace and Mechanical Engineering, University of Southern California, 3650 McClintock Avenue, Room 430, Los Angeles, CA 90089-1453

1

Corresponding author.

J. Heat Transfer 131(11), 111304 (Aug 25, 2009) (7 pages) doi:10.1115/1.3153581 History: Received May 24, 2008; Revised April 29, 2009; Published August 25, 2009

Excessive heat generation within a body can cause unbounded temperature or thermal instability. In this work, a new stability test is established for heat conduction in one-dimensional multilayer composite solids that have internal heat generation at a rate proportional to the interior temperature. In the development, a spatial state formulation in the Laplace transform domain and a root locus analysis yield a stability criterion. This criterion gives an upper bound of heat source for thermal stability and relates the degree of excessive heat production to the number of unstable (positive) eigenvalues. The proposed stability test does not need any information on system eigenvalues, requests minimum computational effort, and is applicable to composites with thermal resistance at layer interfaces and bodies with nonuniformly distributed parameters. The convenience and efficiency of the stability test are demonstrated in three numerical examples.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

An n-layer composite body

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Figure 2

Schematic of the characteristic function Δ(s,μ) versus s; σm is a parameter defined in Eq. 21; circles (○) are the eigenvalues of the composite body

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Figure 3

Characteristic function Δ(0,μ) versus heat gain μ

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Figure 4

Characteristic function Δ(s,μ) versus s for heat gain μ=0 and 10

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