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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November 2009
This article was originally published in
Journal of Heat Transfer
Research Papers
A Thermal Stability Criterion for Heat Conduction in Multilayer Composite Solids
Bingen Yang,
Bingen Yang
Professor
Fellow ASME
Department of Aerospace and Mechanical Engineering,
e-mail: bingen@usc.edu
University of Southern California
, 3650 McClintock Avenue, Room 430, Los Angeles, CA 90089-1453
Search for other works by this author on:
Hang Shi
Hang Shi
Graduate Student
Department of Aerospace and Mechanical Engineering,
University of Southern California
, 3650 McClintock Avenue, Room 430, Los Angeles, CA 90089-1453
Search for other works by this author on:
Bingen Yang
Professor
Fellow ASME
Department of Aerospace and Mechanical Engineering,
University of Southern California
, 3650 McClintock Avenue, Room 430, Los Angeles, CA 90089-1453e-mail: bingen@usc.edu
Hang Shi
Graduate Student
Department of Aerospace and Mechanical Engineering,
University of Southern California
, 3650 McClintock Avenue, Room 430, Los Angeles, CA 90089-1453J. Heat Transfer. Nov 2009, 131(11): 111304 (7 pages)
Published Online: August 25, 2009
Article history
Received:
May 24, 2008
Revised:
April 29, 2009
Published:
August 25, 2009
Citation
Yang, B., and Shi, H. (August 25, 2009). "A Thermal Stability Criterion for Heat Conduction in Multilayer Composite Solids." ASME. J. Heat Transfer. November 2009; 131(11): 111304. https://doi.org/10.1115/1.3153581
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