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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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1569-3945
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Volume 20, Issue 5-6

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Inverse determination of unsteady temperatures and heat fluxes on inaccessible boundaries

Brian H. Dennis
  • Department of Mechanical and Aerospace Engineering, University of Texas at Arlington, 500 W. First St., Arlington, TX 76019, USA
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/ George S. Dulikravich
  • Department of Mechanical and Materials Engineering, Florida International University 10555 W. Flagler St., Miami, FL 33174 , USA
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Published Online: 2012-12-14 | DOI: https://doi.org/10.1515/jip-2012-0052

Abstract.

The direct measurement of temperatures and heat fluxes may be difficult or impossible on boundaries that are inaccessible, such as internal cavities, or exposed to harsh environmental conditions that would destroy the thermal sensors. In such circumstances, one may inversely determine the temperature and heat fluxes on these unknown boundaries by using over-specified conditions on boundaries where such information can be readily collected. This assumes the geometry and material properties of the domain are known. Algorithms for solving these problems, such as those based on finite difference, finite element, and boundary element, are well known for the case where measured boundary conditions are not a function of time. In this work, we demonstrate an inverse finite element method that effectively solves this inverse heat conduction problem using over-specified temperatures and heat fluxes that are time varying. The material properties may be highly heterogeneous and non-linear. A boundary regularization method is used to stabilize the method for cases involving errors in temperature and heat flux measurements. Several three-dimensional examples are given using simulated measurements with and without measurement errors, to demonstrate the accuracy of the method.

Keywords: Inverse problems; heat conduction; finite element method; regularization

About the article

Received: 2012-07-24

Published Online: 2012-12-14

Published in Print: 2012-12-01


Citation Information: , Volume 20, Issue 5-6, Pages 791–803, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jip-2012-0052.

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Citing Articles

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[1]
Mattia Bergagio, Haipeng Li, and Henryk Anglart
International Journal of Heat and Mass Transfer, 2018, Volume 126, Page 281
[2]
George S. Dulikravich, Brian H. Dennis, Daniel P. Baker, Stephen R. Kennon, Helcio R.B. Orlande, and Marcelo J. Colaco
International Journal of Aeronautical and Space Sciences, 2012, Volume 13, Number 4, Page 405

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