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TECHNICAL PAPERS: Conduction Heat Transfer

The Steady Inverse Heat Conduction Problem: A Comparison of Methods With Parameter Selection

[+] Author and Article Information
Robert Throne

Department of Electrical Engineering, University of Nebraska, Lincoln, NE 68588e-mail: rthrone1@unl.edu

Lorraine Olson

Department of Mechanical Engineering and Department of Engineering Mechanics, University of Nebraska, Lincoln, NE 68588

J. Heat Transfer 123(4), 633-644 (Feb 01, 2001) (12 pages) doi:10.1115/1.1372193 History: Received February 18, 2000; Revised February 01, 2001
Copyright © 2001 by ASME
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References

Figures

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Typical geometry for inverse boundary value problem in steady heat conduction
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First cluster for the GESL method for the square with holes geometry
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Second cluster for the GESL method for the square with holes geometry
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Third cluster for the GESL method for the square with holes geometry
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L-curve used for identifying appropriate t values for zero order Tikhonov regularization
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L-curve used for identifying appropriate Nclusters values for GESL
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Geometry and finite element mesh for annulus test case. (Inner circle has radius 0.5, outer circle has radius 1.0.)
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Forward computed temperature contours for second annulus test case. (Temperature is zero on inner boundary; contour level intervals are 0.1.)
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Geometry and finite element mesh for square with holes. The outer square is 1.0×1.0. The first inner rectangle is centered at (0.275,0.375) and is 0.15×0.25. The second inner rectangle is centered at (0.65,0.65) and is 0.2×0.2. The radii of the corners on the inner rectangles is 0.01.
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Temperature contours for first square with holes test case. (Temperature is 1.0 on inner boundaries, 0.0 on outer boundary. Contours are at temperature intervals of 0.1.)
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Temperature contours for second square with holes test case: (a) “true” forward computed solution; (b) a GESL inverse solution when 5 percent noise is added to the outer temperatures and fluxes; and (c) a zero-order Tikhonov inverse solution when 5 percent noise is added to the outer temperatures and fluxes. (Temperature contours at 0.0, 0.1,[[ellipsis]]1.0.)
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Temperature contours for third square with holes test case. (Minimum temperature 0.69, maximum temperature 4.84. Contour 1:1.11 2:1.52 3:1.94 4:2.35 5:2.77 6:3.18 7:3.60 8:4.01 9:4.43).

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