This article addresses the use of boundary element method in conjunction with minimal energy technique for solving a geometrical inverse heat conduction problem. The problem considered in this study is to estimate the unknown inner boundary position in an irregular-shaped hollow body of which the inner boundary surface is subjected to a specified temperature condition. For solving the problem, first boundary element equations are converted into the quadratic programming problem by minimizing the energy functional with a constraint, next a hypothetical inner boundary is defined such that the actual inner boundary is located interior of the hypothetical solution domain, then temperatures at hypothetical inner boundary are determined to meet the constraints of measurement error in inner surface temperatures, and finally boundary element analysis is performed for the position of an unknown boundary. Based on these main solution procedures, an effective detection algorithm is provided. In addition, the solution method is numerically tested to investigate the effects of measurement errors on the accuracy of estimation.

Issue Section:
Technical Papers
Keywords:
heat conduction, inverse problems, boundary-value problems, optimisation
Topics:
Boundary element methods, Heat conduction, Inverse problems, Temperature, Boundary-value problems, Algorithms, Errors
1.
Kurpisz, K., and Nowak, A. I., 1995, Inverse Thermal Problems, Computational Mechanics Publications, Southamption, UK.
2.
Martin
,
T. J.
, and
Dulikravich
,
G. S.
,
1996
, “
Inverse Determination of Boundary Conditions and Sources in Steady Heat Conduction with Heat Generation
,”
ASME J. Heat Transfer
,
118
, pp.
546
–
554
.
3.
Huang
,
C. H.
, and
Chen
,
C. W.
,
1998
, “
A Boundary-Element-Based Inverse Problem of Estimating Boundary Conditions in an Irregular Domain with Statistical Analysis
,”
Numer. Heat Transfer, Part B
,
33
, pp.
251
–
268
.
4.
Dulikravich
,
G. S.
,
1988
, “
Inverse design and Active Control Concepts in Strong Unsteady Heat Conduction
,”
Appl. Mech. Rev.
,
41
, pp.
270
–
277
.
5.
Stanitz
,
J. D.
,
1988
, “
A Review of Certain Inverse Methods for the Design of Ducts with 2- or 3-Dimensional Potential Flow
,”
Appl. Mech. Rev.
,
41
, pp.
217
–
238
.
6.
Huang
,
C. H.
, and
Yan
,
J. Y.
,
1995
, “
An Inverse Problem in Simultaneously Measuring Temperature Dependent Thermal Conductivity and Heat Capacity
,”
Int. J. Heat Mass Transf.
,
38
, pp.
3433
–
3441
.
7.
Gaussorgues, G., 1994, Infrared Thermography, Chapman & Hall, London, UK.
8.
Kassab, A. J., Pollard, J., Hsieh, C. K., and Chew, L. C., 1995, “BEM Solution of the Inverse Geometric Problem-Experimental Results,” Boundary Elements XVII, eds., S. Kim, T. A. Oswald, and H. Power, Computational Mechanics Publications, Boston, MA, pp. 323–329.
9.
Maldague, X., 1992, Nondestructive Evolution of Materials by Infrared Thermography, Springer-Verlag, New York, NY.
10.
Vavilov, V. P., 1994, “Advances in Signal Inversion with Applications to Infrared Thermography,” Advances in Signal Processing for Nondestructive Evaluation of Materials, X. P. V. Maldague, ed., Kluwer Academics Publishers, Dordrecht, The Netherlands, pp. 161–184.
11.
Beck, J. V., Blackwell, B., and St. Clair, C. R., 1985, Inverse Heat Conduction III-Posed Problems, Wiley-Interscience, New York, NY.
12.
Tikhonov, A. N., and Arsenin, V. Y., 19877, Solutions of Ill-Posed Problems, Winston & Sons, Washington, DC.
13.
Ozisik, M. N., 1993, Heat Conduction, 2nd Ed., John Wiley & Sons, New York, NY.
14.
Brebbia, C. A., Telles, J. E., and Wrobel, L. C., 1984, Boundary Element Techniques, Springer-Verlag, New York, NY.
15.
Kassab
,
A. J.
, and
Pollard
,
J. E.
,
1993
, “
Automated Algorithms for the Nondestructive Detection of Subsurface Cavities by the IR-CAT Method
,”
J. Nondestruct. Eval.
,
12
, pp.
175
–
187
.
16.
Meric
,
R. A.
,
1988
, “
Shape Optimization and Identification of Solid Geometrics Considering Discontinuities
,”
ASME J. Heat Transfer
,
110
, pp.
544
–
550
.
17.
Shau
,
R.
,
Batista
,
J.
, and
Carey
,
G. F.
,
1990
, “
An Improved Algorithm for Inverse Design of Thermal Problems with Multiple Materials
,”
ASME J. Heat Transfer
,
112
, pp.
274
–
279
.
18.
Choi, C. Y., and Kim, H. G., 1996, “Boundary Element Solutions of the Geometrical Inverse Heat Conduction Problems Using Regularization Procedure,” Proc. 2nd European Thermal-Sciences and 14th UTT National Heat Transfer Conferences, vol. 2, pp. 1089–1095.
19.
Huang
,
C. H.
, and
Chao
,
B. H.
,
1997
, “
An Inverse Geometry Problem in Identifying Irregular Boundary Configurations
,”
Int. J. Heat Mass Transf.
,
40
(
9
), pp.
2045
–
2053
.
20.
Huang
,
C. H.
, and
Chen
,
H. M.
,
1999
, “
Inverse Geometry Problem of Identifying Growth of Boundary Shapes in a Multiple Region Domain
,”
Numer. Heat Transfer, Part A
,
35
, pp.
435
–
450
.
21.
Ingham, D. B., and Yuan, Y., 1994, The Boundary Element Method for Solving Improperly Posed Problems, Computational Mechanics Publications, Southampton, UK.
22.
Ingham
,
D. B.
, and
Yuan
,
Y.
,
1994
, “
Boundary Element Solutions of the Steady State, Singular, Inverse Heat Transfer Equation
,”
Int. J. Heat Mass Transf.
,
37
, Suppl. 1, pp.
273
–
280
.
23.
Hsieh
,
C. K.
,
Choi
,
C. Y.
, and
Liu
,
K. M.
,
1989
, “
Domain-Extension Method for Quantitative Detection of Cavities by Infrared Scanning
,”
J. Nondestruct. Eval.
,
8 pp.
195
–
211
.
24.
Reddy, J. N., 1984, An Introduction to the Finite Element Method, McGraw-Hill, New York, NY.
25.
Hildebrand, F. B., 1976, Advanced Calculus for Applications, 2nd Edition, Prentice-Hall, Englewood Cliffs, NJ.
26.
IMSL Library, 1997, Visual Numerics, Inc., 9990 Richmond Avenue, Suite 400, Houston, TX 77042.
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