A regularized integral equation method for the inverse geometry heat conduction problem

International Journal of Heat and Mass Transfer

Volumn 51, Issue 21-22, 2008, Pages 5380-5388

  Liu, Chein Shan ^a   Chang, Chih Wen ^a   Chiang, Chia Yen ^a  

^a NATIONAL TAIWAN OCEAN UNIVERSITY   (Taiwan)

Author keywords

Collocation method; Fourier series; Fredholm integral equation; Inverse geometry heat conduction problem; Lavrentiev regularization; Regularized solution; Two point boundary value problem

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; DIFFERENTIAL EQUATIONS; DIFFRACTIVE OPTICAL ELEMENTS; ELECTRIC CURRENTS; FOURIER ANALYSIS; FOURIER SERIES; HARMONIC ANALYSIS; HEAT CONDUCTION; INITIAL VALUE PROBLEMS; LAPLACE EQUATION;

COLLOCATION METHOD; FREDHOLM INTEGRAL EQUATION; INVERSE GEOMETRY HEAT CONDUCTION PROBLEM; LAVRENTIEV REGULARIZATION; REGULARIZED SOLUTION; TWO-POINT BOUNDARY VALUE PROBLEM;

INTEGRAL EQUATIONS;

EID: 51349169389     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijheatmasstransfer.2008.02.043     Document Type: Article

References (19)

1. Alifanov O.M. Solution of an inverse problem of heat conduction by iteration methods. J. Eng. Phys. 26 (1972) 471-476
2. Huang C.H., and Ozisik M.N. Inverse problem of determining unknown wall heat flux in laminar flow through a parallel plate duct. Numer. Heat Transfer A 21 (1992) 55-70
3. Huang C.H., Ozisik M.N., and Sawaf B. Conjugate gradient method for determining unknown contact conductance during metal casting. Int. J. Heat Mass Transfer 35 (1992) 1779-1786
4. Huang C.H., and Yan J.Y. An inverse problem in simultaneously measuring temperature dependent thermal conductivity and heat capacity. Int. J. Heat Mass Transfer 38 (1995) 3433-3441
5. Huang C.H., and Chao B.H. An inverse geometry problem in identifying irregular boundary configurations. Int. J. Heat Mass Transfer 40 (1997) 2045-2053
6. Huang C.H., and Hsiung T.Y. An inverse design problem of estimating optimal shape of cooling passages in turbine blades. Int. J. Heat Mass Transfer 42 (1999) 4307-4319
7. Huang C.H., and Chen H.M. An inverse geometry problem of identifying growth of boundary shapes in a multiple region domain. Numer. Heat Transfer A 35 (1999) 435-450
8. Huang C.H., and Shih C.C. Identify the interfacial configurations in a multiple region domain problem. AIAA J. Thermophys. Heat Transfer 19 (2005) 533-541
9. Huang C.H., and Shih C.C. A shape identification problem in estimating simultaneously two interfacial configurations in a multiple region domain. Appl. Therm. Eng. 26 (2006) 77-88
10. Cheng C.H., and Chang M.H. A simplified conjugate-gradient method for shape identification based on thermal data. Numer. Heat Transfer B 43 (2003) 489-507
11. Huang C.H., and Chiang C.C. Shape identification problem in estimating geometry of multiple cavities. AIAA J. Thermophys. Heat Transfer 12 (1998) 270-277
12. Hsieh C.K., and Su K.C. A methodology of predicting cavity geometry based on the scanned surface temperature data-prescribed surface temperature at the cavity side. J. Heat Transfer 102 (1980) 324-329
13. Das S., and Mitra A. An algorithm for the solution of inverse Laplace problems and its application in flaw identification in materials. J. Comput. Phys. 99 (1992) 99-105
14. Kassab A.J., and Pollard J. A cubic spline anchored grid pattern algorithm for high resolution detection of subsurface cavities by the IR-CAT method. Numer. Heat Transfer B 26 (1994) 63-78
15. Liu C.-S. Elastic torsion bar with arbitrary cross-section using the Fredholm integral equations. CMC: Comput. Mater. Continua 5 (2007) 31-42
16. Liu C.-S. A meshless regularized integral equation method for Laplace equation in arbitrary interior or exterior plane domains. CMES: Comput. Model. Eng. Sci. 19 (2007) 99-109
17. Liu C.-S. A MRIEM for solving the Laplace equation in the doubly-connected domain. CMES: Comput. Model. Eng. Sci. 19 (2007) 145-161
18. Lavrentiev M.M. Some Improperly Posed Problems of Mathematical Physics (1967), Springer, New York
19. Marsaglia G., MacLaren M.D., and Bray T.A. A fast procedure for generating normal random variables. Commun. ACM 7 (1964) 4-10