TECHNICAL PAPERS: Conductive Heat Transfer

On the Solution of Multidimensional Inverse Heat Conduction Problems Using an Efficient Sequential Method

[+] Author and Article Information
H. M. Park, W. S. Jung

Department of Chemical Engineering, Sogang University, Seoul, Korea

J. Heat Transfer 123(6), 1021-1029 (Apr 19, 2001) (9 pages) doi:10.1115/1.1409260 History: Received October 13, 2000; Revised April 19, 2001
Copyright © 2001 by ASME
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Lausterer,  G. K., and Ray,  W. H., 1979, “Distributed Parameter State Estimation and Optimal Feedback Control—An Experimental Study in Two Space Dimensions,” IEEE Trans. Autom. Control, AC-24, pp. 179.
Nulman,  J., Krusius,  J. P., and Gat,  A., 1985, “Rapid Thermal Processing of Thin Gate Dielectrics-Oxidation of Silicon,” IEEE Electron Device Lett., EDL-6, pp. 205.
Beck, J. V., Blackwell, B., and St. Clair, Jr., C. R., 1985, Inverse Heat Conduction: Ill-Posed Problems, Wiley-Interscience, New York.
Jarney,  Y., Özisik,  M. N., and Bardon,  J. P., 1991, “A General Optimization Method Using Adjoint Equation for Solving Multidimensional Inverse Heat Conduction,” Int. J. Heat Mass Transf., 34, pp. 2911–2919.
Kalman,  R. E., and Bucy,  R. S., 1961, “New Results in Linear Filtering and Prediction Theory,” ASME J. Basic Eng., 38D, pp. 95–108.
Grewal, M. S., and Andrews, A. P., 1993, Kalman Filtering, Prentice Hall, Englewood Cliffs, New Jersey.
Jazwinski, A. H., 1970, Stochastic Processes and Filtering Theory, Academic Press, New York.
Scarpa,  F., and Milano,  G., 1995, “Kalman Smoothing Technique Applied to the Inverse Heat Conduction Problem,” Numer. Heat Transfer, Part B, 28, pp. 79–96.
Kaipio,  J., and Somersalo,  E., 1999, “Nonstationary Inverse Problems and State Estimation,” J. Inverse and Ill-Posed Problems, 7, pp. 273–282.
Park,  H. M., and Cho,  D. H., 1996, “Low Dimensional Modeling of Flow Reactors,” Int. J. Heat Mass Transf., 39, pp. 3311–3323.
Park,  H. M., and Lee,  M. W., 1998, “An Efficient Method of Solving the Navier-Stokes Equations for Flow Control,” Int. J. Numer. Methods Eng., 41, pp. 1131–1151.
Park,  H. M., Chung,  O. Y., and Lee,  J. H., 1999, “On the Solution of Inverse Heat Transfer Problem Using the Karhunen-Loève Galerkin Method,” Int. J. Heat Mass Transf., 42, pp. 127–142.
Loève, M., 1977, Probability Theory, Fourth ed., Springer, New York.
Courant, R., and Hilbert, D., 1962, Methods of Mathematical Physics, Vol. 1, Wiley-Interscience, New York.


Grahic Jump Location
The system and relevant boundary conditions
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Definition of shape functions: (a) temporal shape functions; and (b) spatial shape functions.
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Empirical eigenfunctions: (a) the first eigenfunction (λ1=0.741); (b) the second eigenfunction (λ2=0.156); (c) the third eigenfunction (λ3=4.969×10−2); (d) the fourth eigenfunction (λ4=2.127×10−2); (e) the 17th eigenfunction (λ17=2.351×10−4); (f) the 18th eigenfunction (λ18=1.787×10−4); (g) the 19th eigenfunction (λ19=1.391×10−4); and (h) the 20th eigenfunction (λ20=1.127×10−4).
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The estimated profiles of wall heat flux: (a) q(x,t) for the case a (Eq. 27); and (b) q(x,t) for the case b (Eq. 28).
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The effect of initially assumed values of ai(t=0) and q(x,t=0) on the accuracy of the estimation: (a) wall heat flux; and (b) temperature field.
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Estimated q(x,t) from the corrupted temperature measurements: (a) 3 percent relative measurement error; and (b) 15 percent relative measurement error.
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The effect of the number of measurement points on the accuracy of estimation: (a) 10 measurement points; and (b) 50 measurement points.
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The effect of measurement location on the accuracy of estimation



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