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TECHNICAL PAPERS

Recursive Identification of Thermal Convection

[+] Author and Article Information
H. M. Park, W. J. Lee

Department of Chemical Engineering, Sogang University, Seoul, Korea

J. Dyn. Sys., Meas., Control 125(1), 1-10 (Mar 10, 2003) (10 pages) doi:10.1115/1.1540116 History: Received January 01, 2001; Revised September 01, 2002; Online March 10, 2003
Copyright © 2003 by ASME
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References

Series,  R. W., and Hurle,  D. T. J., 1991, “The Use of Magnetic Fields in Semiconductor Crystal Growth,” J. Cryst. Growth, 113, pp. 305–328.
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Grewal, M. S., and Andrews, A. P., 1993, Kalman Filtering, Prentice Hall, Englewood Cliffs, NJ.
Park,  H. M., and Cho,  D. H., 1996, “Low Dimensional Modeling of Flow Reactors,” Int. J. Heat Mass Transf., 39, pp. 3311–3323.
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Loève, M., 1977, Probability Theory, 4th Edition, Springer-Verlag, New York.
Park,  H. M., and Lee,  J. H., 1998, “A Method of Solving Inverse Convection Problems by Means of Mode Reduction,” Chem. Eng. Sci., 53, pp. 1731–1744.
Park,  H. M., and Kim,  O. Y., 2000, “A Reduction Method for the Boundary Control of the Heat Conduction Equation,” ASME J. Dyn. Syst. Meas., Control, 122, pp. 435–444.
Drazin, P. G., and Reid, W. H., 1981, Hydrodynamic Stability, Cambridge University Press, Cambridge.
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Figures

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(a) The system and boundary conditions. Typical flow pattern and isotherms are depicted as well as the measurement locations (indicated by small circles): (b) and (c) heat flux functions q(x).
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The velocity and temperature empirical eigenfunctions: (a) the first velocity eigenfunction (λ1=0.901308), (b) the 19th velocity eigenfunction (λ19=4.20815×10−5), (c) the first temperature eigenfunction (λ1=0.800822), and (d) the 32nd temperature eigenfunction (λ32=5.64908×10−6)
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Relative errors and estimated heat flux from various methods when q(x) is given by Fig. 1b and only temperature measurements are used: (a) velocity errors, (b) temperature errors, and (c) estimated heat flux
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Relative errors and estimated heat flux from various methods when q(x) is given by Fig. 1c: (a) velocity errors, (b) temperature errors, and (c) estimated heat flux
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Relative errors when q(x) is given by Fig. 1b and velocity as well as temperature measurements are used: (a) velocity errors and (b) temperature errors
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Relative errors and estimated heat flux when q(x) is given by Fig. 1b and the temperature measurements with 5% noise are used: (a) velocity errors, (b) temperature errors, and (c) estimated heat flux

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