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TECHNICAL PAPERS: Conduction Heat Transfer

Estimation of Surface Temperature and Heat Flux Using Inverse Solution for One-Dimensional Heat Conduction

[+] Author and Article Information
Masanori Monde, Hirofumi Arima, Yuhichi Mitsutake

Department of Mechanical Engineering, Saga University, Saga 840-8502, Japan

J. Heat Transfer 125(2), 213-223 (Mar 21, 2003) (11 pages) doi:10.1115/1.1560147 History: Received October 21, 2001; Revised October 25, 2002; Online March 21, 2003
Copyright © 2003 by ASME
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References

Alifanov, O. M., 1994, Inverse Heat Transfer Problems, Springer-Verlag, pp. 5–8.
Beck, J. V., Blackwell, B., and Clair, C. R., 1985, Inverse Heat Conduction, Wiley-Interscience.
Hsieh,  C. K., and Su,  K. C., 1980, “A Methodology of Predicting Cavity Geometry Based on Scanned Surface Temperature Data—Prescribed Surface Temperature at the Cavity Side,” ASME J. Heat Transfer, 102(2), pp. 324–329.
Bell,  G. E., 1984, “An Inverse Solution for the Steady Temperature Field within a Solidified Layer,” Int. J. Heat Mass Transf., 27(12), pp. 2331–2337.
Lithouhi,  B., and Beck,  J. V., 1986, “Multinode Unsteady Surface Element Method with Application to Contact Conductance Problem,” ASME J. Heat Transfer, 108(2), pp. 257–263.
Shoji,  M., and Ono,  N., 1988, “Application of the Boundary Element to the Inverse Problem of Heat Conduction (in Japanese),” Trans. Jpn. Soc. Mech. Eng., Ser. B, 54–506, pp. 2893–2900.
Frankel,  J. I., 1997, “A Global Time Treatment for Inverse Heat Conduction Problems,” ASME J. Heat Transfer, 119(4), pp. 673–683.
Burggraf,  O. R., 1964, “An Exact Solution of the Inverse Problem in Heat Conduction Theory and Application,” ASME J. Heat Transfer, 86, pp. 373–382.
Sparrow,  E. M., Haji-Sheikh,  A., and Lundgren,  T. S., 1964, “The Inverse Problem in Transient Heat Conduction,” ASME J. Appl. Mech., 86, pp. 369–375.
Imber,  M., and Khan,  J., 1972, “Prediction of Transient Temperature Distributions With Embedded Thermo-couples,” AIAA J., 10(6), pp. 784–789.
Imber,  M., 1974, “Temperature Extrapolation Mechanism for Two-Dimensional Heat Flow,” AIAA J., 12(8), pp. 1089–1093
Shoji,  M., 1978, “Study of Inverse Problem of Heat Conduction (in Japanese),” Trans. Jpn. Soc. Mech. Eng., 44(381), pp. 1633–1643.
Monde,  M., 2000, “Analytical Method in Inverse Heat Transfer Problem Using Laplace Transform Technique,” Int. J. Heat Mass Transf., 43, pp. 3965–3975.
Monde,  M., Arima,  H., and Mitsutake,  Y., 2000, “Analytical Method In Inverse Heat Transfer Problem Using Laplace Transform Technique—Second And Third Boundary Conditions,” 3rd European thermal Science Conference 2000, Sept. 10–13, Heidelberg.
Monde,  M., and Mitsutake,  Y., 2001, “A New Estimation Method of Thermal Diffusivity Using Analytical Inverse Solution for One Dimensional Heat Conduction,” Int. J. Heat Mass Transf., 44(16), pp. 3169–3177.
Carslaw, H. S., and Jaeger, J. C., 1959, Conduction of Heat in Solids, Oxford Univ. Press.
Kim,  S. K., and Lee,  W. I., 2002, “Solution of Inverse Heat Conduction Problems Using Maximum Entropy Method,” Int. J. Heat Mass Transf., 45(2), pp. 381–391.
Chantasiriwan,  S., 1999, “Comparison of Three Sequential Function Specification Algorithms for the Inverse Heat Conduction Problem,” Int. Commun. Heat Mass Transfer, 16(1), pp. 115–124.
Taler,  J., 1996, “A Semi-Numerical Method for Solving Inverse Heat Conduction Problem,” Heat Mass Transfer, 31, pp. 105–111.

Figures

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(a) Sketch illustrating two measuring points for rectangular coordinates; and (b) Sketch illustrating two measuring points for cylindrical and spherical coordinates
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Approximate solution, Eq. (12) for temperature change at a point (heavy solid line: exact solution, o: data with uncertainties)
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(a) Estimated surface temperature Case 1; (b) Estimated surface temperature Case 2; (c) Estimated surface temperature Case 4; and (d) Estimated surface temperature Case 5.
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(a) Estimated surface heat flux Case 3; and (b) Estimated surface heat flux Case 4.
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Effect of measuring point on accuracy of solution (Case 3, Heat flux)
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Effect of data uncertainty on accuracy of solution (Case 1)
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Comparison between the present, MEM and CGM 17 methods for rectangular change
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Comparison between the present, MEM and CGM 17 methods for triangular change

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