This work presents a comparative study of two alternative procedures for the estimation of surface temperature of a heated body from transient interior temperature measurements. This Inverse Heat Conduction Problem (IHCP) is solved (in both procedures) by using the Function Specification Method. A numerical test was used in order to compare the best estimation achieved in each procedure. The influences of the time step size, the total number of measurements and the noise level in the measurement have been considered in the estimation. Two criteria (minimization of total error and residual principle [3] are used to choose the best hyper-parameter (r). The comparisons confirm that the procedures and criteria used provide similar results, nevertheless this study reveals slight differences with respect to the accurate and the CPU time.

Issue Section:
Technical Notes
Keywords:
Conduction, Heat Transfer, Inverse, Numerical Methods, temperature measurement, inverse problems, heat conduction, estimation theory
Topics:
Errors, Heat conduction, Temperature, Temperature measurement, Noise (Sound)
1.
Beck, J. V., Blackwell, B., and St. Clair, C. R., 1985, Inverse Heat Conduction, Ill-Posed Problems, Wiley-Interscience, New York.
2.
Tikhonov, A. N., and Arsenin, V. Y., 1977, Solution of Ill-Posed Problems, V. H. Winston & Sons, Washington, DC.
3.
Alifanov, O. M., 1994, Inverse Heat Transfer Problems, Springer, New York.
4.
Murio, D. A., 1993, The Mollification Method and the Numerical Solution of Ill-Posed Problems, Wiley-Interscience, New York.
5.
Beck
,
J. V.
,
Litkouhi
,
B.
, and
St. Clair
, Jr.,
C. R.
,
1982
, “
Efficient Sequential Solution of the Nonlinear Heat Conduction Problem
,”
Numer. Heat Transfer
,
5
, pp.
275
–
286
.
6.
Blanc
,
G.
,
Raynaud
,
M.
, and
Chau
,
T. C.
,
1998
, “
A Guide for the Use of the Function Specification Method for 2D Inverse Heat Conduction Problems
,”
Rev. Ge´n. Therm. Elsevier.
,
37
, pp.
17
–
30
.
7.
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
.
8.
Matsevityi
,
Yu. M.
,
Maliarenko
,
V. A.
, and
Multanovskii
,
A. V.
,
1979
, “
Identification of Time-Variable Coefficients of Heat Transfer by Solving a Nonlinear Inverse Problem of Heat Conduction
,”
J. Eng. Phys.
,
35
(
3
), pp.
1094
–
1098
.
9.
Woodbury, K. A., and Jin X., 1995, “A Temperature-Based Sequential Specification Algorithm for the IHCP,” National Heat Transfer Conference, HTD Vol. 312, pp. 141–150.
10.
Flach
,
G. P.
, and
O¨zis¸ik
,
M. N.
,
1988
, “
Inverse Heat Conduction Problem of Periodically Contacting Surfaces
,”
ASME J. Heat Transfer
,
110
, pp.
821
–
829
.
11.
Carslaw, H. S., and Jaeger, J. C., 1959, Conduction of Heat in Solids, Oxford University Press, London.
12.
Blanc
,
G.
,
Beck
,
J. V.
, and
Raynaud
,
M.
,
1997
, “
Solution of the Inverse Heat Conduction Problem With a Time-Variable Numbers of Future Temperatures
,”
Numer. Heat Transfer, Part B
,
32
, pp.
437
–
451
.
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