An inverse computational method has been developed for the nonintrusive and nondestructive evaluation of the temperature-dependence of thermal conductivity. The methodology is based on an inverse computational procedure that can be used in conjunction with an experiment. Given steady-state heat flux measurements or convection heat transfer coefficients on the surface of the specimen, in addition to a finite number of steady-state surface temperature measurements, the algorithm can predict the variation of thermal conductivity over the entire range of measured temperatures. Thus, this method requires only one temperature probe and one heat flux probe. The thermal conductivity dependence on temperature $(k-T$ curve) can be completely arbitrary, although a priori knowledge of the general form of the $k-T$ curve substantially improves the accuracy of the algorithm. The influence of errors of measured surface temperatures and heat fluxes on the predicted thermal conductivity has been evaluated. It was found that measurement errors of temperature up to five percent standard deviation were not magnified by this inverse procedure, while the effect of errors in measured heat fluxes were even lower. The method is applicable to two-dimensional and three-dimensional solids of arbitrary shape and size. [S0022-1481(00)01703-5]

1.
Annual Book of Standards, 1997, Section 4, Vol. 04.06, Thermal Insulation; Environmental Acoustics, ASTM Designation: C 177-97.
2.
Beck, J. V., Blackwell, B., and St. Clair, C. R., 1985, Inverse Heat Conduction: III-Posed Problems, John Wiley and Sons, New York.
3.
Alifanov, O. M., 1994, Inverse Heat Transfer Problems, Springer-Verlag, Berlin.
4.
Artyukhin, E. A., 1993, “Iterative Algorithms for Estimating Temperature-Dependent Thermophysical Characteristics,” Proceedings of Inverse Problems in Engineering, Theory and Practice, N. Zabaras, et al., eds., ASME, New York, pp. 101–108.
5.
Beck, J. V., and Arnold, K. J., 1997, Parameter Estimation in Engineering and Science, John Wiley and Sons, New York.
6.
Orlande, H. R. B., and Ozisik, M. N., 1993, “Determination of the Reaction Function in a Reaction-Diffusion Parabolic Problem,” Inverse Problems in Engineering: Theory and Practice, N. Zabaras et al., eds., ASME, New York, pp. 117–124.
7.
Dantas
,
L. B.
, and
Orlande
,
H. R. B.
,
1996
, “
A Function Estimation Approach for Determining Temperature-Dependent Thermophysical Properties
,”
Inverse Probl. Eng.
,
3
, No.
4
, pp.
261
280
.
8.
Lam
,
T. T.
, and
Yeung
,
W. K.
,
1995
, “
Inverse Determination of Thermal Conductivity for One-Dimensional Problems
,”
J. Thermophys. Heat Transfer
,
9
, No.
2
, pp.
335
344
.
9.
Yang
,
C.-Y.
,
1997
, “
Non-Iterative Solution of Inverse Heat Conduction Problems in One Dimension
,”
Commun. Numer. Meth. Eng.
,
13
, pp.
419
427
.
10.
Huang
,
C.-H.
,
Yan
,
J.-Y.
, and
Chen
,
H.-T.
,
1995
, “
Function Estimation in Predicting Temperature-Dependent Thermal Conductivity Without Internal Measurements
,”
AIAA J. Thermophys. Heat Transf.
,
9
, No.
4
, Oct.–Dec., pp.
667
673
.
11.
Sawaf
,
B.
,
Ozisik
,
M. N.
, and
Jarny
,
Y.
,
1995
, “
An Inverse Analysis to Estimate Linearly Temperature Dependent Thermal Conductivity Components and Heat Capacity of an Orthotropic Medium
,”
Int. J. Heat Mass Transf.
,
38
, No.
16
, pp.
3005
3010
.
12.
13.
Hansen, P. C., 1997, Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion, SIAM, Philadelphia, PA.
14.
Dulikravich, G. S., and Martin, T. J., 1996, “Inverse Shape and Boundary Condition Problems and Optimization in Heat Conduction,” Advances in Numerical Heat Transfer, W. J. Minkowycz and E. M. Sparrow, eds., Taylor & Francis, London, pp. 324–367.
15.
Martin, T. J., and Dulikravich, G. S., 1997, “Non-Iterative Inverse Determination of Temperature-Dependent Heat Conductivities,” Symposium on Inverse Design Problems in Heat Transfer and Fluid Flow, Vol. 2, G. S. Dulikravich, and K. A. Woodbury, eds., ASME, New York, pp. 141–150.
16.
Banerjee, P. K., and Raveendra, S. T., 1981, Boundary Element Methods in Engineering Science, McGraw-Hill, London.
17.
Brebbia, C. A., 1978, The Boundary Element Method for Engineers, John Wiley and Sons, New York.
18.
Martin
,
T. J.
, and
Dulikravich
,
G. S.
,
1996
, “
Inverse Determination of Boundary Conditions in Steady Heat Conduction with Heat Generation
,”
ASME J. Heat Transfer
,
118
, No.
3
,pp.
546
554
.
19.
Brebbia, C. A., and Dominguez, J., 1989, Boundary Elements: An Introductory Course, McGraw-Hill, New York.
20.
Tikhonov, A. N., and Arsenin, V. Y., 1977, Solutions of Ill-Posed Problems, V. H. Winston, Washington, DC.
21.
Golub, G. H., and Van Loan, C. F., 1996, Matrix Computations, 3rd Ed., Johns Hopkins Press, Baltimore, MD.
22.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., 1986, Numerical Recipes in FORTRAN, The Art of Scientific Computing, 2nd Ed., Cambridge University Press, Cambridge, UK.
23.
Twomey
,
S.
,
1963
, “
On the Numerical Solution of Fredholm Integral Equations of the First Kind by the Inversion of the Linear System Produced by Quadrature
,”
J. Assoc. Comput. Mach.
,
10
, No.
1
, pp.
78
101
.
24.
Barsky, B. A., 1988, Computer Graphics and Geometric Modeling Using Beta-Splines, Springer-Verlag, Berlin.
25.
Chapman, A. J., 1960, Heat Transfer, McMillan, New York.
26.
Ho, C. Y., Powell, R. W., and Liley P. E., 1974, Thermal Conductivity of the Elements: A Comprehensive Review, Journal of Physical and Chemical Reference Data, Vol. 3, Supplement No. 1.