Inverse Determination of Temperature-Dependent Thermal Conductivity Using Steady Surface Data on Arbitrary Objects

Abstract

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]