Inverse determination of temperature-dependent thermal conductivity using steady surface data on arbitrary objects

An inverse computational method has been developed for the nonintrusive and nondestructive evaluation of the temperature-dependence of thermal conduct ivity. 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 th e specimen, in addition to a finite number of steady-state surface temperat ure measurements, the algorithm can predict the variation of thermal conduc tivity over the entire range of measured temperatures. Thus, this method re quires only one temperature probe and one heat flux probe. The thermal cond uctivity dependence on temperature (k-T curve) can be completely arbitrary, although a priori knowledge of the general form of the k-T curve substanti ally improves the accuracy of the algorithm. The influence of errors of mea sured surface temperatures and heat fluxes on the predicted thermal conduct ivity has been evaluated. It was found that measurement errors of temperatu re up to five percent standard deviation were not magnified by this inverse procedure, while the effect of errors in measured heat fluxes were even lo wer. The method is applicable to two-dimensional and three-dimensional soli ds of arbitrary shape and size.