A LINEAR INVERSE MODEL FOR THE TEMPERATURE-DEPENDENT THERMAL-CONDUCTIVITY DETERMINATION IN ONE-DIMENSIONAL PROBLEMS

A direct procedure is presented for the inverse determination of the t hermal conductivity in the one-dimensional heat conduction problem. A linear inverse model is proposed to estimate the thermal conductivity. The model is constructed from the approximated model of the heal equa tion when the temperature measurements are available in the problem do main. Distinguishing features of the proposed model are that the itera tions in the process can be done only once and that the inverse proble m can be solved in a linear domain. This provides a contrast to the tr aditional approach, which needs numerous iterations in the computing p rocess and is operated in a nonlinear domain. Results from the example s confirm that the proposed method is applicable in solving the therma l conductivity in inverse heat conduction problems. The result shows t hat the exact solution can be found when measurement errors are neglec ted. When measurement errors are considered, the close agreement betwe en the exact solutions and the estimated results shows the potential o f the proposed model in finding the accurate value of the thermal cond uctivity in one-dimensional heat conduction problems. (C) 1998 Elsevie r Science Inc. All rights reserved.