A linear inverse model for the temperature-dependent thermal conductivity determination in one-dimensional problems

Abstract

A direct procedure is presented for the inverse determination of the thermal 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 heat equation when the temperature measurements are available in the problem domain. Distinguishing features of the proposed model are that the iterations in the process can be done only once and that the inverse problem can be solved in a linear domain. This provides a contrast to the traditional approach, which needs numerous iterations in the computing process and is operated in a nonlinear domain. Results from the examples confirm that the proposed method is applicable in solving the thermal conductivity in inverse heat conduction problems. The result shows that the exact solution can be found when measurement errors are neglected. When measurement errors are considered, the close agreement between the exact solutions and the estimated results shows the potential of the proposed model in finding the accurate value of the thermal conductivity in one-dimensional heat conduction problems.