Estimation of the temperature-dependent thermal conductivity in inverse heat conduction problems

An iterative approach is presented to determine the temperature-dependent thermal conductivity from the temperature measurements taken at one side of boundary. On the basis of the proposed method, the undetermined thermal conductivity is first denoted as the unknown variables in a set of nonlinear equations, which are formulated from the measured temperature and the calculated temperature. Then, a linearization method is used to solve the set of nonlinear equations. In the examples, one sensor is used to measure the temperature profile whether the measurement errors are included or excluded. The results show that the speed of convergence is considerably fast, since the number of iterations to approach a satisfied solution is within nine to eleven times. Comparisons between the exact thermal conductivity and the estimated ones are made to confirm the validity of the proposed method. The close agreement between the exact solutions and the estimated results show's the potential of the proposed method in finding the accurate value of the temperature-dependent thermal conductivity in inverse heat conduction problem. (C) 1999 Elsevier Science Inc. All rights reserved.