Numerical algorithm for estimating temperature-dependent thermal conductivity

The hybrid scheme of the Laplace transform technique and the central difference approximation is applied to estimate the temperature-dependent thermal conductivity by utilizing temperature measurements inside the material at an arbitrary specified time. In the present study the functional form of the thermal conductivity is not known a priori. Thus, this problem can be regarded as the functional estimation in inverse calculation. The accuracy of the predicted results is examined from various illustrated cases using simulated exact and inexact temperature measurements obtained within the medium. Results show that a good estimation on the thermal conductivity can be obtained with any arbitrary initial guesses of the thermal conductivity. The advantage of the present method in the inverse analysis is that, for most types of boundary conditions, the relation between the thermal conductivity and temperature at any specified time can be determined without measuring the early temperature data.