A new method for identifying temperature-dependent thermal conductivity in transient heat conduction problems based on element differential method

Abstract

In order to accurately identify the temperature-dependent thermal conductivity of solids, a novel method which combines the element differential method (EDM) with the modified Levenberg-Marquardt algorithm (LMA) is firstly proposed to solve the inverse heat conduction problems, where complex variable derivative method (CVDM) is introduced to obtain the derivatives of the observed temperature with respect to the unknown variables. In this paper, the conventional EDM is transformed from the real domain to the complex domain, and then the transient heat conduction problems with complex-variable temperature-dependent thermal conductivity are solved to obtain the numerical temperature solutions of the measuring points using the EDM. The real part of numerical temperature and the corresponding measured temperature are used to build the objective function, and the imaginary part of numerical temperature is used to calculate the sensitivity coefficients of the LMA using the CVDM. Thus, the LMA is modified to stably obtain the sensitivity of the temperature to the unknown variables, and it is used to iteratively optimize the unknown temperature-dependent thermal conductivity by minimizing the objective function. Finally, three numerical examples with the different forms of temperature-dependent thermal conductivity are considered in this paper, and the effects of the different initial values and measurement errors on the inversion results are fully investigated. The results show that the proposed method shows good accuracy, efficiency and robustness in identifying the temperature-dependent thermal conductivity with specific function and that without function form in 2D and 3D models.