A general and novel approach for predicting the effective thermal conductivity for randomly generated porous media by solving inverse heat conduction problems

Porous media are widely used in scientific research and engineering applications, where the effective thermal conductivity (ETC) serves as a critical thermo-physical parameter governing heat transfer behaviors. However, accurately predicting the ETC remains a significant challenge. In this paper, a novel approach is introduced for predicting the ETC of porous media, which is general and could be even employed to determine temperature-dependent nonlinear or anisotropic ETC. Firstly, the heat conduction problem in porous media is solved by using the finite element method to obtain temperature data. Subsequently, based on the acquired temperature data, the Levenberg-Marquardt (LM) algorithm is combined with the equivalent model to predict the ETC of porous media by solving the corresponding inverse heat conduction problem. Finally, the predicted ETC values are compared with theoretical models and experimental data, and the predicted temperatures of the equivalent model are compared with those of the porous media model. The results demonstrate that the proposed method can efficiently and accurately determine the isotropic or anisotropic ETC of porous media with high reliability, stability, and robustness, regardless of the linear or nonlinear physical properties and the randomness and complexity of the structures. An advantage of the approach is that it only requires temperature data, which does not rely on heat flux measurements. • A general method is proposed to predict the ETC of porous media by using FEM and LM algorithm. • The method can predict the ETC with higher accuracy compared with other theoretical methods. • The method is efficient and accurate for predicting the nonlinear ETC with the IPC experiment. • The method is accurate to predict the anisotropic ETC with high stability and good robustness.