Image-based numerical prediction for effective thermal conductivity of heterogeneous materials: A quadtree based scaled boundary finite element method

Abstract

Integrating advantages of the quadtree technique, the SBFEM, the image-based modelling approach, and inverse analysis, a new numerical technique is presented for the evaluation of Effective Thermal Conductivity (ETC) of heterogeneous materials. The quadtree technique provides a convenient way for mesh generation, and facilitates to image-based analysis. The inconvenience of hanging nodes caused in the quadtree mesh generation can be naturally avoided by SBFEM, consequently the temperature solutions of heterogeneous materials can be determined by the combination of quadtree technique and SBFEM, and are partially regarded as ‘experiments values’ for equivalent homogeneous materials. Utilizing a group of such ‘experiments’, the ETC can be obtained by solving a group of inverse heat transfer problems of parameters identification. Numerical examples are provided to demonstrate the effectiveness of the proposed approach, and the impacts of distributions and shapes of inclusions, and volume fractions are taken into account.