Estimation Of Effective Thermal Conductivity For Heterogeneous Materials Based On Quadtree-SBFEM

Heterogeneous materials play an important role in many engineering applications.The Effective Thermal Conductivity(ETC)is one of the most important parameters for the applications and design of the heterogeneous materials.Generally the analytical solution and numerical solution are two mainly used methods in this field.The analytical models are usually based on some assumptions of the inclusions with the shape and distribution,and the results could be affected by the volume fraction.Therefore,it is of interest to develop the numerical models for estimating the ETC.A challenge for numerical computations for ETC is that the conventional FEM could require large number of meshes due to the heterogeneous inclusions,causing huge computational cost,especially for the analysis considering the random distribution of inclusions.In this paper,a new numerical method based on quadtree/octree-SBFEM is proposed for heat transfer analysis,and a new inverse analysis method is presented for estimating the ETC of 2D and 3D heterogeneous material based on the quadtree/octree-SBFEM.The advantage include: 1.The quadtree/octree is a kind of technique suitable for adaptively generating the mesh and image-based analysis.2.The SBFEM can naturally avoid the difficulties due to the ‘hanging node' by constructing arbitrary polygon elements.The contribution of this thesis includes:1.Combining quadtree/octree mesh with SBFEM,the numerical models are established for 2D and 3D heat transfer problems.Compared with ANSYS,the numerical method proposed in this paper can obtain the same accuracy results with fewer elements for both 2D and 3D cases.2.In order to estimate the ETC of 2D and 3D heterogeneous material,a technique based on the solving of inverse heat transfer problem is proposed.In the method,the temperature field obtained from quadtree/octree SBFEM is used as ‘artificial measurement',and the ETC is regarded as the unknown to be identified.The Gauss-Newton method is employed to solve this inverse problem.With the computation for large number of samples,the influence of the shape of inclusions and random distribution for ETC are researched.The numerical results of the proposed method agree well with the analytical models,and even perform better as the volume fraction is increased compared with the analytical models.3.In the process of both the heat transfer analysis and the estimation of ETC,all the computation is based on the image-based analysis,and the computational results have good convergence with the number of pixels/voxels.The work of this paper will provide a valuable reference for the numerical computations of heat transfer problem,the prediction of ETC for heterogeneous material and image-based analysis.