In recent years, the engineering technologies, which help to reduce over design of structure sizes, is being applied to deliver multi-function. As we simulate the mechanical behaviors for these advanced structures or materials brought by the new technologies, it becomes nonsense to characterize the macroscopic behavior without considering local heterogeneities. On the other hand, many experimental efforts came up with the evaluation of characteristics of the advanced structure. The multi-scale analyses, which can be applied to micro-structural design, have been proposed in order to reduce the development period and experimental efforts. Though the various multi-scale analyses have been widely applied to mechanics and dynamics, they have not been applied with great success in the field of thermal problem, which is an important issue for structural design.
@@We have proposed the formulation of heat transfer problem based on the mesh superposition method, which is one of the multi-scale analyses with two independent finite element meshes and spotlighted in the stress analysis field. One is eglobal meshf expressed with objective whole area roughly. The other is elocal meshf, which is including local heterogeneity and expressed microscopic area in detail. The advanced point of the proposed method is that it enables to reduce efforts of modeling. According to the formulation, the computer program for the unsteady heat transfer problem has been developed. Moreover, accuracy of our proposed method and the program has been made certain with a brick model containing an inclusion. By comparing our proposed method with that of conventional finite element method, it has been verified that the developed program has good accuracy and the proposed method is useful to the structural design.

Keywords : Multi-scale Numerical Analysis, Finite Element Method, Mesh Superposition Method, Unsteady-state Transfer Analysis, Local Heterogeneity