Transient and steady-state heat conduction analysis of two-dimensional functionally graded materials using particle method

The moving-particle semi-implicit (MPS) method, one of the particle methods, is an effective numerical simulation method for incompressible inviscid flows with free surfaces. The discretization scheme of the particle method can be utilized for discretizations of gradient, divergence and Laplace operators in the partial differential equations such as the diffusion equation and the wave equation. In recent years, advanced materials known as Functionally Graded Materials (FGMs) have drawn considerable interest. These FGMs are expected to be highly heat resistant materials that can be used under high temperature and high temperature gradient conditions. Because of this, it is important to investigate the temperature distributions in the FGMs. The purpose of this work is to present a numerical analysis of the heat conduction for two-dimensional FGMs where the thermal conductivity is a function of the spatial coordinates using the particle method. Analytical solutions and finite element solutions are compared with the present results, and the validity of the present method is shown.