The Study of Heat Conduction in Functionally Graded Plate Based on Hybrid Numerical Method Loading by Linear Heat Source

Abstract

In this paper, a physical model of functionally graded materials (FGM) with a linear change of volume fraction of ceramic and metal in its thickness direction is established. The thermal conductivity of the FGM under a linear heat source is studied by a hybrid numerical method. Based on the weighted residual method, the heat conduction equation under a third boundary condition is studied using a hybrid numerical method which takes into account both the accuracy of the analytical method and the efficiency of the finite element method. A linear heat source is applied to the FGM, the temperature of the heat source changes linearly with time, and the temperature distribution in the space-time domain is obtained by finite element discretization in one direction and Fourier transform in the other. The results show that the closer to the heat source, the greater influence of the heat source it is. The influence of the heat source is local, which is similar to the influence of the force field on structure described by Saint Venant theory. In the heat transfer process, the heat transfer efficiency of each surface is different, that is closely related to the material properties. Using this proposed physical model, it is demonstrated that FGM can avoid the sudden change of temperature and relieve the thermal stress.