Effect of different thermal conductivity functions on temperature fields in FGM

It is usually very difficult to obtain the analytical solution of thermal conduction problems for functionally graded materials (FGMs). Therefore, a numerical method is of great importance. The method of lines (MOLs) is introduced to solve the temperature field of FGM. The basic idea of the method is to semi-discretized the governing equation of problem into a system of ordinary differential equations (ODEs) defined on discrete lines by means of the finite difference method. The functions of thermal properties are directly embodied in these equations. Then, the temperature field of FGM can be obtained by solving the ODEs. As a numerical example, the temperature field of a plane problem for three kinds of material thermal property functions is analyzed by the MOLs. Then, the effect of different material thermal property functions on the temperature field is discussed.