Method of Lines to Solve 2-D Steady Temperature Field of FGM
Method of Lines (MOLs) is introduced to solve 2-Dimension steady temperature field of functionally graded materials (FGMs). The main idea of the method is to semi–discretized the governing equation of thermal transfer problem into a system of ordinary differential equations (ODEs) defined on discrete lines by means of the finite difference method. The temperature field of FGM can be obtained by solving the ODEs with functions of thermal properties. As numerical examples, six kinds of material thermal conductivity functions, i.e. three kinds of polynomial functions, an exponent function, a logarithmic function, and a sine function are selected to simulate spatial thermal conductivity profile in FGMs respectively. The steady-state temperature fields of 2-D thermal transfer problem are analyzed by the MOLs. Numerical results show that different material thermal conductivity function has obvious different effect on the temperature field.
Yu Zhou, Shan-Tung Tu and Xishan Xie
W. Tan et al., "Method of Lines to Solve 2-D Steady Temperature Field of FGM", Key Engineering Materials, Vols. 353-358, pp. 2003-2006, 2007