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Method of lines for temperature field of functionally graded materials

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Abstract

The finite element method (FEM) and the boundary element method (BEM) are often adopted. However, they are not convenient to spatially vary thermal properties of functionally graded material (FGM). Therefore, the method of lines (MOL) is introduced to solve the temperature field of FGM. The basic idea of the method is to semi-discretize the governing equation 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. The functions of thermal properties are directly embodied in these equations and these properties are not discretized in the domain. Thus, difficulty of FEM and BEM is overcome by the method. As a numerical example, the temperature field of a plane problem is analyzed for FGMs through varying thermal conductivity coefficient by the MOL.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Armored Force Engineering Institute, 100072, Beijing, China

    Dai Yao PhD (Professor), Sun Qi, Hao Gui-xiang, Yan Xiu-fa & Li Yong-dong

Authors
  1. Dai Yao PhD
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  2. Sun Qi
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  3. Hao Gui-xiang
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  4. Yan Xiu-fa
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  5. Li Yong-dong
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Correspondence to Dai Yao PhD.

Additional information

Foundation item: Project (90305023 and 59731020) supported by the National Natural Science Foundation of China

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Dai, Y., Sun, Q., Hao, Gx. et al. Method of lines for temperature field of functionally graded materials. J Cent. South Univ. Technol. 12, 230–232 (2005). https://doi.org/10.1007/s11771-005-0047-4

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  • DOI: https://doi.org/10.1007/s11771-005-0047-4

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