Boundary element analysis of heat conduction problems in anisotropic media with variable coefficients

doi:10.3969/j.issn.0438-1157.2014.z1.009

Abstract

Abstract: A method for establishing fundamental solutions of general variable coefficient heat conduction problems in anisotropic media using the boundary element method was presented. The pure boundary integral equation is derived for solving general two- and three- dimensional steady heat conduction problems in anisotropic media. The established fundamental solutions are suitable for the situation that the thermal conductivity is a function of spatial coordinates, and therefore the developed integral equation can be used to solve the heterogeneous material heat transfer problems. The domain integrals induced by heat sources can be transformed into a boundary integral using the radial integral method, so a pure boundary element method which does not need any interior points is formed. Three examples for two- and three- dimensional problems are provided and the correctness and effectiveness of the proposed method is validated by comparing the results using the current method with that of using finite element method.

Key words: boundary element method, anisotropy, steady state, heat conduction, fundamental solution, radial integration method, numerical analysis

摘要： 提出了一种用边界元法求解一般变系数各向异性热传导问题时建立基本解的方法，并导出了求解一般二维和三维各向异性稳态热传导问题的纯边界积分方程。所建立的基本解考虑了热导率是空间坐标的函数，因此所导出的积分方程可用于求解非均质材料传热问题。由热源项引起的域积分，运用径向积分法将其转换成边界积分，形成不需要内部点的纯边界元算法。给出了二维和三维问题3个分析算例，并通过将边界元法结果与有限元法结果进行对比，证明了方法的正确性和有效性。

关键词: 边界元法, 各向异性, 稳态, 热传导, 基本解, 径向积分法, 数值分析

CLC Number:

TK124

GAO Xiaowei, ZHAO Jinjun, LIU Jian, HU Jinxiu. Boundary element analysis of heat conduction problems in anisotropic media with variable coefficients[J]. CIESC Journal, 2014, 65(S1): 51-60.

高效伟, 赵金军, 刘健, 胡金秀. 变系数各向异性热传导问题边界元解法[J]. 化工学报, 2014, 65(S1): 51-60.

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