## 留言板

 引用本文: 周焕林, 徐兴盛, 李秀丽, 陈豪龙. 反演二维瞬态热传导问题随温度变化的导热系数[J]. 应用数学和力学, 2014, 35(12): 1341-1351.
ZHOU Huan-lin, XU Xing-sheng, LI Xiu-li, CHEN Hao-long. Identification of Temperature-Dependent Thermal Conductivity for 2-D Transient Heat Conduction Problems[J]. Applied Mathematics and Mechanics, 2014, 35(12): 1341-1351. doi: 10.3879/j.issn.1000-0887.2014.12.006
 Citation: ZHOU Huan-lin, XU Xing-sheng, LI Xiu-li, CHEN Hao-long. Identification of Temperature-Dependent Thermal Conductivity for 2-D Transient Heat Conduction Problems[J]. Applied Mathematics and Mechanics, 2014, 35(12): 1341-1351.

• 中图分类号: TK124

## Identification of Temperature-Dependent Thermal Conductivity for 2-D Transient Heat Conduction Problems

Funds: The National Natural Science Foundation of China（11072073）
• 摘要: 基于边界元法反演二维瞬态热传导问题随温度变化的导热系数.采用Kirchhoff变换将非线性的控制方程转变为线性方程.边界元法用于构建二维瞬态热传导问题的数值分析模型.将反演参数作为优化变量，测点温度计算值与测量值之间的残差平方和作为优化目标函数.引入复变量求导法求解目标函数的梯度矩阵，梯度正则化法用于优化目标函数获得反演结果.探讨时间步长、测点数量和随机偏差对反演结果的影响.减小步长、增加测点数量收敛速度加快.降低了随机偏差，计算结果更精确.算例证明了算法的有效性与稳定性.
•  [1] Huang C H, Yan J Y. An inverse problem in simultaneously measuring temperature-dependent thermal conductivity and heat capacity[J]. International Journal of Heat and Mass Transfer,1995,38(18): 3433-3441. [2] Huang C H, Chin S C. A two-dimensional inverse problem in imaging the thermal conductivity of a non-homogeneous medium[J]. International Journal of Heat and Mass Transfer,2000,43(22): 4061-4071. [3] Cui M, Gao X W, Zhang J B. A new approach for the estimation of temperature-dependent thermal properties by solving transient inverse heat conduction problems[J]. International Journal of Thermal Sciences,2012,58: 113-119. [4] 贺国强, 孟泽红. 求解热传导反问题的一种正则化Newton型迭代法[J]. 应用数学和力学, 2007,28(4): 479-486.(HE Guo-qiang, MENG Ze-hong. A Newton type iterative method for heat-conduction inverse problems[J]. Applied Mathematics and Mechanics,2007,28(4): 479-486.(in Chinese)) [5] Lesnic D, Elliott L, Ingham D B. Identification of the thermal conductivity and heat capacity in unsteady nonlinear heat conduction problems using the boundary element method[J]. Journal of Computational Physics,1996,126(2): 410-420. [6] 薛齐文, 魏伟, 杨海天. 多宗量瞬态热传导反演识别[J]. 固体力学学报, 2009,30(1): 65-69.(XUE Qi-wen, WEI Wei, YANG Hai-tian. Parameters identification of inverse heat conduction problems in transient state with multi-variables[J]. Chinese Journal of Solid Mechanics,2009,30(1): 65-69.(in Chinese)) [7] 唐中华, 钱国红, 钱炜祺. 材料热传导系数随温度变化函数的反演方法[J]. 计算力学学报, 2011,28(3): 377-382.(TANG Zhong-hua, QIAN Guo-hong, QIAN Wei-qi. Estimation of temperature-dependent function of thermal conductivity for a material[J]. Chinese Journal of Computational Mechanics,2011,28(3): 377-382.(in Chinese)) [8] Zhang W H, Xie G N, Zhang D. Application of an optimization method and experiment in inverse determination of interfacial heat transfer coefficients in the blade casting process[J]. Experimental Thermal and Fluid Science,2010,34(8): 1068-1076. [9] Chang C L, Chang M. Inverse determination of thermal conductivity using semi-discretization method[J]. Applied Mathematical Modelling,2009,33(3): 1644-1655. [10] 王登刚, 刘迎曦, 李守巨. 非线性二维热传导反问题的混沌正则化混合解法[J]. 应用数学和力学,2002,23(8): 864-870.(WANG Deng-gang, LIU Ying-xi, LI Shou-ju. Chaos-regularization hybrid algorithm for nonlinear two-dimensional inverse heat conduction problem[J]. Applied Mathematics and Mechanics,2002,23(8): 864-870.(in Chinese)) [11] 程荣军, 程玉民. 带源参数的热传导反问题的无网格方法[J]. 物理学报, 2007,56(10): 5569-5574.(CHENG Rong-jun, CHENG Yu-min. The meshless method for solving the inverse heat conduction problem with a source parameter[J]. Acta Physica Sinica,2007,56(10): 5569-5574. (in Chinese)) [12] 钱炜祺, 何开锋, 汪清. 三维非稳态热传导逆问题反演算法研究[J]. 力学学报, 2008,40(5): 611-618.(QIAN Wei-qi, HE Kai-feng, WANG Qing. Inverse estimation of heat source term in three-dimensional transient heat conduction problem[J]. Chinese Journal of Theoretical and Applied Mechanics,2008,40(5): 611-618.(in Chinese)) [13] 张涛, 卢玫, 李博汉, 陶亮. 用于寻源导热反问题的自适应蚁群算法研究[J]. 应用数学和力学, 2014,35(7): 823-830.(ZHANG Tao, LU Mei, LI Bo-han, TAO Liang. Study of self-adaptive ant colony optimization for heat source search in inverse heat conduction problems[J]. Applied Mathematics and Mechanics,2012,35(7): 823-830.(in Chinese)) [14] Lyness N, Moler C B. Numerical differentiation of analytic functions[J]. SIAM Journal on Numerical Analysis,1967,4(2): 202-210.
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##### 出版历程
• 收稿日期:  2014-07-23
• 修回日期:  2014-10-25
• 刊出日期:  2014-12-15

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