Precise Integral Algorithm Based Solution for Transient Inverse Heat Conduction Problems With Multi-Variables

WANG Yi-bo; YANG Hai-tian; WU Rui-feng

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Article Navigation > Applied Mathematics and Mechanics > 2005 > 26(5): 512-518

WANG Yi-bo, YANG Hai-tian, WU Rui-feng. Precise Integral Algorithm Based Solution for Transient Inverse Heat Conduction Problems With Multi-Variables[J]. Applied Mathematics and Mechanics, 2005, 26(5): 512-518.

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Precise Integral Algorithm Based Solution for Transient Inverse Heat Conduction Problems With Multi-Variables

1.
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P. R. China;

Received Date: 2003-11-11
Rev Recd Date: 2005-02-01
Publish Date: 2005-05-15

Abstract

Abstract

By modeling direct transient heat conduction problems via finite element method (FEM) and precise integral algorithm, a new approach is presented to solve transient inverse heat conduction problems with multi-variables. Firstly, the spatial space and temporal domain are discretized by FEM and precise integral algorithm respectively. Then, the high accuracy semi-analytical solution of direct problem can be got. Finally, based on the solution, the computing model of inverse problem and expression of sensitivity analysis are established. Single variable and variables combined identifications including thermal parameters, boundary conditions and source-related terms etc. are given to validate the approach proposed in 1-D and 2-D cases. The effects of noise data and initial guess on the results are investigated. The numerical examples show the effectiveness of this approach.
- heat conduction,
- inverse problem,
- multi-variables,
- precise integral algorithm,
- finite element

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References(11)

References

[1]	Huang C H, Yan J Y. An inverse problem in simultaneously measuring temperature-dependent thermal conductivity and heat capacity[J].Int J Heat and Mass Transfer,1995,38(18):3433—3441. doi: 10.1016/0017-9310(95)00059-I
[2]	Tervola P.A method to determine the thermal conductivity from measured temperature profile[J].Int J Heat and Mass Transfer,1989,32(8):1425—1430. doi: 10.1016/0017-9310(89)90066-5
[3]	Huang C H, Chao B H. An inverse geometry problem in identifying irregular boundary configurations[J].Int J Heat and Mass Transfer,1997,40(9):2045—2053. doi: 10.1016/S0017-9310(96)00280-3
[4]	Huang C H, Osizik M N. Inverse problem of determining unknown wall heat flux in laminar flow through a parallel plate duct[J].Numerical Heat Transfer, Part A,1992,21(1):55—70. doi: 10.1080/10407789208944865
[5]	Huang C H, Osizik M N. Optimal regularization method to determine the unknown strength of a surface heat source[J].Int J of Heat and Fluid Flow,1991,12(2):173—178. doi: 10.1016/0142-727X(91)90045-W
[6]	Refahi A K, Yvon J. Determination of heat sources and heat transfer coefficient for two-dimensional heat flow-numerical and experimental study[J].Int J Heat and Mass Transfer,2001,44(7):1309—1322. doi: 10.1016/S0017-9310(00)00186-1
[7]	Tseng A A, Chen T C, Zhao F Z. Direct sensitivity coefficient method for solving two-dimensional inverse heat conduction problems by finite-element scheme[J].Numerical Heat Transfer, Part B,1995,27(3):291—307. doi: 10.1080/10407799508914958
[8]	Zhong W X, Williams F W. A precise time step integration method[J].J Mech Eng Sci,Part C，1994,208(6):427—430. doi: 10.1243/PIME_PROC_1994_208_148_02
[9]	蔡志勤.逐步积分及其部分演化[D].博士论文,大连:大连理工大学,1998,17—38.
[10]	王勖成,邵敏.有限单元法基本原理和数值方法[M].北京:清华大学出版社,1997，421—728.
[11]	王德人.非线性方程组解法与最优化方法[M].北京:人民教育出版社,1979，236—261.