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

ZHOU Huan-lin; XU Xing-sheng; LI Xiu-li; CHEN Hao-long

doi:10.3879/j.issn.1000-0887.2014.12.006

Volume 35 Issue 12

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Article Navigation > Applied Mathematics and Mechanics > 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

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

doi: 10.3879/j.issn.1000-0887.2014.12.006

School of Civil Engineering, Hefei University of Technology, Hefei 230009, P.R.China

Funds: The National Natural Science Foundation of China（11072073）

Received Date: 2014-07-23
Rev Recd Date: 2014-10-25
Publish Date: 2014-12-15

Abstract

Abstract

The temperature-dependent thermal conductivity was identified for 2-D transient heat conduction problems with the boundary element method (BEM). The nonlinear governing equations were transformed into linear ones through the Kirchhoff transformation. The BEM was used to build the numerical model for the 2-D transient heat conduction problems. The inversion parameters were defined as the optimization variables. The quadratic sum of residual errors between the calculated temperature values and the measured temperature values at the measuring points was regarded as the objective function. The complex variable differentiation method was employed to compute the gradient matrix of the objective function. The gradient-regulation method was developed to optimize the objective function. Effects of the time step length, the number of measuring points and the random noise on the inverse results were discussed. With decrease of the time step length and increase of the number of the measuring points, the converging rate quickens. With decrease of the random noise, the results grow accurate. Numerical tests show the effectiveness and stability of the presented method.
- boundary element method,
- inverse problem,
- transient heat conduction,
- thermal conductivity,
- gradient-regulation method

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References

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