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Research Papers: Conduction

A Modified Conjugate Gradient Method for Transient Nonlinear Inverse Heat Conduction Problems: A Case Study for Identifying Temperature-Dependent Thermal Conductivities

[+] Author and Article Information
Miao Cui, Xiaowei Gao

Faculty of Vehicle Engineering and Mechanics,
School of Aeronautics and Astronautics,
State Key Laboratory of Structural Analysis for
Industrial Equipment,
Dalian University of Technology,
Dalian 116024, China

Qianghua Zhu

Faculty of Vehicle Engineering and Mechanics,
School of Aeronautics and Astronautics,
State Key Laboratory of Structural Analysis for
Industrial Equipment,
Dalian University of Technology,
Dalian 116024, China
e-mail: zhuqianghua80@126.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 17, 2013; final manuscript received April 27, 2014; published online June 17, 2014. Assoc. Editor: Giulio Lorenzini.

J. Heat Transfer 136(9), 091301 (Jun 17, 2014) (7 pages) Paper No: HT-13-1490; doi: 10.1115/1.4027771 History: Received September 17, 2013; Revised April 27, 2014

Despite numerous studies of conjugate gradient methods (CGMs), the “sensitivity problem” and the “adjoint problem” are inevitable for nonlinear inverse heat conduction problems (IHCPs), which are accompanied by some assumptions and complicated differentiating processes. In this paper, a modified CGM (MCGM) is presented for the solution of a specified transient nonlinear IHCP, to recover temperature-dependent thermal conductivities for a case study. By introducing the complex-variable-differentiation method (CVDM) for sensitivity analysis, the sensitivity problem and the adjoint problem are circumvented. Five test examples are given to validate and assess the performance of the MCGM.

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Figures

Grahic Jump Location
Fig. 1

Positions of the measurement points

Grahic Jump Location
Fig. 2

The convergence history of the two recovered parameters A = 11.309 and B = 0.00431

Grahic Jump Location
Fig. 3

The objective function with the iteration number

Grahic Jump Location
Fig. 4

The convergence history for temperature-dependent thermal conductivities at specified temperatures

Grahic Jump Location
Fig. 5

The objective function with the iteration number

Grahic Jump Location
Fig. 6

Recovered thermal conductivities at specified temperatures with different measurement errors

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