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Research Papers

Evaluation of a Diffusion Coefficient Based on Proper Solution Space

[+] Author and Article Information
Yuanlong Wang

Department of Mechanical Engineering,
University of Colorado Denver,
Denver, CO 80204
e-mail: yuanlong.wang@ucdenver.ed

Abdalkaleg Hamad

Department of Mechanical Engineering,
University of Colorado Denver,
Denver, CO 80204
e-mail: abdalkaleg.hamad@ucdenver.edu

Mohsen Tadi

Department of Mechanical Engineering,
University of Colorado Denver,
Campus Box 112, P.O. Box 17336,
Denver, CO 80217
e-mail: mohsen.tadi@ucdenver.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received February 10, 2018; final manuscript received July 30, 2018; published online October 23, 2018. Assoc. Editor: Steve Q. Cai.

J. Thermal Sci. Eng. Appl 11(1), 011017 (Oct 23, 2018) (5 pages) Paper No: TSEA-18-1079; doi: 10.1115/1.4041343 History: Received February 10, 2018; Revised July 30, 2018

This note is concerned with the evaluation of the unknown diffusion coefficient in a steady-state heat conduction problem. The proposed method is iterative and, starting with an initial guess, updates the assumed value at every iteration. The updating stage is achieved by generating a set of functions that satisfy some of the required boundary conditions. The correction to the assumed value is then computed by imposing the remaining boundary conditions. Numerical examples are used to study the applicability of this method.

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References

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Figures

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Fig. 2

Recovered conductivity after 174 iterations for Exam. 1

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Fig. 3

Error reduction for Exam. 1 as a function of the number of iteration

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Fig. 1

Thermal conductivity for Exam. 1

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Fig. 4

Thermal conductivity for Exam. 2

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Fig. 5

Recovered conductivity after 700 iterations for Exam. 2

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Fig. 6

Error reduction for Exam. 2 as a function of the number of iteration

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Fig. 7

Comparison of the recovered and the actual conductivity at the diagonal cross section for Exam. 2

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Fig. 8

Comparison of the recovered and the actual conductivity at the diagonal cross section for Exam. 2 for different levels of noise

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Fig. 9

Thermal conductivity for Exam. 3

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Fig. 10

Recovered conductivity for Exam. 3

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Fig. 11

Comparison of the recovered and the actual conductivity at the diagonal cross section for Exam. 3 for two values of β

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Fig. 12

Error reduction for Exam. 2 as a function of the number of iteration

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