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Technical Brief

On Elliptic Inverse Heat Conduction Problems

[+] Author and Article Information
M. Tadi

Department of Mechanical Engineering,
University of Colorado at Denver,
Campus Box 112,
P.O. Box 173364,
Denver, CO 80217-3364
e-mail: mohsen.tadi@ucdenver.edu

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received October 13, 2016; final manuscript received February 7, 2017; published online April 4, 2017. Assoc. Editor: George S. Dulikravich.

J. Heat Transfer 139(7), 074504 (Apr 04, 2017) (4 pages) Paper No: HT-16-1660; doi: 10.1115/1.4036006 History: Received October 13, 2016; Revised February 07, 2017

This note is concerned with a new method for the solution of an elliptic inverse heat conduction problem (IHCP). It considers an elliptic system where no information is given at part of the boundary. The method is iterative in nature. Starting with an initial guess for the missing boundary condition, the algorithm obtains corrections to the assumed value at every iteration. The updating part of the algorithm is the new feature of the present algorithm. The algorithm shows good robustness to noise and can be used to obtain a good estimate of the unknown boundary condition. A number of numerical examples are used to show the applicability of the method.

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Figures

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Fig. 1

A 2D domain for the error field with the over-specified boundary conditions, ey|y=0=∇nu−∇nû=η1(x)

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Fig. 2

The reduction in error for the first example as a function of the number of iterations. Only one set of data is used. The error is the difference between the given data and the computed normal derivative at the boundaries, i.e., ∫[∇nu(x)−∇nû(x)]2dx, for x ∈ Γ2.

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Fig. 3

The recovered function for Example 1 at different iterations. The figure also compares them to the actual function.

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Fig. 4

A cylindrical geometry

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Fig. 5

The reduction in error for Example 2 as a function of the number of iterations

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Fig. 6

The recovered function for Example 2 at different iterations. The figure also compares them to the actual function.

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Fig. 7

The reduction in error for Example 3 as a function of the number of iterations

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Fig. 8

The recovered function for Example 3 at different iterations. The figure also compares them to the actual function.

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