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A Quasi-Boundary Semi-Analytical Approach for Two-Dimensional Backward Heat Conduction Problems

Chih-Wen Chang1, Chein-Shan Liu2, Jiang-Ren Chang3

Grid Application Division, National Center for High-Performance Computing, Taichung 40763,Taiwan
Department of Civil Engineering, National Taiwan University, Taipei 10617, Taiwan. Corresponding author, Tel.:+886-2-33664233. E-mail:
Department of Systems Engineering and Naval Architecture, National Taiwan Ocean University, Keelung 20224, Taiwan

Computers, Materials & Continua 2010, 15(1), 45-66.


In this article, we propose a semi-analytical method to tackle the two-dimensional backward heat conduction problem (BHCP) by using a quasi-boundary idea. First, the Fourier series expansion technique is employed to calculate the temperature field u(x, y, t) at any time t < T. Second, we consider a direct regularization by adding an extra termau(x, y, 0) to reach a second-kind Fredholm integral equation for u(x, y, 0). The termwise separable property of the kernel function permits us to obtain a closed-form regularized solution. Besides, a strategy to choose the regularization parameter is suggested. When several numerical examples were tested, we find that the proposed scheme is robust and applicable to the two-dimensional BHCP.


Cite This Article

C. . Chang, C. . Liu and J. . Chang, "A quasi-boundary semi-analytical approach for two-dimensional backward heat conduction problems," Computers, Materials & Continua, vol. 15, no.1, pp. 45–66, 2010.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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