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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: liucs@ntu.edu.tw
Department of Systems Engineering and Naval Architecture, National Taiwan Ocean University, Keelung 20224, Taiwan

Computers, Materials & Continua 2010, 15(1), 45-66. https://doi.org/10.3970/cmc.2010.015.045

Abstract

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.

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Cite This Article

APA Style
Chang, C., Liu, C., Chang, J. (2010). A quasi-boundary semi-analytical approach for two-dimensional backward heat conduction problems. Computers, Materials & Continua, 15(1), 45-66. https://doi.org/10.3970/cmc.2010.015.045
Vancouver Style
Chang C, Liu C, Chang J. A quasi-boundary semi-analytical approach for two-dimensional backward heat conduction problems. Comput Mater Contin. 2010;15(1):45-66 https://doi.org/10.3970/cmc.2010.015.045
IEEE Style
C. Chang, C. Liu, and J. Chang "A Quasi-Boundary Semi-Analytical Approach for Two-Dimensional Backward Heat Conduction Problems," Comput. Mater. Contin., vol. 15, no. 1, pp. 45-66. 2010. https://doi.org/10.3970/cmc.2010.015.045



cc Copyright © 2010 The Author(s). Published by Tech Science Press.
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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