Open Access

ARTICLE

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

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

1 Grid Application Division, National Center for High-Performance Computing, Taichung 40763,Taiwan
2 Department of Civil Engineering, National Taiwan University, Taipei 10617, Taiwan. Corresponding author, Tel.:+886-2-33664233. E-mail: liucs@ntu.edu.tw
3 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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Keywords

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