Open Access

ARTICLE

A New Quasi-Boundary Scheme for Three-Dimensional Backward Heat Conduction Problems

Chih-Wen Chang¹

1 Grid Application Technology Division, National Center for High-Performance Computing,Taichung 40763, Taiwan. Tel.:+886-4-24620202#860. Fax.: +886-4-24627373. E-mail address:0903040@nchc.narl.org.tw

Computers, Materials & Continua 2011, 24(3), 209-238. https://doi.org/10.3970/cmc.2011.024.209

Abstract

In this study, we employ a semi-analytical scheme to resolve the three-dimensional backward heat conduction problem (BHCP) by utilizing a quasi-bound -ary concept. First, the Fourier series expansion method is used to estimate the temperature field u(x, y, z, t) at any time t < T. Second, we ponder a direct regularization by adding an extra term a(x, y, z, 0) to transform a second-kind Fredholm integral equation for u(x, y, z, 0). The termwise separable property of the kernel function allows us to acquire a closed-form regularized solution. In addition, a tactic to determine the regularization parameter is recommended. We find that the proposed method is robust and applicable to the three-dimensional BHCP when several numerical experiments are examined.

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Keywords

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