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Mathematical Problems in Engineering
Volume 2017, Article ID 2861342, 9 pages
Research Article

Solution to Two-Dimensional Steady Inverse Heat Transfer Problems with Interior Heat Source Based on the Conjugate Gradient Method

1School of Control and Mechanical Engineering, Tianjin Chengjian University, Tianjin 300384, China
2School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China

Correspondence should be addressed to Shoubin Wang; moc.621@008nibsw

Received 5 February 2017; Revised 14 May 2017; Accepted 28 May 2017; Published 11 July 2017

Academic Editor: Francisco Alhama

Copyright © 2017 Shoubin Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The compound variable inverse problem which comprises boundary temperature distribution and surface convective heat conduction coefficient of two-dimensional steady heat transfer system with inner heat source is studied in this paper applying the conjugate gradient method. The introduction of complex variable to solve the gradient matrix of the objective function obtains more precise inversion results. This paper applies boundary element method to solve the temperature calculation of discrete points in forward problems. The factors of measuring error and the number of measuring points zero error which impact the measurement result are discussed and compared with L-MM method in inverse problems. Instance calculation and analysis prove that the method applied in this paper still has good effectiveness and accuracy even if measurement error exists and the boundary measurement points’ number is reduced. The comparison indicates that the influence of error on the inversion solution can be minimized effectively using this method.