Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 2861342, 9 pages
https://doi.org/10.1155/2017/2861342
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.

Linked References

  1. C. Sheng, Direct And Inverse Heat Conduction Problems Solving by The Boundary Element Method, Hunan University, 2007.
  2. K. A. Woodbury, J. V. Beck, and H. Najafi, “Filter solution of inverse heat conduction problem using measured temperature history as remote boundary condition,” International Journal of Heat and Mass Transfer, vol. 72, pp. 139–147, 2014. View at Publisher · View at Google Scholar · View at Scopus
  3. L. Zhu, G. Wang, and H. Chen, “Estimating steady multi-variables inverse heat conduction problem by using conjugate gradient method,” Proceedings of the Chinese Society of Electrical Engineering, vol. 31, no. 8, pp. 58–61, 2011. View at Google Scholar
  4. L. Zhu, Fuzzy Inverse for Two-Dimensional Steady Heat Conduction System And Application, Chongqing University.
  5. M. Cui, W.-W. Duan, and X.-W. Gao, “Conjugate Gradient Method Based on Complex-variable-differentiation Method and Its Application for Identification of Boundary Conditions in Inverse Heat Conduction Problem,” CIESC Journal, vol. 90, supplement 1, pp. 106–110, 2015. View at Google Scholar
  6. X. Yu, INverse Analysis of Thermal Conductivities in Non-Homogeneous Heat Conductions Using Boundary Element Method, Dalian University of Technology, 2013.
  7. Z. Qian, “Optimal modified method for a fractional-diffusion inverse heat conduction problem,” Inverse Problems in Science and Engineering, vol. 18, no. 4, pp. 521–533, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. B. T. Johansson, D. Lesnic, and T. Reeve, “A method of fundamental solutions for the radially symmetric inverse heat conduction problem,” International Communications in Heat and Mass Transfer, vol. 39, no. 7, pp. 887–895, 2012. View at Publisher · View at Google Scholar · View at Scopus
  9. S. Tapaswini, S. Chakraverty, and D. Behera, “Numerical solution of the imprecisely defined inverse heat conduction problem,” Chinese Physics B, vol. 24, no. 5, Article ID 050203, 2015. View at Publisher · View at Google Scholar · View at Scopus
  10. P. Duda, “Numerical and experimental verification of two methods for solving an inverse heat conduction problem,” International Journal of Heat and Mass Transfer, vol. 84, pp. 1101–1112, 2015. View at Publisher · View at Google Scholar · View at Scopus
  11. Y. B. Wang, J. Cheng, J. Nakagawa, and M. Yamamoto, “A numerical method for solving the inverse heat conduction problem without initial value,” Inverse Problems in Science and Engineering, vol. 18, no. 5, pp. 655–671, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. Q. Xue and w. Wei, “Parameters identification of non-linear inverse heat conduction problem,” Engineering Mechanics, vol. 27, no. 8, pp. 5–9, 2010. View at Google Scholar
  13. L. Wang, L. Mei, and J. Huang, “Inverse heat conduction problem based on least squares prediction,” CIESC Journal, vol. 67, supplement 1, pp. 103–110, 2016. View at Google Scholar
  14. N. Yaparova, “Numerical methods for solving a boundary-value inverse heat conduction problem,” Inverse Problems in Science and Engineering, vol. 22, no. 5, pp. 832–847, 2014. View at Google Scholar
  15. N. Tian, Numerical Methods for The PDE-Based Inverse Problems and Applications, Jiangnan University, 2012.
  16. H. Zhou, X. Xu, X. Li, and H. Chen, “Identification of temperature-dependent thermal conductivity for 2-d transient heat conduction problems,” Applied Mathematics and Mechanics, vol. 12, no. 35, pp. 1341–1351, 2014. View at Google Scholar
  17. V. L. Baranov, A. A. Zasyad'ko, and G. A. Frolov, “Integro-differential method of solving the inverse coefficient heat conduction problem,” Journal of Engineering Physics and Thermophysics, vol. 83, no. 1, pp. 60–71, 2010. View at Publisher · View at Google Scholar · View at Scopus
  18. H. Wu, Heat Conduction Problem Solving By Boundary Element Method, National Defence Industry Press, Beijing, China, 2008.
  19. L. J. M. Jesus, C. A. Cimini, and E. L. Albuquerque, “Application of the radial integration method into dynamic formulation of anisotropic shallow shells using boundary element method,” Key Engineering Materials, vol. 627, pp. 465–468, 2015. View at Publisher · View at Google Scholar · View at Scopus
  20. X. W. Gao, “The radial integration method for evaluation of domain integrals with boundary-only discretization,” Engineering Analysis with Boundary Elements, vol. 26, no. 10, pp. 905–916, 2002. View at Publisher · View at Google Scholar · View at Scopus
  21. S. Qu, S. Li, H.-R. Chen, and Z. Qu, “Radial integration boundary element method for acoustic eigenvalue problems,” Engineering Analysis with Boundary Elements, vol. 37, supplement 6-7, pp. 1043–1051, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  22. M.-W. Liu, Y.-R. Zheng, and Y.-F. Zhang, “A new inversion method of rock-soils parameters based on complex-variable-differentiation method,” Chinese Journal of Computational Mechanics, vol. 26, no. 5, pp. 676–683, 2009. View at Google Scholar · View at Scopus
  23. J. N. Lyness and C. B. Moler, “Numerical differentiation of analytic functions,” SIAM Journal on Numerical Analysis, vol. 4, pp. 202–210, 1967. View at Publisher · View at Google Scholar · View at MathSciNet
  24. S. Kim, J. Ryu, and M. Cho, “Numerically generated tangent stiffness matrices using the complex variable derivative method for nonlinear structural analysis,” Computer Methods in Applied Mechanics and Engineering, vol. 200, no. 1-4, pp. 403–413, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus