Open AccessInverse heat conduction problems by using particular solutions
Author(s) -
Wen P.H.,
Hon Y.C.,
Xu Y.G.
Publication year - 2011
Publication title -
heat transfer—asian research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.41
H-Index - 30
eISSN - 1523-1496
pISSN - 1099-2871
DOI - 10.1002/htj.20335
Subject(s) - thermal conduction , laplace transform , mathematics , singular value decomposition , inverse problem , algebraic equation , inverse , heat equation , mathematical analysis , algorithm , physics , thermodynamics , nonlinear system , geometry , quantum mechanics
Based on the method of fundamental solutions, we develop in this paper a new computational method to solve two‐dimensional transient heat conduction inverse problems. The main idea is to use particular solutions as radial basis functions (PSRBF) for approximation of the solutions to the inverse heat conduction problems. The heat conduction equations are first analyzed in the Laplace transformed domain and the Durbin inversion method is then used to determine the solutions in the time domain. Least‐square and singular value decomposition (SVD) techniques are adopted to solve the ill‐conditioned linear system of algebraic equations obtained from the proposed PSRBF method. To demonstrate the effectiveness and simplicity of this approach, several numerical examples are given with satisfactory accuracy and stability. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20335