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Mathematical Problems in Engineering
Volume 2013, Article ID 816385, 8 pages
Research Article

Analytic Solutions for Heat Conduction in Functionally Graded Circular Hollow Cylinders with Time-Dependent Boundary Conditions

Department of Mechanical Engineering, National Cheng Kung University, Tainan 701, Taiwan

Received 16 May 2013; Revised 27 June 2013; Accepted 1 July 2013

Academic Editor: Abdelouahed Tounsi

Copyright © 2013 Sen-Yung Lee and Chih-Cheng Huang. 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.


An analytic solution method, without integral transformation, is developed to find the exact solutions for transient heat conduction in functionally graded (FG) circular hollow cylinders with time-dependent boundary conditions. By introducing suitable shifting functions, the governing second-order regular singular differential equation with variable coefficients and time-dependent boundary conditions is transformed into a differential equation with homogenous boundary conditions. The exact solution of the system with thermal conductivity and specific heat in power functions with different orders is developed. Finally, limiting studies and numerical analyses are given to illustrate the efficiency and the accuracy of the analysis.