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Journal of Applied Mathematics
Volume 2015, Article ID 203404, 9 pages
Research Article

Analytical Solution of Heat Conduction for Hollow Cylinders with Time-Dependent Boundary Condition and Time-Dependent Heat Transfer Coefficient

1Department of Mechanical Engineering, Air Force Institute of Technology, No. 198 Jieshou W. Road, Gangshan Township, Kaohsiung 820, Taiwan
2Department of Mechanical Engineering, National Cheng Kung University, No. 1 University Road, Tainan 701, Taiwan

Received 5 May 2015; Accepted 21 July 2015

Academic Editor: Assunta Andreozzi

Copyright © 2015 Te-Wen Tu and Sen-Yung Lee. 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 analytical solution for the heat transfer in hollow cylinders with time-dependent boundary condition and time-dependent heat transfer coefficient at different surfaces is developed for the first time. The methodology is an extension of the shifting function method. By dividing the Biot function into a constant plus a function and introducing two specially chosen shifting functions, the system is transformed into a partial differential equation with homogenous boundary conditions only. The transformed system is thus solved by series expansion theorem. Limiting cases of the solution are studied and numerical results are compared with those in the literature. The convergence rate of the present solution is fast and the analytical solution is simple and accurate. Also, the influence of physical parameters on the temperature distribution of a hollow cylinder along the radial direction is investigated.