Analytical Solution of Heat Conduction for Hollow Cylinders with Time-Dependent Boundary Condition and Time-Dependent Heat Transfer Coefficient
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 i...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2015/203404 |
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| author | Te-Wen Tu Sen-Yung Lee |
| author_facet | Te-Wen Tu Sen-Yung Lee |
| author_sort | Te-Wen Tu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-0a268a3cf5214d89895f40f8365d2020 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-0a268a3cf5214d89895f40f8365d20202025-02-03T05:50:18ZengWileyJournal of Applied Mathematics1110-757X1687-00422015-01-01201510.1155/2015/203404203404Analytical Solution of Heat Conduction for Hollow Cylinders with Time-Dependent Boundary Condition and Time-Dependent Heat Transfer CoefficientTe-Wen Tu0Sen-Yung Lee1Department of Mechanical Engineering, Air Force Institute of Technology, No. 198 Jieshou W. Road, Gangshan Township, Kaohsiung 820, TaiwanDepartment of Mechanical Engineering, National Cheng Kung University, No. 1 University Road, Tainan 701, TaiwanAn 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.http://dx.doi.org/10.1155/2015/203404 |
| spellingShingle | Te-Wen Tu Sen-Yung Lee Analytical Solution of Heat Conduction for Hollow Cylinders with Time-Dependent Boundary Condition and Time-Dependent Heat Transfer Coefficient Journal of Applied Mathematics |
| title | Analytical Solution of Heat Conduction for Hollow Cylinders with Time-Dependent Boundary Condition and Time-Dependent Heat Transfer Coefficient |
| title_full | Analytical Solution of Heat Conduction for Hollow Cylinders with Time-Dependent Boundary Condition and Time-Dependent Heat Transfer Coefficient |
| title_fullStr | Analytical Solution of Heat Conduction for Hollow Cylinders with Time-Dependent Boundary Condition and Time-Dependent Heat Transfer Coefficient |
| title_full_unstemmed | Analytical Solution of Heat Conduction for Hollow Cylinders with Time-Dependent Boundary Condition and Time-Dependent Heat Transfer Coefficient |
| title_short | Analytical Solution of Heat Conduction for Hollow Cylinders with Time-Dependent Boundary Condition and Time-Dependent Heat Transfer Coefficient |
| title_sort | analytical solution of heat conduction for hollow cylinders with time dependent boundary condition and time dependent heat transfer coefficient |
| url | http://dx.doi.org/10.1155/2015/203404 |
| work_keys_str_mv | AT tewentu analyticalsolutionofheatconductionforhollowcylinderswithtimedependentboundaryconditionandtimedependentheattransfercoefficient AT senyunglee analyticalsolutionofheatconductionforhollowcylinderswithtimedependentboundaryconditionandtimedependentheattransfercoefficient |