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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Main Authors: Te-Wen Tu, Sen-Yung Lee
Format: Article
Language:English
Published: Wiley 2015-01-01
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
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publishDate 2015-01-01
publisher Wiley
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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