Application of Heat Balance Integral Methods to One-Dimensional Phase Change Problems
We employ the Heat Balance Integral Method (HBIM) to solve a number of thermal and phase change problems which occur in a multitude of industrial contexts. As part of our analysis, we propose a new error measure for the HBIM that combines the least-squares error with a boundary immobilisation method...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2012/187902 |
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| _version_ | 1832553551982755840 |
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| author | S. L. Mitchell T. G. Myers |
| author_facet | S. L. Mitchell T. G. Myers |
| author_sort | S. L. Mitchell |
| collection | DOAJ |
| description | We employ the Heat Balance Integral Method (HBIM) to solve a number of thermal and phase change problems which occur in a multitude of industrial contexts. As part of our analysis, we propose a new error measure for the HBIM that combines the least-squares error with a boundary immobilisation method. We describe how to determine this error for three basic thermal problems and show how it can be used to determine an optimal heat balance formulation. We then show how the HBIM, with the new error measure, may be used to approximate the solution of an aircraft deicing problem. Finally we apply the new method to two industrially important phase change problems. |
| format | Article |
| id | doaj-art-6e3d14b1b75044c384393ab1e0919409 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-6e3d14b1b75044c384393ab1e09194092025-02-03T05:53:43ZengWileyInternational Journal of Differential Equations1687-96431687-96512012-01-01201210.1155/2012/187902187902Application of Heat Balance Integral Methods to One-Dimensional Phase Change ProblemsS. L. Mitchell0T. G. Myers1MACSI, Department of Mathematics and Statistics, University of Limerick, Limerick, IrelandCentre de Recerca Matemàtica, Campus de Bellaterra, Edifici C, Bellaterra, 08193 Barcelona, SpainWe employ the Heat Balance Integral Method (HBIM) to solve a number of thermal and phase change problems which occur in a multitude of industrial contexts. As part of our analysis, we propose a new error measure for the HBIM that combines the least-squares error with a boundary immobilisation method. We describe how to determine this error for three basic thermal problems and show how it can be used to determine an optimal heat balance formulation. We then show how the HBIM, with the new error measure, may be used to approximate the solution of an aircraft deicing problem. Finally we apply the new method to two industrially important phase change problems.http://dx.doi.org/10.1155/2012/187902 |
| spellingShingle | S. L. Mitchell T. G. Myers Application of Heat Balance Integral Methods to One-Dimensional Phase Change Problems International Journal of Differential Equations |
| title | Application of Heat Balance Integral Methods to One-Dimensional Phase Change Problems |
| title_full | Application of Heat Balance Integral Methods to One-Dimensional Phase Change Problems |
| title_fullStr | Application of Heat Balance Integral Methods to One-Dimensional Phase Change Problems |
| title_full_unstemmed | Application of Heat Balance Integral Methods to One-Dimensional Phase Change Problems |
| title_short | Application of Heat Balance Integral Methods to One-Dimensional Phase Change Problems |
| title_sort | application of heat balance integral methods to one dimensional phase change problems |
| url | http://dx.doi.org/10.1155/2012/187902 |
| work_keys_str_mv | AT slmitchell applicationofheatbalanceintegralmethodstoonedimensionalphasechangeproblems AT tgmyers applicationofheatbalanceintegralmethodstoonedimensionalphasechangeproblems |