Application of Heat Balance Integral Methods to One-Dimensional Phase Change Problems

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: S. L. Mitchell, T. G. Myers
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:International Journal of Differential Equations
Online Access:http://dx.doi.org/10.1155/2012/187902
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spelling doaj-6e3d14b1b75044c384393ab1e09194092020-11-25T00:31:57ZengHindawi LimitedInternational 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
collection DOAJ
language English
format Article
sources DOAJ
author S. L. Mitchell
T. G. Myers
spellingShingle S. L. Mitchell
T. G. Myers
Application of Heat Balance Integral Methods to One-Dimensional Phase Change Problems
International Journal of Differential Equations
author_facet S. L. Mitchell
T. G. Myers
author_sort S. L. Mitchell
title 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_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_sort application of heat balance integral methods to one-dimensional phase change problems
publisher Hindawi Limited
series International Journal of Differential Equations
issn 1687-9643
1687-9651
publishDate 2012-01-01
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.
url http://dx.doi.org/10.1155/2012/187902
work_keys_str_mv AT slmitchell applicationofheatbalanceintegralmethodstoonedimensionalphasechangeproblems
AT tgmyers applicationofheatbalanceintegralmethodstoonedimensionalphasechangeproblems
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