Application of heat balance integral methods to one-dimensional phase change problems

S. L. Mitchell, T. G. Myers

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Article number187902
JournalInternational Journal of Differential Equations
Volume2012
DOIs
Publication statusPublished - 2012

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