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2012 Application of Heat Balance Integral Methods to One-Dimensional Phase Change Problems
S. L. Mitchell, T. G. Myers
Int. J. Differ. Equ. 2012(SI1): 1-22 (2012). DOI: 10.1155/2012/187902


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.


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S. L. Mitchell. T. G. Myers. "Application of Heat Balance Integral Methods to One-Dimensional Phase Change Problems." Int. J. Differ. Equ. 2012 (SI1) 1 - 22, 2012.


Received: 15 December 2011; Accepted: 12 February 2012; Published: 2012
First available in Project Euclid: 25 January 2017

zbMATH: 1250.35013
MathSciNet: MR2914891
Digital Object Identifier: 10.1155/2012/187902

Rights: Copyright © 2012 Hindawi


Vol.2012 • No. SI1 • 2012
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