THERMAL SCIENCE

International Scientific Journal

Nacer Sadoun

,

El-Khider Si-Ahmed

,

Pierre Collinet

,

Jack Legrand

ON THE GOODMAN HEAT-BALANCE INTEGRAL METHOD FOR STEFAN LIKE-PROBLEMS: FURTHER CONSIDERATIONS AND REFINEMENTS

ABSTRACT
Since the pioneering studies of Goodman on the application of the integral method to transient non-linear heat diffusion, much attention has been devoted nowadays to what is called heat balance integral method. The present paper considers this technique fifty years later. The genesis and earlier developments, when applied to Stefan like-problems, are reported hereafter. Its simplicity and efficiency are demonstrated. Some numerical results obtained using methods developed on the basis of the heat balance integral are compared. Furthermore, for problems including temperature profile behavior, such as Stefan problem with forcing term (source or sink) this technique gives highly precise results and may, in some cases, lead to exact solutions.
KEYWORDS
heat balance integral, Stefan problems, analytical solution, source-sink term, phase-change, non-linear heat diffusion, moving boundary
PAPER SUBMITTED: 2008-04-04
PAPER REVISED: 2008-05-15
PAPER ACCEPTED: 2008-06-15
DOI REFERENCE: https://doi.org/10.2298/TSCI0902081S
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2009, VOLUME 13, ISSUE Issue 2, PAGES [81 - 96]
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On the goodman heat-balance integral method for Stefan like-problems: Further considerations and refinements

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