THERMAL SCIENCE

International Scientific Journal

Alastair S. Wood

,

Farida Mosally

,

Abdul Al-Fhaid

ON HIGH-ORDER POLYNOMIAL HEAT-BALANCE INTEGRAL IMPLEMENTATIONS

ABSTRACT
This article reconsiders aspects of the analysis conventionally used to establish accuracy, performance and limitations of the heat balance integral method: theoretical and practical rates of convergence are confirmed for a familiar piecewise heat-balance integral based upon mesh refinement, and the use of boundary conditions is discussed with respect to fixed and moving boundaries. Alternates to mesh refinement are increased order of approximation or non-polynomial approximants. Here a physically intuitive high-order polynomial heat balance integral formulation is described that exhibits high accuracy, rapid convergence, and desirable qualitative solution properties. The simple approach combines a global approximant of prescribed degree with spatial sub-division of the solution domain. As a variational-type method, it can be argued that heat-balance integral is simply 'one amongst many'. The approach is compared with several established variational formulations and performance is additionally assessed in terms of 'smoothness'.
KEYWORDS
heat balance integral, high-order polynomial approximants
PAPER SUBMITTED: 2008-05-27
PAPER REVISED: 2008-06-10
PAPER ACCEPTED: 2008-06-10
DOI REFERENCE: https://doi.org/10.2298/TSCI0902011W
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2009, VOLUME 13, ISSUE Issue 2, PAGES [11 - 25]
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On high-order polynomial heat-balance integral implementations

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