On high-order polynomial heat-balance integral implementations

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...

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Bibliographic Details
Main Authors: Wood Alastair S., Mosally Farida, Al-Fhaid Abdul
Format: Article
Language:English
Published: VINCA Institute of Nuclear Sciences 2009-01-01
Series:Thermal Science
Subjects:
Online Access:http://www.doiserbia.nb.rs/img/doi/0354-9836/2009/0354-98360902011W.pdf
Description
Summary: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'.
ISSN:0354-9836
2334-7163