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Zbl 1183.80091
Myers, T.G.
Optimal exponent heat balance and refined integral methods applied to Stefan problems. (English)
[J] Int. J. Heat Mass Transfer 53, No. 5-6, 1119-1127 (2010). ISSN 0017-9310

Summary: When using a polynomial approximating function the most contentious aspect of the Heat Balance Integral Method is the choice of power of the highest order term. In this paper we employ a method recently developed for thermal problems, where the exponent is determined during the solution process, to analyse Stefan problems. This is achieved by minimising an error function. The solution requires no knowledge of an exact solution and generally produces significantly better results than all previous HBI models. The method is illustrated by first applying it to standard thermal problems. A Stefan problem with an analytical solution is then discussed and results compared to the approximate solution. An ablation problem is also analysed and results compared against a numerical solution. In both examples the agreement is excellent. A Stefan problem where the boundary temperature increases exponentially is analysed. This highlights the difficulties that can be encountered with a time dependent boundary condition. Finally, melting with a time-dependent flux is briefly analysed without applying analytical or numerical results to assess the accuracy.

MSC 2000:: *80A22 Stefan problems, etc.
80A20 Heat and mass transfer
80M25 Other numerical methods

Keywords: heat balance integral method; refined integral method; Stefan problem; phase change

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Zentralblatt MATH Berlin [Germany]