Optimizing the exponent in the heat balance and refined integral methods

The most contentious aspect of the Heat Balance Integral Method is the choice of power of the highest order term in the approximating function. In this paper we develop a new method, where the exponent is determined during the solution process. This is achieved by minimising the square of the difference of the terms in the heat equation. The solution requires no knowledge of an exact solution and generally produces significantly better results than previous models. The method is illustrated by applying it to three standard thermal problems.

[1]  W. H. Stevenson,et al.  Diffusion of heat and solute during freezing of salt solutions , 1976 .

[2]  Alaattin Esen,et al.  A heat balance integral solution of the thermistor problem with a modified electrical conductivity , 2006 .

[3]  Marcia B. H. Mantelli,et al.  Approximate Analytical Solution for One-Dimensional Finite Ablation Problem with Constant Time Heat Flux , 2004 .

[4]  Michael Spearpoint,et al.  Predicting the piloted ignition of wood in the cone calorimeter using an integral model — effect of species, grain orientation and heat flux , 2001 .

[5]  Sarah L. Mitchell,et al.  Unsteady contact melting of a rectangular cross-section material on a flat plate , 2008 .

[6]  Alastair S. Wood,et al.  A new look at the heat balance integral method , 2001 .

[7]  Application of the heat-balance and refined integral methods to the Korteweg-de Vries equation , 2009 .

[8]  Jordan Hristov,et al.  The heat-balance integral method by a parabolic profile with unspecified exponent: Analysis and benchmark exercises , 2010, 1012.2533.

[9]  Pierre Colinet,et al.  On the refined integral method for the one-phase Stefan problem with time-dependent boundary conditions , 2006 .

[10]  Sarah L. Mitchell,et al.  Heat Balance Integral Method for One-Dimensional Finite Ablation , 2008 .

[11]  David Langford,et al.  The heat balance integral method , 1973 .

[12]  Sarah L. Mitchell,et al.  Approximate solution methods for one-dimensional solidification from an incoming fluid , 2008, Appl. Math. Comput..

[13]  Sarah L. Mitchell,et al.  A cubic heat balance integral method for one-dimensional melting of a finite thickness layer , 2007 .

[14]  Alexsandar Antic,et al.  The double-diffusivity heat transfer model for grain stores incorporating microwave heating , 2003 .