Mosally, F.Wood, Alastair S.Al-Fhaid, A.2009-07-282009-07-282009-07-28Mosally, F., Wood, A.S. and Al-Fhaid, A. (2005) On the convergence of the heat balance integral method. Applied Mathematical Modelling. Vol. 19, No. 10, pp. 903-912.90007485http://hdl.handle.net/10454/3174NoConvergence properties are established for the piecewise linear heat balance integral solution of a benchmark moving boundary problem, thus generalising earlier results [Numer. Heat Transfer 8 (1985) 373]. A convergence rate of O(n¿1) is identified with minor effects at large values of the Stefan number ß (slow interface movement). The correct O(n¿1/2) behaviour for incident heat flux is recovered for ß ¿ 0 (pure heat conduction) as previously found [Numer. Heat Transfer 8 (1985) 373¿382]. Numerical illustrations support the theoretical findings.enHeat balance integralPhase changeConvergenceArticlehttps://doi.org/10.1016/j.apm.2004.12.001