On the convergence of the heat balance integral method

Convergence 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 β (slow interface movement). The correct O(n−1/2) behaviour for incident heat flux is recovered for β → 0 (pure heat conduction) as previously found [Numer. Heat Transfer 8 (1985) 373-382]. Numerical illustrations support the theoretical findings.