Heat balance integral methods applied to the one-phase Stefan problem with a convective boundary condition at the fixed face

BOLLATI, J.; SEMITIEL, J.; TARZIA, D.A.

APPLIED MATHEMATICS AND COMPUTATION

ELSEVIER SCIENCE INC

Año: 2018 vol. 331 p. 1 - 19

0096-3003

In this paper we consider a one-dimensional one-phase Stefan problem corresponding to the solidification process of a semi-infinite material with a convective boundary condition at the fixed face. The exact solution of this problem, available recently in the literature, en- able us to test the accuracy of the approximate solutions obtained by applying the classical technique of the heat balance integral method and the refined integral method, assuming a quadratic temperature profile in space. We develop variations of these methods which turn out to be optimal in some cases. Throughout this paper, a dimensionless analysis is carried out by using the parameters: Stefan number (Ste) and the generalized Biot number (Bi). In addition it is studied the case when Bi goes to infinity, recovering the approximate solutions when a Dirichlet condition is imposed at the fixed face. Some numerical simu- lations are provided in order to estimate the errors committed by each approach for the corresponding free boundary and temperature profiles.