Freezing and Thawing: Heat Balance Integral Approximations

The study of conductive heat transfer with phase change — often called the Stefan problem — includes some of the most intractable mathematical areas of heat transfer. Exact solutions are extremely limited and approximate methods are widely used. This paper discusses the heat balance integral approximation using the collocation method. The method is applied to some standard problems of phase change — Neumann’s problem — and a new solution is presented for the case of a semi-infinite body with surface convection. Numerical results are given for soil systems and also for materials of interest in latent heat thermal storage.