Perturbation solutions for the finite radially symmetric Stefan problem

The beginning of the ice-growth from a nucleus in the freezing process of a single supercooled droplet is modelled through a two-phase Stefan problem which is characterized by an unknown boundary separating the two distinct phases. A semi-analytical solution for the ice water interface is presented using a perturbation method followed by an iterative procedure. The method offers a quantitatively good approximation of the interface position as well as the temperature distribution in the ice and in the water phase in comparison with the considered reference numerical results. Furthermore, it is less expensive in terms of time and memory resources. The results obtained for the initial radially symmetric ice growth of the small ice particle can be used as subgrid models in a direct numerical simulation of the dendritic ice growth in a supercooled droplet. (C) 2016 Elsevier Masson SAS. All rights reserved.