Perturbation solutions for the finite radially symmetric Stefan problem

• The beginning of recalescence from one nucleus in a supercooled droplet is described.
• A semi-analytical solution of the radially symmetric Stefan problem is proposed.
• The method is based on perturbation methods followed by an iterative procedure.
• The proposed algorithm is easy to implement, converges fast and needs less CPU time.
• A good approximation of the solution with respect to reference results is provided.

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.