Abstract— The classical Stefan problem is a linear onedimensional heat equation with a free boundary at one end, modelling a column of liquid (e.g. water) in contact with an infinite strip of solid (ice). Given the fixed boundary conditions, the column temperature and free boundary motion can be uniquely determined. In the inverse problem, one specifies the free boundary motion, say from one st...

This paper considers a class of one-dimensional solidification problem in which kinetic undercooling is incorporated into the temperature condition at the interface. A model problem with nonlinear kinetic law is considered. The main result is an existence theorem. The mathematical effects of the kinetic term are discussed

in this present study, volume of fluid method in openfoam open source cfd package will be extended to consider phase change phenomena with modified model due to condensation and boiling processes. this model is suitable for the case in which both unsaturated phase and saturated phase are present and for beginning boiling and condensation process needn't initial interface. both phases (liqu...

An approximation procedure for the identi cation of a nonlinear boundary heat transfer function in a one phase Stefan problem is presented. Alternatively the problem can be viewed as constructing a feedback control law for the control of the solidi cation surface in the Stefan problem. The analysis is based on Hilbert space methods and convex analysis techniques. Numerical results combining two...

Amathematical model for the diffusion process of ferromagnetic particles in a magnetic fluid is described. The unique solvability of the steady-state particle concentration problem is investigated and an analytical expression for its solution is found. In case that the fluid is under the action of a high-gradient magnetic field a Stefan-type diffusion problem can arise. An algorithm for solving...

Abstract