Model of a two-dimensional free boundary problem in an cylindrical shape electrical contact

A method for the numerical solution of an axisymmetric problem in a model that describes the change in temperature and coordinates of the free boundary in a cylindrical contact is considered. The mathematical model consists of an inhomogeneous heat equation with variable coefficients and an additional differential equation for the kinetics of phase changing, but there is no differential equation for a free boundary in it. This is the main difference from Stefan's free-boundary approach, where solving 2-3-dimensional problems is very difficult. The method was used earlier to solve a one-dimensional problem and a satisfactory agreement with the solution of the corresponding Stefan problem was obtained.