THERMAL POLYNOMIALS FOR THE INVERSE STEFAN PROBLEM

Abstract

The study of processes in the field of contact technology has
an important role all over the world. This article considers a mathematical model
of closed contact elements during heating. When an electrical contact is heated,
many thermophysical processes occur. The Stefan problem is a mathematical
model of a process with a phase change, where heat is either absorbed or
released. For example, the solidification of metals, the freezing of soil and water,
the melting of ice, the growth of crystals, etc. There are two types of Stefan's
problem, direct and inverse. In the first, the goal of the task is to find the
temperature distribution over the contact element and find the position of the
movable boundaries. In the latter case, assuming that the moving boundaries are
known, we can create a heat flow function that determines the temperature
distribution. This work gives an approximate solution by the method of heat
polynomials.