Exact solution of an inverse spherical two phase Stefan problem

TL;DR

This paper presents an exact analytical solution to a two-phase inverse spherical Stefan problem involving unknown temperature and heat flux functions, using a novel integral error function series approach.

Contribution

It introduces a new series-based solution method for inverse Stefan problems, enabling precise modeling of arc phenomena in electrical contacts.

Findings

Derived an exact solution using a new integral error function series

Applicable to modeling arc phenomena in electrical contacts

Provides a framework for inverse heat transfer problems

Abstract

In this paper, we represent the exact solution of a two phase inverse spherical Stefan problem, where along with unknown temperature functions heat flux function has to be determined. Suggested solution is obtained from new form of integral error function and its properties which are represented in the form of series whose coefficients have to be determined. The model problem can be used for mathematical modeling and investigation of arc phenomena in electrical contacts.