Solution of an Inverse Two Phase Spherical Stefan Test Problem

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.MSC: 80A22; 33B20

Exact solution of the one phase inverse Stefan problem

“…Solution is found both exactly and approximately. For the problem α(t) = α √ t (moving boundary), solution should be sought by formula (6). Coefficients A n , B n can be determined from (11), (13) and P n from (15) or straightforwardly by satisfying conditions and equating like terms as following:…”

“…This study is a sequel of series of studies [6,7], whose ultimate purpose is to determine and investigate components of arc occurring during opening electrical contacts and it is an attempt to model arcing process on the base of inverse one phase Stefan problem.…”