An approach for solving an inverse spherical two-phase Stefan problem arising in modeling of electric contact phenomena. (English) Zbl 1387.80005
Summary: In this paper, a model problem that can be used for mathematical modeling and investigation of arc phenomena in electrical contacts is considered. An analytical approach for the solution of a two-phase inverse spherical Stefan problem where along with unknown temperature functions heat flux function has to be determined is presented. The suggested solution method is obtained from a new form of integral error function and its properties that are represented in the form of series whose coefficients have to be determined. Using integral error function and collocation method, the solution of a test problem is obtained in exact form and approximately.
MSC:
| 80A22 | Stefan problems, phase changes, etc. |
| 33B20 | Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) |
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