Abstract
We study a non-classical one-phase Stefan problem for heat transfer in spherical domain of electrical contact materials when heating process on electrical contact surface arises.Mathematical model involves non-linear thermal coefficients and heat flux condition at a known free boundary.Solution of the problem based on similarity principle.Moreover, we determine the temperature distribution in melted zone and the free boundary on melting interface whether direct Stefan problem is considered.The existence and uniqueness of similarity solution to the problem is established.Solutions for constant and linear thermal coefficients and existence of uniqueness for particular cases are provided.