Two-phase Stefan problem for generalized heat equation with nonlinear thermal coefficients

In this article we study a mathematical model of the heat transfer in semi infinite material with variable cross section, when radial component temperature gradient can be neglected comparison axial component. particular, distribution liquid and solid phases such kind body modeled by Stefan problem for generalized equation. The method solution is based on similarity principle, which enables us to reduce equation nonlinear ordinary differential Moreover, determine two free boundaries describe position boiling melting interfaces. Existence uniqueness type provided using fixed point Banach theorem.