Two-phase Stefan problem with nonlinear thermal coefficients and a convective boundary condition. (April 2021)

• Record Type: Journal Article
• Authors: Briozzo, Adriana C.; Natale, María Fernanda
• Is Part Of: Nonlinear analysis. Volume 58(2021)
• Publication Date: 2021-04
• Subjects: Stefan problem -- Free boundary problem -- Phase-change process -- Similarity solution -- Kirchhoff transformation; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103204
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: A solidification process for a semi-infinite material is presented through a non-linear two-phase unidimensional Stefan problem, where a convective boundary condition is imposed at the fixed face x = 0 . The volumetric heat capacity and the thermal conductivity are non-linear functions of the temperature in both solid and liquid phases and they verify a Storm-type relation. A certain inequality on the heat transfer coefficient h is established in order to get an instantaneous phase change process. We determine sufficient conditions on the parameters of the problem in order to prove the existence and uniqueness of a parametric explicit solution for the Stefan problem.