2014/05/21 by Andrea N. Ceretani, Ceretani, Andrea N., Domingo A. Tarzia +1
Computer Science · Mathematics · #35C06 #35R35 #80A22 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1405.5489
openalex publication_date 2014/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Similarity solutions for a one-dimensional mathematical model for thawing in a saturated semi-infinite porous media is considered when change of phase induces a density jump and a convective boundary condition is imposed at the fixed face x=0. Different cases depending on physical parameters are analysed and an explicit solution of a similarity type is obtained if and only if an inequality for data is verified. Moreover, a monotony property respect to the coefficient which characterizes the heat transfer at the fixed face x=0 is obtained for the coefficient involved in the definition of the free boundary. Relationship between the Stefan problem with convective condition at x=0 considered in this paper and the Stefan problem with temperature condition at the same face studied in (Fasano-Primicerio-Tarzia, Math. Models Meth. Appl. Sci., 9 (1999), 1-10) is analized and conditions for physical parameters under which both problems became equivalents are obtained. Furthermore, an inequality to be satisfied for the coefficient which characterizes the free boundary of the problem with a temperature or a convective boundary condition at the fixed face x=0 is also obtained.