Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2015, Article ID 637852, 8 pages
Research Article

Determination of One Unknown Thermal Coefficient through a Mushy Zone Model with a Convective Overspecified Boundary Condition

1CONICET, Departamento de Matemática, Facultad de Ciencias Empresariales, Universidad Austral, Paraguay 1950, S2000FZF Rosario, Argentina
2Departamento de Matemática, Facultad de Ciencias Exactas, Ingeniería y Agrimensura, Universidad Nacional de Rosario, Pellegrini 250, S2000BTP Rosario, Argentina

Received 8 May 2015; Accepted 9 June 2015

Academic Editor: Mohsen Torabi

Copyright © 2015 Andrea N. Ceretani and Domingo A. Tarzia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A semi-infinite material under a solidification process with the Solomon-Wilson-Alexiades mushy zone model with a heat flux condition at the fixed boundary is considered. The associated free boundary problem is overspecified through a convective boundary condition with the aim of the simultaneous determination of the temperature, the two free boundaries of the mushy zone and one thermal coefficient among the latent heat by unit mass, the thermal conductivity, the mass density, the specific heat, and the two coefficients that characterize the mushy zone, when the unknown thermal coefficient is supposed to be constant. Bulk temperature and coefficients which characterize the heat flux and the heat transfer at the boundary are assumed to be determined experimentally. Explicit formulae for the unknowns are given for the resulting six phase-change problems, besides necessary and sufficient conditions on data in order to obtain them. In addition, relationship between the phase-change process solved in this paper and an analogous process overspecified by a temperature boundary condition is presented, and this second problem is solved by considering a large heat transfer coefficient at the boundary in the problem with the convective boundary condition. Formulae for the unknown thermal coefficients corresponding to both problems are summarized in two tables.