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Similarity solution for a two-phase one-dimensional Stefan problem with a convective boundary condition and a mushy zone model
Fecha
2018-05Registro en:
Ceretani, Andrea Noemí; Tarzia, Domingo Alberto; Similarity solution for a two-phase one-dimensional Stefan problem with a convective boundary condition and a mushy zone model; Sociedade Brasileira de Matemática Aplicada e Computacional; Matematica Aplicada E Computacional; 37; 2; 5-2018; 2201-2217
0101-8205
CONICET Digital
CONICET
Autor
Ceretani, Andrea Noemí
Tarzia, Domingo Alberto
Resumen
A two-phase solidification process for a one-dimensional semi-infinite material is considered. It is assumed that it is ensued from a constant bulk temperature present in the vicinity of the fixed boundary, which it is modelled through a convective condition (Robin condition). The interface between the two phases is idealized as a mushy region and it is represented following the model of Solomon, Wilson, and Alexiades. An exact similarity solution is obtained when a restriction on data is verified, and it is analysed the relation between the problem considered here and the problem with a temperature condition at the fixed boundary. Moreover, it is proved that the solution to the problem with the convective boundary condition converges to the solution to a problem with a temperature condition when the heat transfer coefficient at the fixed boundary goes to infinity, and it is given an estimation of the difference between these two solutions.