2016/09/15 by Andrea N. Ceretani, Ceretani, Andrea N., Domingo A. Tarzia +1
Computer Science · Materials Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Solidification and crystal growth phenomena
paper · pdf · doi:10.48550/arxiv.1609.04690
openalex publication_date 2016/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A two-phase solidification process for a one-dimensional semi-infinite\nmaterial is considered. It is assumed that it is ensued from a constant bulk\ntemperature present in the vicinity of the fixed boundary, which it is modelled\nthrough a convective condition (Robin condition). The interface between the two\nphases is idealized as a mushy region and it is represented following the model\nof Solomon, Wilson and Alexiades. An exact similarity solution is obtained when\na restriction on data is verified, and it is analysed the relation between the\nproblem considered here and the problem with a temperature condition at the\nfixed boundary. Moreover, it is proved that the solution to the problem with\nthe convective boundary condition converges to the solution to a problem with a\ntemperature condition when the heat transfer coefficient at the fixed boundary\ngoes to infinity, and it is given an estimation of the difference between these\ntwo solutions. Results in this article complete and improve the ones obtained\nin Tarzia, Compt. Appl. Math., 9 (1990), 201-211.\n