Open AccessQuasi-approximation for Stefan problem of nearly spherical phase change materials
Author(s) -
Jiayan Li,
Yue Chan
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1324/1/012069
Subject(s) - stefan problem , ellipse , boundary (topology) , phase (matter) , free boundary problem , phase change material , latent heat , boundary value problem , mathematical analysis , phase change , boundary problem , mechanics , physics , mathematics , classical mechanics , geometry , thermodynamics , quantum mechanics
Phase change occurs when a phase change material exchanges its energy with the external environment. In this paper, we investigate the solidification of nearly spherical materials, which is famously known as Stefan problem and is of practically important. When the material solidifies, the inner moving boundary (see Figure 1) can be determined by solving the elliptic-typed partial differential equation, equipped with the outer fixed and the inner moving boundary conditions, derived from the Newton cooling law and the latent heat, respectively. Since the shape of materials induces a huge impact on the retreating speed of the moving boundary. To demonstrate this idea, we consider the perfect spherical object and certain irregular objects, such as an ellipse. We derive the analytical solutions for both cases and find that the shape of the moving boundary changes from the ellipse into the sphere during the solidification process.