Stefan-like problems (original) (raw)
This paper presents an overview of the free boundary problems connected to the problem of Stefan type or, more generally, to problems describing a change of phase. After a sketch of the historical development of the research in the area, some specific questions are addressed, such as classical solvability of the problem in several space dimensions, regularization of supercooling, dynamical contact angle, SOMMARIO. I1 lavoro presenta una visione generale dei problemi a frontiera libera del tipo di Stefan o ad esso collegati, e piti in generale dei problemi che descrivono cambiamenti di fase. Dopo aver riassunto 1o sviluppo storico delle ricerche in questo campo, viene dedicata maggiore attenzione ad alcuni problemi specifici come la risoluzione ciassica di problemi multidimensionali, la regolarizzazione dei problemi con sovraraffreddamento, il problema dell'angolo di contatto.
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Approximate solutions to the Stefan problem with internal heat generation
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Using a quasi-static approach valid for Stefan numbers less than one, we derive approximate equations governing the movement of a phase change front for materials which generate internal heat. These models are applied for both constant surface temperature and constant surface heat flux boundary conditions, in cylindrical, spherical, plane wall and semi-infinite geometries. Exact solutions with the constant surface temperature condition are obtained for the steady-state solidification thickness using the cylinder, sphere, and plane wall geometries which show that the thickness depends on the inverse square root of the internal heat generation. Under constant surface heat flux conditions, closed form equations can be obtained for the three geometries. In the case of the semiinfinite wall, we show that for constant temperature and constant heat flux out of the wall conditions, the solidification layer grows then remelts.
Quasi-approximation for Stefan problem of nearly spherical phase change materials
Journal of Physics: Conference Series, 2019
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.
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