Displaying similar documents to “Mathematical and computational aspects of solidification of pure substances.”

Introduction to the models of phase transitions

A. Visintin (1998)

Bollettino dell'Unione Matematica Italiana

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Le transizioni di fase si presentano in svariati processi fisici: un esempio tipico è la transizione solido-liquido. Il classico modello matematico, noto come , tiene conto solo dello scambio del calore latente e della diffusione termica nelle fasi. Si tratta di un problema di frontiera libera, poiché l'evoluzione dell'interfaccia solido liquido è una delle incognite. In questo articolo si rivedono le formulazioni forte e debole di tale problema, e quindi si considerano alcune generalizzazioni...

On the importance of solid deformations in convection-dominated liquid/solid phase change of pure materials

Daniela Mansutti, Edoardo Bucchignani (2011)

Applications of Mathematics

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We analyse the effect of the mechanical response of the solid phase during liquid/solid phase change by numerical simulation of a benchmark test based on the well-known and debated experiment of melting of a pure gallium slab counducted by Gau & Viskanta in 1986. The adopted mathematical model includes the description of the melt flow and of the solid phase deformations. Surprisingly the conclusion reached is that, even in this case of pure material, the contribution of the solid...

Hysteresis operators in phase-field models of Penrose-fife type

Pavel Krejčí, Jürgen Sprekels (1998)

Applications of Mathematics

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Phase-field systems as mathematical models for phase transitions have drawn a considerable attention in recent years. However, while they are suitable for capturing many of the experimentally observed phenomena, they are only of restricted value in modelling hysteresis effects occurring during phase transition processes. To overcome this shortcoming of existing phase-field theories, the authors have recently proposed a new approach to phase-field models which is based on the mathematical...