We propose here a model for solidification of the liquid content of an elastic bottle in a freezer. The main goal is to explain the occurrence of high stresses inside the bottle. As a byproduct, we derive a formula for the undercooling coefficient in terms of the elasticity constants, latent heat, and the phase expansion coefficient. We investigate the well-posedness of the three-dimensional model: we prove the existence and uniqueness of a solution for the corresponding initial-boundary value problem which couples a PDE with an integrodifferential equation and an ordinary differential inclusion ruling the evolution of the phase parameter. Finally, we prove some results on the long time behavior of solutions.
A bottle in a freezer / P. Krejci, E. Rocca, J. Sprekels. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 41:5(2009), pp. 1851-1873.
A bottle in a freezer
E. RoccaSecondo
;
2009
Abstract
We propose here a model for solidification of the liquid content of an elastic bottle in a freezer. The main goal is to explain the occurrence of high stresses inside the bottle. As a byproduct, we derive a formula for the undercooling coefficient in terms of the elasticity constants, latent heat, and the phase expansion coefficient. We investigate the well-posedness of the three-dimensional model: we prove the existence and uniqueness of a solution for the corresponding initial-boundary value problem which couples a PDE with an integrodifferential equation and an ordinary differential inclusion ruling the evolution of the phase parameter. Finally, we prove some results on the long time behavior of solutions.Pubblicazioni consigliate
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