A bottle in a freezer
Analysis of PDEs
2014-01-10 v1
Abstract
We propose here a model for solidification of a liquid contents of an elastic bottle in a freezer. The main goal is to explain the occurrence of high stresses inside the bottle. As a by-product, 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.
Cite
@article{arxiv.0904.4380,
title = {A bottle in a freezer},
author = {Pavel Krejci and Elisabetta Rocca and Juergen Sprekels},
journal= {arXiv preprint arXiv:0904.4380},
year = {2014}
}