Pressure effects in the planar solidification of a finite slab: convective cooling and prescribed heat flux boundary conditions

Abstract

The classical Stefan problem assumes a fixed melting temperature. However, when the solid phase is the one with lower density (e.g., water) the solidification of the system causes an overall volume increase that is often contrasted by the container walls. In that case the growing pressure determines a continuous lowering of the freezing point, and the temperature field as well as the interface motion are strongly affected. This paper is concerned with these aspects of the problem; the planar solidification of a slab of finite thickness, contrasted by an opposing elastic force, is numerically simulated. The effects of two different boundary conditions are analysed. When the solidification is driven by convective cooling, the continuous advancement of the melting front is replaced by an asymptotic behaviour, until thermal equilibrium is attained. When the boundary condition is specified in terms of a prescribed heat flow, the melting front velocity is slowed down by a growing adverse temperature gradient. The influence of various parameters on the process is presented and discussed.