1-D diffusion based solidification model with volumetric expansion and shrinkage effect: A semi-analytical approach

Volumetric expansion and shrinkage due to different densities of solid and liquid phases are common phenomena during solidification process. Simple analytical models addressing effect of volumetric expansion/shrinkage during solidification are rarely found. The few existing 1-D solidification models are valid only for semi-infinite domain with limitations of their application for finite domain size. The focus of the present work is to develop a 1-D semi-analytical solidification model addressing effects of volumetric expansion/shrinkage in a finite domain. The proposed semi-analytical scheme involves finding simultaneous solution of transient 1-D heat diffusion equations at solid and liquid domain coupled at the interface by Stefan condition. The change of the total domain length during solidification due to volumetric expansion/shrinkage is addressed by using mass conservation. For validation of the proposed model, solidification of water in a finite domain is studied without considering volumetric expansion/shrinkage effect and results are compared with those obtained from existing enthalpy updating based numerical model. After validation, case studies pertaining to volumetric expansion and shrinkage are performed considering solidification of water and paraffin respectively and physically consistent results are obtained. The study is relevant for understanding unidirectional crystal growth under the effect of controlled boundary condition.