Influence of the relative dimensions of the cavity on the conjugate convective heat transfer and on the shape of crystallization fronts in the method of Horizontal Directed Crystallization

Stepan A Kislitsyn,D.M Markovich,P.A Kuibin,M.A Vorobyev

doi:10.1051/epjconf/201919600034

Abstract

The process of water crystallization in rectangular cavities is numerically studied. The liquid being studied is water having an inverse temperature dependence of the density. Calculations were carried out with a suddenly cooled vertical wall of a rectangular cavity. The initial temperature of the melt is maintained on the opposite wall. The finite element method was used to solve a system of equations for the nonstationary free convection of a melt, taking into account the dependence of the density on temperature. The heat conduction equation in the solidified substance was also solved. The problems were solved in a conjugate formulation taking into account the release of the latent heat of crystallization at the liquid-solid interface.

Highlights

The method of Horizontal Directed Crystallization (HDC) is one of the popular methods for obtaining single crystals from melts [1]
In the HDC method, depending on the conditions at the upper boundary, the growth occurs in the regime of nonstationary thermogravitational or gravitational-capillary convection [2, 3] complicated by a phase transition
A simplified model of the technological process of HDC is the process of crystallization of the melt in a rectangular cavity with vertical walls heated up at different temperatures

Summary

Introduction

The method of Horizontal Directed Crystallization (HDC) is one of the popular methods for obtaining single crystals from melts [1]. As in other methods of directed crystallization, crystal growth occurs under conditions of conjugated convective heat transfer. In the HDC method, depending on the conditions at the upper boundary, the growth occurs in the regime of nonstationary thermogravitational or gravitational-capillary convection [2, 3] complicated by a phase transition. The shape of crystallization fronts and the temperature field and the temperature gradients in the solidified material depend on the features of local heat transfer, on which the homogeneity of crystallographic characteristics of crystals is depended. The use of water as a melt imitation fluid in the physical and numerical modeling of convective heat transfer is due to the inverse dependence of its density on temperature in the vicinity of 4°C. A consequence is the effect on the shape of the crystallization front

Formulation of the problem

Numerical results

Conclusions