Numerical investigation of heat transfer and solidification in a cavity filled with molten metal alloys in the presence of thermodiffusion

Abstract

The objective of this research was to study the solidification process of binary molten metals. This study was conducted in three phases. One was to estimate the thermodiffusion factor, two was to simulate the effect of natural convection and radiation on the velocity, temperature, and concentration distributions, and the third was to investigate the solidification process of binary molten metals using the proposed thermodiffusion factors. The proposed expression for the estimation of thermodiffusion factor was based on the physical properties of the mixture constituents. The estimated thermodiffusion factor was used to study thermosolutal convection in a quartz enclosure filled with molten Sn-Bi alloy. Two simulations were carried out: top heating and bottom heating. The sidewalls in both cases were exposed to convection and radiation. Numerical results show that in the case of top heating, the distribution of temperature and concentration are linear, but species segregation occurs due to the thermodiffusion effect. In the bottom heating case, boundary-driven convective flow develops with a large Rayleigh number (Ra) where an increase in the Ra number negates thermodiffusion due to the development of strong mixing. The results of these simulations showed that the effect of convection and radiation are negligible. In phase three, finite element method (FE) was employed to investigate the effect of thermodiffusion during vertical solidification of binary molten metal alloys with bottom cooling. The systems considered here are tin-bismuth (Sn-Bi), tin-cadmium (Sn-Cd), tin-zinc (Sn-Zn), tin-lead (Sn-Pb), tin-gallium (Sn-Ga), and bismuth-lead (Bi-Pb) binary molten metals. The geometry under study was a cylindrical cavity. The FE model was constructed using a 2D axisymmetric element to represent a 3D cyclindrical model. Two cases were studied: one without and one with the effect of thermodiffusion. The simulation including thermodiffusion showed slight variation from the simulation without thermodiffusion, in that thermodiffusion causes a slightly faster solidification and a more uniform concentration distribution if the thermodiffusion coefficient is greater than zero (DT > 0). The main object of this research is development of a more accurate thermodiffusion factor, and applying it in a numerical simulation to study its effects on radiation, natural convection, and solidification processes.