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.
Highlights
General IntroductionNatural convection in a closed cavity is a rather complex and interesting subject in heat transfer
The proposed model is within the framework of linear non-equilibrium thermodynamics and considers the thermodiffusion factor in terms of the net heats of transport of the electronic and ion-ion thermal interactions
For the Reynolds number of 136 that is characteristic of laminar flow, our results showed that the effect of external natural convection and radiation are negligible and the temperature and concentration distributions do not vary significantly compared to the insulated wall conditions
Summary
Natural convection in a closed cavity is a rather complex and interesting subject in heat transfer It has been studied mainly in two-dimensional rectangular enclosures where a temperature gradient has been applied across the enclosure from two opposing walls, either vertically or horizontally. The temperature gradient acting on a binary system, such as a two-component molten metal alloy, causes separation of the constituents in a process called thermodiffusion This makes the modeling and prediction of flow in a binary system much more complex that for a system with a single component. Once the model was validated, it was used to simulate the solidification process for 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 metal alloys to study the temperature, velocity, and concentration distributions in the presence and absence of the newly proposed thermodiffusion factor. Using the same axisymmetric finite element (FE) model, solidification processes for the remaining five alloys were studied and the results are explained and discussed
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