One-Dimensional Solidification

Figure 20.4 One-dimensional solidification of liquid binary alloy, (a) Phase diagram...

In Fig. 22.1a one-dimensional solidification is depicted a liquid binary alloy initially of uniform composition cq is placed in a bar-shaped crucible of length L. The bar is progressively cooled from one end, so it solidifies from one end to the other... 

Krumbhaar. Solidification in the one-dimensional model for a disordered binary alloy under diffusion. Eur Phys J. B 5 663, 1998. 

As shown by Fig. 22.16, the concentrations of solute atoms are significantly reduced in the material that is solidified early in the solidification process when k < 1. One-dimensional plane-front solidification can therefore be used as a method of purification. However, purification is carried more effectively out by modifying the process and adopting a zone-melting technique. 

When viewed from a reference frame that is stationary with respect to the solidification interface, the melt moves uniaxially toward the interface and the crystal moves away. Then solute transport in the melt is governed by the one-dimensional balance equation... 

Once a mould is full, there is effectively one-dimensional heat flow in the direction perpendicular to the mould wall, while the plastic soHdifies. The moulding must solidify all the way through, before it can be ejected, so the cycle time is determined mainly by this through-thickness solidification time s- In Appendix A, Fig. A.4 is a dimensionless graph of mouldings temperature profiles versus time. If the plastic is solid at T — Tq = 0.4, the melt is fully solid when the Fourier number Fo = 0.5. Hence, the solidification time is given by... 

Dhiman and Chandra [20] developed an analytical model to predict the substrate temperature at which splashing would occur by using a one-dimensional model for solidification of a molten metal droplet in contact with a semi-infinite substrate. They assumed that splashing occurred if the thickness of the solid layer reached that of the splat by the time the droplet had finished spreading. The thermal contact resistance between the droplet and surface was found to play a critical role in... 

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