Solidification heat-transport-limited

For the case of the solidification of Fe(s) discussed in Example 6.7, if = 25 W/(m K), we could estimate the heat-transport-limited solidification rate as... 

The heat-transport-limited solidification rate estimated by this approach is almost one order of magnitude slower than the mass-transport-limited growth rate that was calculated in Example 6.7. Thus, it is likely that heat transport will limit the solidification of this ingot under these conditions. 

We see from this example that heat transport is a key factor influencing stabiUty. In solidification of binary mixtures or alloys both heat and mass transport must be eonsidraed. If the solute is preferentially soluble in the hquid phase, for example, solute must diffuse from the interfaee to the bulk hquid as sohdification proeeeds. Sinee diffusion coefficimts are often mueh smalf than thermal diffu-sivities in liquids, the sohdification rate is often limited primarily by solute diffusion. By an argument similar to that given above for heat transport, we eonclude that solute (hffusion in the hquid is destabilizing and ean lead to dendritic growth. 

Here is the equilibrium melting temperature of a flat interface and b is an empirical coefficient. In the limiting case of large b, we have 7 = T. In this special case, crystal formation kinetics are unimportant and the solidification rate is limited solely by heat transport in the liquid. 

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