Countercurrent melt crystallization in a column

We have studied crystallization from a solution in a CSTS in Section 6.4.1.1. Crystallization from a melt was studied in Section 6.3.2.3 under conditions where there was bulk 

Generally, mass fraction based concentration units are used in melt crystallization. The corresponding equation is as follows  

For an end-feed column with the feed having a crystal flow rate of impurity mass fraction a low-melting product flow rate of Wau impurity mass fraction of Uul, an adhering liquid flow rate of u/,d and an impurity mass fraction of Uid, the value of NTUot has been calculated as (Wankat, 1990, p. 182) 

Further, Uia, is usually specified in terms of the purity of the crystal product. An additional impurity balance at the melter end of the column yields the melted product composition Uico via 

Knowing um, Uj and the two flow rates, um, can be determined. The unknowns in this analysis from a parametric point of view are the fraction of adhering melt, u/ici/ tcL, and the value of HTUot- Albertins et al. (1967) obtained a value of HTUot = 12.3 cm for a particular eutectic system (purifying azobenzene). 

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