A bar of 98 wt% Al with 2 wt% of Fe impurity is subjected to one pass of zone refining. The solid–liquid distribution coefficient for the impurity is 0.29. If z/l = 10 and the resulting bar is cut off at z₂ = 0.75z, calculate the concentration profile for Fe and the average concentration from (1) in Exercise 17.33.

Exercise 17.33

Derive the following expression for the average impurity concentration over a particular length of crystal layer, z₂ = z₁, after one pass or partial pass of zone melting.

Using the results of Example 17.14, calculate w_avg for z₁ = 0 and z₂/l = 9.

Transcribed Image Text:

Wavg = Wo fl(1-K) K(22-21) -[exp(-2₂K/l) - exp(-z₁K/l)] + +1} (1)