Consider $Al-25wt.\%Cu$ system which is solidified with a planar interface. $(15$ point$)$

$($a$)$ If the solidification rate $=1{10}^{-2}c\frac{m}{s},=0\mathrm{.}025cm$ due to convection in liquid. Draw composition$-$

distance diagram, indicating single phase and two$-$phase region, after fully solidified.

$($b$)$ From $($a$),$ convection in liquid is increased resulted in decreased in $=0\mathrm{.}01cm.$ Draw composition$-$

distance diagram, indicating single phase and two$-$phase region, after fully solidified.

$($c$)$ From $($a$)$ and $($b$),$ show the conditions for maintaining planar interface at $50\%$ solidified.