$($Poirier and Geiger problem $10\mathrm{.}2)$ How long does it take to freeze a $\backslash (100-\backslash$mathrm$\{$mm$\}\backslash )$ diameter sphere of pure iron in a silica sand mold, assuming: a$)$ no superheat and neglecting the heat flow divergence? b$)$ no superheat and realizing that a sphere is being cast? c$)110$ K superheat and realizing that a sphere is being cast?