Problem $\backslash$#$4.[$Solidification$]($Poirier and Geiger problem $10\mathrm{.}2)$ How long does it take to freeze a $100-$mm 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?