A solid sphere made of steel, $76\mathrm{.}2cm$ in diameter is suddenly immersed for hardening purposes in a water bath maintained at a uniform temperature of $35C$ after it has been initially heated to $900C$ in a furnace. How long it will take for the surface of the sphere to cool down to $200C?$ The heat transfer coefficient $h$ is $60W{m}^{-2}{K}^{-1},$ and the properties of the steel are $=8100kg{m}^{-3},c=465Jk{g}^{-1}{K}^{-1},$ and $k=44W{m}^{-1}{K}^{-1}.$ Use provided Heisler Charts for a sphere.

$[15$ MARKS$]$

List and briefly explain three industrial or real$-$life cases when engineers and material scientists deal with processes of unsteady conduction.

$[10$ MARKS$].$

$(\frac{k}{h}{r}_0)=B{t}^{-}$