$7.($In$-$class problem$)$ A stainless steel $304$ spherical ball $($diameter$=50$ cm$)$ is placed in an oven at a uniform temperature of $500$C$,$ initially. Then the ball is taken into a chamber at $100$C $($h $=50$ W$/$m$2.$C$)$ and allowed to cool slowly. Properties for stainless steel $304$: k $=14\mathrm{.}9$ W$/$m$.$C$,=7900$ kg$/$m$3,$ Cp $=477$ J$/$kg$.$C$,$ and $=3\mathrm{.}95$ x $10-6$ m$2/$s$.$ a$.$ Determine the temperature at the center of the ball $15$ min after the start of the cooling process. b$.$ Determine the heat transfer during this time period.