A steel ball initially at a uniform temperature of $100\backslash$deg C is dropped into an insulated vessel containing water at $20\backslash$deg C$.$ Derive the appropriate governing equations for the temperature of the steel ball $()$ and the temperature of the water $($Tw$).$ Determine the transient and steady state solutions for the temperature of water and steel ball as a function of the system parameters. Plot these profiles for the set of parameters with the mass of the ball $(=1\mathrm{.}25$ kg$),$ the mass of the water $($mw$=5$ kg$),$ and the specific heats $($ C$=3360$ J$/$g$\backslash$deg C$,$ Cw$=4200$ J$/$g$\backslash$deg C$)$ and hA $($the heat transfer rate$)=4200$ J$/$s$\backslash$deg C$.$ What do you observe?