(30 pt) A steel long-cylinder ($\alpha$=1.5x10$^{-6}$ m$^2$/s, k=30 W/m.$^\circ$C, c=500 J/kg.$^\circ$C, p=5000 kg/m$^3$) having radius of 30 cm, initially at uniform temperature of 600 $^\circ$C, is suddenly immersed in a water bath at 25 $^\circ$C. The convection heat transfer coefficient between the water and the cylinder surface is 1000 W/m$^2$.$^\circ$C.
a. Find the centre temperature of the cylinder after 30 minutes.
b. Calculate the energy (Q) removed per unit length of the cylinder during 30-minute period.