A 1m-long metal cylinder of 25cm radius is heated such that the axial temperature distribution at a certain instant of time is T(z)=a+bz+cz2 where a=900K, b=-500K/m and c=150K/m2 . What is the rate of energy change of the cylinder at this instant if the side surface is well insulated and the cylinder's thermal conductivity is 40W/mK?