A long steel bar of radius R = 2.5 cm, k =50 W/(m .°C), p = 7800 kg/m3, and c = 0.5 kJ/(kg. .°C) is to be annealed by cooling slowly from 800.°C to 100.°C in an environment at temperature 50.°C. If the heat transfer coefficient between the environment and the surface of the bars is h = 45 W/(m .°C), determine the time required for the annealing process using lumped system analysis