Long carbon steel shafts (k = 51.2 W/mºC,  = 1.21  10-5 m2 /s) of 0.1 m diameter are treated in a gas-fired furnace whose gases are at 927 ºC and provide a convection coefficient of 100 W/m2 ºC. The shafts enter the furnace at 27 ºC. Disregard radiation heat transfer. Determine the time (s) the shafts must remain in the furnace to achieve a centerline temperature of 527 ºC.