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.

Tom is having a problem with his washing machine. he notices that the machine vibrates violently at a frequency of 1500 rpm due to an unknown rotating unbalance. the machine is mounted on 4 springs each having a stiffness of 10 kn/m. tom wishes to add an undamped vibration absorber attached by a spring under the machine the machine working frequency ranges between 800 rpm to 2000 rpm and its total mass while loaded is assumed to be 80 kg a) what should be the mass of the absorber added to the machine so that the natural frequency falls outside the working range? b) after a first trial of an absorber using a mass of 35 kg, the amplitude of the oscillation was found to be 10 cm. what is the value of the rotating unbalance? c) using me-3.5 kg. m, find the optimal absorber (by minimizing its mass). what would be the amplitude of the oscillation of the absorber?