The walls of a furnace are made of 1.6-ft-thick concrete (k = 0.64 btu/h⋅ft⋅°f and α = 0.023 ft2/h). initially, the furnace and the surrounding air are in thermal equilibrium at 70°f. the furnace is then fired, and the inner surfaces of the furnace are subjected to hot gases at 1800°f with a very large heat transfer coefficient. determine how long it will take for the temperature of the outer surface of the furnace walls to rise to 70.1°f.

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?