Astraight rectangular fin is attached to a wall at a temperature of 100 c to dissipate excess heat that is produced. the fin material is an integral part of the cast-iron wall (k-50 w/m-k). the surface of the fin is exposed to an ambient air temperature of 20°c and the convection coefficient is estimated to be 60 w/m-.k. the fin thickness is 2 mm and space limitations require that the width of fin be no larger than 20 cm. assuming constant material properties, one-dimensional heat transfer along the length, and an adiabatic fin tip: a) find the smallest value of the fin length l for which the temperature of the fin tip at x l does not exceed 52 °c. b) find the heat transfer rate.

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?