1.) A shaft with a 20mm radius, rotates at 3600rpm in a bearing. The length of the bearing is 20cm. The shaft and the bearing are at 45C at steady conditions. The thermal conductivity and the viscosity of the oil in between are 0.12W/mC and 0.03N.s/m2, respectively. Assuming that there is a uniform clearance of 0.3mm between the shaft and bearing, simplify and solve the continuity, momentum, and energy equations to determine: (a) The maximum temperature of the oil (b) The rates of heat transfer to the bearing and the shaft (c) The mechanical power wasted by the viscous dissipation in the oil