A 5-cm-diameter shaft rotates at 4500 rpm in a 15-cmlong, 8-cm-outer-diameter cast iron bearing (k = 70 W/m · K) with a uniform clearance of 0.6 mm filled with lubricating oil (m = 0.03 N·s/m² and k = 0.14 W/m · K). The bearing is cooled externally by a liquid, and its outer surface is maintained at 40°C. Disregarding heat conduction through the shaft and assuming one-dimensional heat transfer, determine

(a) The rate of heat transfer to the coolant,

(b) The surface temperature of the shaft,

(c) The mechanical power wasted by the viscous dissipation in oil.

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4500 rpm 5 cm 15 cm 8 cm