A 6-cm-diameter shaft rotates at 3000 rpm in a 20-cm-long bearing with a uniform clearance of 0.2 mm. At steady operating conditions, both the bearing and the shaft in the vicinity of the oil gap are at 50°C, and the viscosity and thermal conductivity of lubricating oil are 0.05 N·s/m² and 0.17 W/m · K. By simplifying and solving the continuity, momentum, and energy equations, determine

(a) The maximum temperature of 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.

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3000 rpm 6 cm 20 cm