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A DC motor delivers mechanical power to a rotating stainless steel shaft (k = 15.1 W/m·K) with a length of 25 cm and a diameter of 25 mm. In a surrounding with ambient air temperature of 20°C and convection heat transfer coefficient of 25 W/m2·K, the surface area of the motor housing that is exposed to the ambient air is 0.075 m2. The motor uses 300 W of electrical power and delivers 55% of it as mechanical power to rotate the stainless steel shaft. If the tip of the stainless steel shaft has a temperature of 22°C, determine the surface temperature of the motor housing. Assume the base temperature of the shaft is equal to the surface temperature of the motor housing.
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