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 and convection heat transfer coefficient of the surface area of the motor housing that is exposed to the ambient air is . 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 , 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.
