PROBLEM 1 (10 points) A 2-cm long aluminum alloy pin fin has a reduction in diameter from 2 mm to 1 mmat a location 8 mm from its base. The fin is attached to a wall at 200 °C and is exposed to gas flow at 20 °C. The heat transfer coefficient on the larger section is 42 W/m2-K and the heat transfercoefficient on the smaller section is 60 W/m2-K. Calculate the total heat loss from the fin, and the temperature at the contraction and at the tip. Use k = 185 W/m for the aluminum alloy.
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PROBLEM 2 (10 points) A 25-cm diameter oil line is buried with its centerline 60 cm below the ground. Assuming a soil temperature of 10 °C and a soilthermal conductivity of 0.8 W/m-K, estimate the steady-state heat loss from the pipe (in W/m) when the oil is at 90 °C. Assume the heat transfer coefficient between the oil and the pipe wall is 300W/m2-K.
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PROBLEM 3 (10 points) You will need a computer to solve this problem. A thick slab of copper alloy is initially at 25 °C. This is a special copperalloy, with the following properties: = 8900 kg/m3, c = 231 J/kg-K, and k = 100 + 300T W/m-K. The thermal conductivity is calculated using the copper temperature in degrees C, such that k = 100 W/m-K at0 °C and k = 400 W/m-K at 100 °C. At t = 0, the copper surface is at 100 °C and is held at that temperature for 500 seconds. At t = 500, the copper surface is 25 C and is held at that temperature for500 seconds. On one figure, plot T(x) for the domain 0 < x < 0.5 m at t = 0, 100, 250, 500, 750, and 1000 seconds. This should be one figure, with a common x-axis, y-axis, and 6 different curves....