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QUIZ 1 ME 420 – PROFESSOR KING Write your name on every page. Pages without names will not be scored. All problems are 10 points, but the problems are of varying difficulty. No collaboration isallowed. Do not discuss this quiz with anyone.





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.








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.




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....
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