final_exam - 10.302 Fall 2004 FINAL EXAMINATION GOOD LUCK...

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10.302 Fall 2004 FINAL EXAMINATION December 14, 1004 GOOD LUCK! Problem 1 ( 40 points) Consider a small droplet (d p = 1 mm) of n-butane that falls through still air at 325K. As the droplet evaporates, it will cool, but then reach a steady temperature. It is agreed that radiation and diffusion-induced convection may be neglected. A. What is the value of the steady temperature? B. What is the value of the convective heat transfer coefficient that characterizes heat transfer from the air to the droplet? C. Very approximately (seconds, minutes, or hours), how long will it take to reach this steady temperature? Justify. D. If diffusion-induced convection had been included in the analysis, would the steady state temperature have been higher or lower? Explain. DATA 4 air / c D = 0.22 cm 2 /s ρ air = 1.16 kg/m 3 υ air = 1.6 x 10 -5 m 2 /s c p, air = 1000 J/kg K α air = 2.2 x 10 -5 m 2 /s H VAP = 400,000 J kg 4 c MW = 58 4 c (liq.) ρ = 580 kg/m 3 4 p, c c (liq.) = 2000 J/kg K 4 c k (liq.) = 0.15 w/m K The vapor pressure curve for n-butane is attached.
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FIGURE 1
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Problem 2 (60 points) Many current models of automobiles have a readout in the passenger compartment that indicates ambient temperature. The temperature sensor for this instrument is usually located in the air intake manifold for the motor, downstream of the air filter. A sketch of the sensor, and the long circular duct in which it is located, is shown in Figure 2. A thermocouple is located inside a small diameter stainless steel sheath that protrudes through the wall of the duct. FIGURE 2 The duct is 7.5 cm in diameter and carries air at between 2000 and 8000 liters/min depending on engine speed. The driver of the car would like the thermocouple to indicate an accurate air temperature independent of the engine speed and temperature of the wall of the air duct. An expanded sketch of the thermocouple and its sheath is given in Figure 3. 7.5 cm Thermocouple Sheath Long Plastic Duct Enlarged in Figure 3 Air Intake NOT TO SCALE
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FIGURE 3 The thermocouple sheath is made of stainless steel and has an outside diameter of 3 mm, an inside diameter of 2 mm, and a length from duct wall to thermocouple bead of 2.0 cm.
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This note was uploaded on 11/27/2011 for the course CHEMICAL E 10.302 taught by Professor Clarkcolton during the Fall '04 term at MIT.

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final_exam - 10.302 Fall 2004 FINAL EXAMINATION GOOD LUCK...

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