How can you determine the maximum possible amount of

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Unformatted text preview: when they come out of the oven. Furnace, 700°C 4–30C How can we use the transient temperature charts when the surface temperature of the geometry is specified instead of the temperature of the surrounding medium and the convection heat transfer coefficient? 4–31C A body at an initial temperature of Ti is brought into a medium at a constant temperature of T . How can you determine the maximum possible amount of heat transfer between the body and the surrounding medium? 4–32C The Biot number during a heat transfer process between a sphere and its surroundings is determined to be 0.02. 3 cm Brass plate 25°C FIGURE P4–36 cen58933_ch04.qxd 9/10/2002 9:13 AM Page 255 255 CHAPTER 4 4–37 Reconsider Problem 4–36. Using EES (or other) software, investigate the effects of the temperature of the oven and the heating time on the final surface temperature of the plates. Let the oven temperature vary from 500°C to 900°C and the time from 2 min to 30 min. Plot the surface temperature as the functions of the oven temperature and the time, and discuss the results. 4–38 A long 35-cm-diameter cylindrical shaft made of stainless steel 304 (k 14.9 W/m · °C, 7900 kg/m3, Cp 477 6 2 J/kg · °C, and 3.95 10 m /s) comes out of an oven at a uniform temperature of 400°C. The shaft is then allowed to cool slowly in a chamber at 150°C with an average convection heat transfer coefficient of h 60 W/m2 · °C. Determine the temperature at the center of the shaft 20 min after the start of the cooling process. Also, determine the heat transfer per unit length of the shaft during this time period. Answers: 390°C, 16,015 kJ/m 4–39 Reconsider Problem 4–38. Using EES (or other) software, investigate the effect of the cooling time on the final center temperature of the shaft and the amount of heat transfer. Let the time vary from 5 min to 60 min. Plot the center temperature and the heat transfer as a function of the time, and discuss the results. 4–40E Long cylindrical AISI stainless steel rods (k 7.74 Btu/h · ft · °F and 0.135 ft2/h) of 4-in. diameter are heattreated by drawing them at a velocity of 10 ft/min through a 30-ft-long oven maintained at 1700°F. The heat transfer coefficient in the oven is 20 Btu/h · ft2 · °F. If the rods enter the oven at 85°F, determine their centerline temperature when they leave. 500°C in a fireplace with a heat transfer coefficient of 13.6 W/m2 · °C on the surface. If the ignition temperature of the wood is 420°C, determine how long it will be before the log ignites. 4–43 In Betty Crocker ’s Cookbook, it is stated that it takes 2 h 45 min to roast a 3.2-kg rib initially at 4.5°C “rare” in an oven maintained at 163°C. It is recommended that a meat thermometer be used to monitor the cooking, and the rib is considered rare done when the thermometer inserted into the center of the thickest part of the meat registers 60°C. The rib can be treated as a homogeneous spherical object with the properties 1200 kg/m3, Cp 4.1 kJ/kg · °C, k 0.45 W/m · °C, and 0.91 10 7 m2/s. Determine (a) the heat transfer coefficient at the surface of the rib, (b) the temperature of the outer surface of the rib when it is done, and (c) the amount of heat transferred to the rib. (d) Using the values obtained, predict how long it will take to roast this rib to “medium” level, which occurs when the innermost temperature of the rib reaches 71°C. Compare your result to the listed value of 3 h 20 min. If the roast rib is to be set on the counter for about 15 min before it is sliced, it is recommended that the rib be taken out of the oven when the thermometer registers about 4°C below the indicated value because the rib will continue cooking even after it is taken out of the oven. Do you agree with this recommendation? Answers: (a) 156.9 W/m2 · °C, (b) 159.5°C, (c) 1629 kJ, (d) 3.0 h Oven, 163°C Oven 1700°F 10 ft/min 30 ft Stainless steel 85°F FIGURE P4–40E 4–41 In a meat processing plant, 2-cm-thick steaks (k 0.45 W/m · °C and 0.91 10 7 m2/s) that are initially at 25°C are to be cooled by passing them through a refrigeration room at 11°C. The heat transfer coefficient on both sides of the steaks is 9 W/m2 · °C. If both surfaces of the steaks are to be cooled to 2°C, determine how long the steaks should be kept in the refrigeration room. 4–42 A long cylindrical wood log (k 0.17 W/m · °C and 1.28 10 7 m2/s) is 10 cm in diameter and is initially at a uniform temperature of 10°C. It is exposed to hot gases at Rib Ti = 4.5°C FIGURE P4–43 4–44 Repeat Problem 4–43 for a roast rib that is to be “welldone” instead of “rare.” A rib is considered to be well-done when its center temperature reaches 77°C, and the roasting in this case takes about 4 h 15 min. 4–45 For heat transfer purposes, an egg can be considered to be a 5.5-cm-diameter sphere having the properties of water. An egg that is initially at 8°C is dropped into the boiling water at 100°C. The heat transfer coefficien...
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This note was uploaded on 01/28/2010 for the course HEAT ENG taught by Professor Ghaz during the Spring '10 term at University of Guelph.

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