The heat transfer coefficient at the surface of the

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Unformatted text preview: or would it make no difference? Base your answer on calculations. 2°C 42°C 30 cm FIGURE P4–106 4–107 The water main in the cities must be placed at sufficient depth below the earth’s surface to avoid freezing during extended periods of subfreezing temperatures. Determine the minimum depth at which the water main must be placed at a location where the soil is initially at 15°C and the earth’s surface temperature under the worst conditions is expected to remain at 10°C for a period of 75 days. Take the properties of soil at that location to be k 0.7 W/m · °C and Answer: 7.05 m 1.4 10 5 m2/s. 4–108 A hot dog can be considered to be a 12-cm-long cylinder whose diameter is 2 cm and whose properties are 980 kg/m3, Cp 3.9 kJ/kg · °C, k 0.76 W/m · °C, and Review Problems 4–105 Consider two 2-cm-thick large steel plates (k 43 W/m · °C and 1.17 10 5 m2/s) that were put on top of each other while wet and left outside during a cold winter night at 15°C. The next day, a worker needs one of the plates, but the plates are stuck together because the freezing of the water Hot dog Water, 100°C FIGURE P4–108 cen58933_ch04.qxd 9/10/2002 9:13 AM Page 262 262 HEAT TRANSFER 2 10 7 m2/s. A hot dog initially at 5°C is dropped into boiling water at 100°C. The heat transfer coefficient at the surface of the hot dog is estimated to be 600 W/m2 · °C. If the hot dog is considered cooked when its center temperature reaches 80°C, determine how long it will take to cook it in the boiling water. 4–109 A long roll of 2-m-wide and 0.5-cm-thick 1-Mn manganese steel plate coming off a furnace at 820°C is to be 2.0 kJ/kg · °C) at 45°C. The quenched in an oil bath (Cp metal sheet is moving at a steady velocity of 10 m/min, and the oil bath is 5 m long. Taking the convection heat transfer coefficient on both sides of the plate to be 860 W/m2 · °C, determine the temperature of the sheet metal when it leaves the oil bath. Also, determine the required rate of heat removal from the oil to keep its temperature constant at 45°C. During a fire, the trunks of some dry oak trees (k 0.17 W/m · °C and 1.28 10 7 m2/s) that are initially at a uniform temperature of 30°C are exposed to hot gases at 520°C for a period of 5 h, with a heat transfer coefficient of 65 W/m2 · °C on the surface. The ignition temperature of the trees is 410°C. Treating the trunks of the trees as long cylindrical rods of diameter 20 cm, determine if these dry trees will ignite as the fire sweeps through them. Hot gases 520°C 30°C 20 cm Furnace 10 m/min 4–111 Steel plate FIGURE P4–111 Oil bath, 45°C FIGURE P4–109 4–110E In Betty Crocker ’s Cookbook, it is stated that it takes 5 h to roast a 14-lb stuffed turkey initially at 40°F in an oven maintained at 325°F. It is recommended that a meat thermometer be used to monitor the cooking, and the turkey is considered done when the thermometer inserted deep into the thickest part of the breast or thigh without touching the bone registers 185°F. The turkey can be treated as a homogeneous spheri0.98 cal object with the properties 75 lbm/ft3, Cp Btu/lbm · °F, k 0.26 Btu/h · ft · °F, and 0.0035 ft2/h. Assuming the tip of the thermometer is at one-third radial distance from the center of the turkey, determine (a) the average heat transfer coefficient at the surface of the turkey, (b) the temperature of the skin of the turkey when it is done, and (c) the total amount of heat transferred to the turkey in the oven. Will the reading of the thermometer be more or less than 185°F 5 min after the turkey is taken out of the oven? 4–112 We often cut a watermelon in half and put it into the freezer to cool it quickly. But usually we forget to check on it and end up having a watermelon with a frozen layer on the top. To avoid this potential problem a person wants to set the timer such that it will go off when the temperature of the exposed surface of the watermelon drops to 3°C. Consider a 30-cm-diameter spherical watermelon that is cut into two equal parts and put into a freezer at 12°C. Initially, the entire watermelon is at a uniform temperature of 25°C, and the heat transfer coefficient on the surfaces is 30 W/m2 · °C. Assuming the watermelon to have the properties of water, determine how long it will take for the center of the exposed cut surfaces of the watermelon to drop to 3°C. Freezer –12°C Watermelon, 25°C FIGURE P4–112 FIGURE P4–110 4–113 The thermal conductivity of a solid whose density and specific heat are known can be determined from the relation k / Cp after evaluating the thermal diffusivity . Consider a 2-cm-diameter cylindrical rod made of a sample material whose density and specific heat are 3700 kg/m3 and 920 J/kg · °C, respectively. The sample is initially at a uniform temperature of 25°C. In order to measure the temperatures of cen58933_ch04.qxd 9/10/2002 9:13 AM Page 263 263 CHAPTER 4 Tsurface Thermocouples Rod Tcenter Boiling water 100°C FIGURE P4–113 the sample at its surface and its center, a thermocouple...
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