Air 2c 4 ms potato ti 25c figure p454 455e oranges of

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Unformatted text preview: ermine (a) how long the potato is baked in the oven and (b) the final equilibrium temperature of the potato after it is wrapped. 4–54 White potatoes (k 0.50 W/m · °C and 0.13 10 6 m2/s) that are initially at a uniform temperature of 25°C and have an average diameter of 6 cm are to be cooled by refrigerated air at 2°C flowing at a velocity of 4 m/s. The average heat transfer coefficient between the potatoes and the air is experimentally determined to be 19 W/m2 · °C. Determine how long it will take for the center temperature of the potatoes to drop to 6°C. Also, determine if any part of the potatoes will experience chilling injury during this process. Air 2°C 4 m/s Potato Ti = 25°C FIGURE P4–54 4–55E Oranges of 2.5-in. diameter (k 0.26 Btu/h · ft · °F and 1.4 10 6 ft2/s) initially at a uniform temperature of 78°F are to be cooled by refrigerated air at 25°F flowing at a velocity of 1 ft/s. The average heat transfer coefficient between the oranges and the air is experimentally determined to be 4.6 Btu/h · ft2 · °F. Determine how long it will take for the center temperature of the oranges to drop to 40°F. Also, determine if any part of the oranges will freeze during this process. 4–56 A 65-kg beef carcass (k 0.47 W/m · °C and 0.13 10 6 m2/s) initially at a uniform temperature of 37°C is to be cooled by refrigerated air at 6°C flowing at a velocity of 1.8 m/s. The average heat transfer coefficient between the carcass and the air is 22 W/m2 · °C. Treating the carcass as a cylinder of diameter 24 cm and height 1.4 m and disregarding heat transfer from the base and top surfaces, determine how long it will take for the center temperature of the carcass to drop to 4°C. Also, determine if any part of the carcass will Answer: 14.0 h freeze during this process. Air – 6°C 1.8 m/s Beef 37°C FIGURE P4–56 4–57 Layers of 23-cm-thick meat slabs (k 0.47 W/m · °C and 0.13 10 6 m2/s) initially at a uniform temperature of 7°C are to be frozen by refrigerated air at 30°C flowing at a velocity of 1.4 m/s. The average heat transfer coefficient between the meat and the air is 20 W/m2 · °C. Assuming the size of the meat slabs to be large relative to their thickness, determine how long it will take for the center temperature of the slabs to drop to 18°C. Also, determine the surface temperature of the meat slab at that time. 4–58E Layers of 6-in.-thick meat slabs (k 0.26 Btu/h · ft · °F and 1.4 10 6 ft2/s) initially at a uniform temperature of 50°F are cooled by refrigerated air at 23°F to a temperature of 36°F at their center in 12 h. Estimate the average heat transfer coefficient during this cooling process. Answer: 1.5 Btu/h · ft2 · °F 4–59 Chickens with an average mass of 1.7 kg (k 0.45 W/m · °C and 0.13 10 6 m2/s) initially at a uniform temperature of 15°C are to be chilled in agitated brine at 10°C. The average heat transfer coefficient between the chicken and the brine is determined experimentally to be 440 W/m2 · °C. Taking the average density of the chicken to be 0.95 g/cm3 and treating the chicken as a spherical lump, determine the center and the surface temperatures of the chicken in 2 h and 30 min. Also, determine if any part of the chicken will freeze during this process. Chicken 1.7 kg Brine –10°C FIGURE P4–59 cen58933_ch04.qxd 9/10/2002 9:13 AM Page 258 258 HEAT TRANSFER Transient Heat Conduction in Semi-Infinite Solids 4–60C What is a semi-infinite medium? Give examples of solid bodies that can be treated as semi-infinite mediums for heat transfer purposes. 4–61C Under what conditions can a plane wall be treated as a semi-infinite medium? 4–62C Consider a hot semi-infinite solid at an initial temperature of Ti that is exposed to convection to a cooler medium at a constant temperature of T , with a heat transfer coefficient of h. Explain how you can determine the total amount of heat transfer from the solid up to a specified time to. 4–63 In areas where the air temperature remains below 0°C for prolonged periods of time, the freezing of water in underground pipes is a major concern. Fortunately, the soil remains relatively warm during those periods, and it takes weeks for the subfreezing temperatures to reach the water mains in the ground. Thus, the soil effectively serves as an insulation to protect the water from the freezing atmospheric temperatures in winter. The ground at a particular location is covered with snow pack at 8°C for a continuous period of 60 days, and the average soil properties at that location are k 0.35 W/m · °C and 0.15 80 6 m2/s. Assuming an initial uniform temperature of 8°C for the ground, determine the minimum burial depth to prevent the water pipes from freezing. 4–64 The soil temperature in the upper layers of the earth varies with the variations in the atmospheric conditions. Before a cold front moves in, the earth at a location is initially at a uniform temperature of 10°C. Then the area is subjected to a temperature of 10°C and high winds that resulted in a convection heat transfer co...
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