Plate 1 in sphere cylinder 1 in 1 in figure p4115

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Unformatted text preview: is inserted to the center of the sample along the centerline, and another thermocouple is welded into a small hole drilled on the surface. The sample is dropped into boiling water at 100°C. After 3 min, the surface and the center temperatures are recorded to be 93°C and 75°C, respectively. Determine the thermal diffusivity and the thermal conductivity of the material. 4–114 In desert climates, rainfall is not a common occurrence since the rain droplets formed in the upper layer of the atmosphere often evaporate before they reach the ground. Consider a raindrop that is initially at a temperature of 5°C and has a diameter of 5 mm. Determine how long it will take for the diameter of the raindrop to reduce to 3 mm as it falls through ambient air at 18°C with a heat transfer coefficient of 400 W/m2 · °C. The water temperature can be assumed to remain constant and uniform at 5°C at all times. 4–115E Consider a plate of thickness 1 in., a long cylinder of diameter 1 in., and a sphere of diameter 1 in., all initially at 400°F and all made of bronze (k 15.0 Btu/h · ft · °F and 0.333 ft2/h). Now all three of these geometries are exposed to cool air at 75°F on all of their surfaces, with a heat transfer coefficient of 7 Btu/h · ft2 · °F. Determine the center temperature of each geometry after 5, 10, and 30 min. Explain why the center temperature of the sphere is always the lowest. Plate 1 in. Sphere Cylinder 1 in. 1 in. FIGURE P4–115 4–116E Repeat Problem 4–115E for cast iron geometries (k 29 Btu/h · ft · °F and 0.61 ft2/h). 4–117E Reconsider Problem 4–115E. Using EES (or other) software, plot the center temperature of each geometry as a function of the cooling time as the time varies fom 5 min to 60 min, and discuss the results. 4–118 Engine valves (k 48 W/m · °C, Cp 440 J/kg · °C, and 7840 kg/m3) are heated to 800°C in the heat treatment section of a valve manufacturing facility. The valves are then quenched in a large oil bath at an average temperature of 45°C. The heat transfer coefficient in the oil bath is 650 W/m2 · °C. The valves have a cylindrical stem with a diameter of 8 mm and a length of 10 cm. The valve head and the stem may be assumed to be of equal surface area, and the volume of the valve head can be taken to be 80 percent of the volume of steam. Determine how long will it take for the valve temperature to drop to (a) 400°C, (b) 200°C, and (c) 46°C and (d) the maximum heat transfer from a single valve. 4–119 A watermelon initially at 35°C is to be cooled by dropping it into a lake at 15°C. After 4 h and 40 min of cooling, the center temperature of watermelon is measured to be 20°C. Treating the watermelon as a 20-cm-diameter sphere and using the properties k 0.618 W/m · °C, 0.15 10 6 m2/s, 3 995 kg/m , and Cp 4.18 kJ/kg · °C, determine the average heat transfer coefficient and the surface temperature of watermelon at the end of the cooling period. 4–120 10-cm-thick large food slabs tightly wrapped by thin paper are to be cooled in a refrigeration room maintained at 0°C. The heat transfer coefficient on the box surfaces is 25 W/m2 · °C and the boxes are to be kept in the refrigeration room for a period of 6 h. If the initial temperature of the boxes is 30°C determine the center temperature of the boxes if the boxes contain (a) margarine (k 0.233 W/m · °C and 0.11 10 6 m2/s), (b) white cake (k 0.082 W/m · °C and 0.106 0.10 10 6 m2/s), and (c) chocolate cake (k W/m · °C and 0.12 10 6 m2/s). 4–121 A 30-cm-diameter, 3.5-m-high cylindrical column of a house made of concrete (k 0.79 W/m · °C, 5.94 1600 kg/m3, and Cp 0.84 kJ/kg · °C) cooled 10 7 m2/s, to 16°C during a cold night is heated again during the day by being exposed to ambient air at an average temperature of 28°C with an average heat transfer coefficient of 14 W/m2 · °C. Determine (a) how long it will take for the column surface temperature to rise to 27°C, (b) the amount of heat transfer until the center temperature reaches to 28°C, and (c) the amount of heat transfer until the surface temperature reaches to 27°C. 4–122 Long aluminum wires of diameter 3 mm ( 2702 0.896 kJ/kg · °C, k 236 W/m · °C, and kg/m3, Cp 9.75 10 5 m2/s) are extruded at a temperature of 350°C and exposed to atmospheric air at 30°C with a heat transfer coefficient of 35 W/m2 · °C. (a) Determine how long it will take for the wire temperature to drop to 50°C. (b) If the wire is extruded at a velocity of 10 m/min, determine how far the wire travels after extrusion by the time its temperature drops to 50°C. What change in the cooling process would you propose to shorten this distance? (c) Assuming the aluminum wire leaves the extrusion room at 50°C, determine the rate of heat transfer from the wire to the extrusion room. Answers: (a) 144 s, (b) 24 m, (c) 856 W cen58933_ch04.qxd 9/10/2002 9:13 AM Page 264 264 HEAT TRANSFER 350°C body as 28-cm diameter, 1.80-m-long cylinder, estimate how long it has been since he died. Ta...
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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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