Problems designated by a c are concept questions and

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Unformatted text preview: e likely to be larger for highly conducting solids or poorly conducting ones? *Problems designated by a “C” are concept questions, and students are encouraged to answer them all. Problems designated by an “E” are in English units, and the SI users can ignore them. Problems with an EES-CD icon are solved using EES, and complete solutions together with parametric studies are included on the enclosed CD. Problems with a computer-EES icon are comprehensive in nature, and are intended to be solved with a computer, preferably using the EES software that accompanies this text. 4–7C Consider two identical 4–kg pieces of roast beef. The first piece is baked as a whole, while the second is baked after being cut into two equal pieces in the same oven. Will there be any difference between the cooking times of the whole and cut roasts? Why? 4–8C Consider a sphere and a cylinder of equal volume made of copper. Both the sphere and the cylinder are initially at the same temperature and are exposed to convection in the same environment. Which do you think will cool faster, the cylinder or the sphere? Why? 4–9C In what medium is the lumped system analysis more likely to be applicable: in water or in air? Why? 4–10C For which solid is the lumped system analysis more likely to be applicable: an actual apple or a golden apple of the same size? Why? 4–11C For which kind of bodies made of the same material is the lumped system analysis more likely to be applicable: slender ones or well-rounded ones of the same volume? Why? 4–12 Obtain relations for the characteristic lengths of a large plane wall of thickness 2L, a very long cylinder of radius ro, and a sphere of radius ro. 4–13 Obtain a relation for the time required for a lumped T ), where system to reach the average temperature 1 (Ti 2 Ti is the initial temperature and T is the temperature of the environment. 4–14 The temperature of a gas stream is to be measured by a thermocouple whose junction can be approximated as a 1.2-mm-diameter sphere. The properties of the junction are k 35 W/m · °C, 8500 kg/m3, and Cp 320 J/kg · °C, and the heat transfer coefficient between the junction and the gas is h 65 W/m2 · °C. Determine how long it will take for the thermocouple to read 99 percent of the initial temperature Answer: 38.5 s difference. 4–15E In a manufacturing facility, 2-in.-diameter brass balls 0.092 (k 64.1 Btu/h · ft · °F, 532 lbm/ft3, and Cp Btu/lbm · °F) initially at 250°F are quenched in a water bath at 120°F for a period of 2 min at a rate of 120 balls per minute. If the convection heat transfer coefficient is 42 Btu/h · ft2 · °F, determine (a) the temperature of the balls after quenching and (b) the rate at which heat needs to be removed from the water in order to keep its temperature constant at 120°F. cen58933_ch04.qxd 9/10/2002 9:13 AM Page 253 253 CHAPTER 4 250°F Brass balls 120°F Water bath FIGURE P4–15E 4–16E 4–20 Consider a 1000-W iron whose base plate is made of 0.5-cm-thick aluminum alloy 2024-T6 ( 2770 kg/m3, Cp 5 2 875 J/kg · °C, 7.3 10 m /s). The base plate has a surface area of 0.03 m2. Initially, the iron is in thermal equilibrium with the ambient air at 22°C. Taking the heat transfer coefficient at the surface of the base plate to be 12 W/m2 · °C and assuming 85 percent of the heat generated in the resistance wires is transferred to the plate, determine how long it will take for the plate temperature to reach 140°C. Is it realistic to assume the plate temperature to be uniform at all times? Repeat Problem 4–15E for aluminum balls. Air 22°C 4–17 To warm up some milk for a baby, a mother pours milk into a thin-walled glass whose diameter is 6 cm. The height of the milk in the glass is 7 cm. She then places the glass into a large pan filled with hot water at 60°C. The milk is stirred constantly, so that its temperature is uniform at all times. If the heat transfer coefficient between the water and the glass is 120 W/m2 · °C, determine how long it will take for the milk to warm up from 3°C to 38°C. Take the properties of the milk to be the same as those of water. Can the milk in this case be Answer: 5.8 min treated as a lumped system? Why? 4–18 Repeat Problem 4–17 for the case of water also being stirred, so that the heat transfer coefficient is doubled to 240 W/m2 · °C. 4–19E During a picnic on a hot summer day, all the cold drinks disappeared quickly, and the only available drinks were those at the ambient temperature of 80°F. In an effort to cool a 12-fluid-oz drink in a can, which is 5 in. high and has a diameter of 2.5 in., a person grabs the can and starts shaking it in the iced water of the chest at 32°F. The temperature of the drink can be assumed to be uniform at all times, and the heat transfer coefficient between the iced water and the aluminum can is 30 Btu/h · ft2 · °F. Using the properties of water for the drink, estimate how long it will take for the canned drink to cool to 45°F. 1000 W iron FIGURE P4–20 4–2...
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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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