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Unformatted text preview: or would it make no
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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 12cmlong 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 2cmthick 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 2mwide and 0.5cmthick 1Mn 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 14lb 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 onethird 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 30cmdiameter 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 2cmdiameter 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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 Spring '10
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