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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 20cmdiameter 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 10cmthick 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 30cmdiameter, 3.5mhigh 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 28cm diameter, 1.80mlong 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.
 Spring '10
 Ghaz

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