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 EESCD icon
are solved using EES, and
complete solutions together with parametric studies are included
on the enclosed CD. Problems with a computerEES 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 wellrounded 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
1.2mmdiameter 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, 2in.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 1000W iron whose base plate is made of
0.5cmthick aluminum alloy 2024T6 (
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 thinwalled 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
12fluidoz 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.
 Spring '10
 Ghaz

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