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Unformatted text preview: 1 Reconsider Problem 4–20. Using EES (or other)
software, investigate the effects of the heat transfer coefficient and the final plate temperature on the time it will
take for the plate to reach this temperature. Let the heat transfer coefficient vary from 5 W/m2 · °C to 25 W/m2 · °C and the
temperature from 30°C to 200°C. Plot the time as functions of
the heat transfer coefficient and the temperature, and discuss
4–22 Stainless steel ball bearings (
8085 kg/m3, k 15.1
3.91 10 6 m2/s)
W/m · °C, Cp 0.480 kJ/kg · °C, and
having a diameter of 1.2 cm are to be quenched in water. The
balls leave the oven at a uniform temperature of 900°C and are
exposed to air at 30°C for a while before they are dropped into
the water. If the temperature of the balls is not to fall below
850°C prior to quenching and the heat transfer coefficient in
the air is 125 W/m2 · °C, determine how long they can stand in
Answer: 3.7 s
the air before being dropped into the water.
4–23 Carbon steel balls (
Cp 0.465 kJ/kg · °C, and Air, 35°C Furnace
900°C FIGURE P4–19E 7833 kg/m3, k 54 W/m · °C,
1.474 10 6 m2/s) 8 mm in FIGURE P4–23 Steel ball 100°C cen58933_ch04.qxd 9/10/2002 9:13 AM Page 254 254
HEAT TRANSFER diameter are annealed by heating them first to 900°C in a furnace and then allowing them to cool slowly to 100°C in ambient air at 35°C. If the average heat transfer coefficient is
75 W/m2 · °C, determine how long the annealing process will
take. If 2500 balls are to be annealed per hour, determine the
total rate of heat transfer from the balls to the ambient air.
4–24 Reconsider Problem 4–23. Using EES (or other)
software, investigate the effect of the initial temperature of the balls on the annealing time and the total rate of
heat transfer. Let the temperature vary from 500°C to 1000°C.
Plot the time and the total rate of heat transfer as a function of
the initial temperature, and discuss the results.
4–25 An electronic device dissipating 30 W has a mass of
20 g, a specific heat of 850 J/kg · °C, and a surface area of
5 cm2. The device is lightly used, and it is on for 5 min and
then off for several hours, during which it cools to the ambient
temperature of 25°C. Taking the heat transfer coefficient to be
12 W/m2 · °C, determine the temperature of the device at the
end of the 5-min operating period. What would your answer be
if the device were attached to an aluminum heat sink having a
mass of 200 g and a surface area of 80 cm2? Assume the device
and the heat sink to be nearly isothermal. Would you use lumped system analysis or the transient temperature charts when determining the midpoint temperature of
the sphere? Why?
4–33 A student calculates that the total heat transfer from
a spherical copper ball of diameter 15 cm initially at 200°C
and its environment at a constant temperature of 25°C during
the first 20 min of cooling is 4520 kJ. Is this result reasonable? Why?
4–34 An ordinary egg can be approximated as a 5.5-cmdiameter sphere whose properties are roughly k 0.6 W/m ·
0.14 10 6 m2/s. The egg is initially at a uniform
temperature of 8°C and is dropped into boiling water at 97°C.
Taking the convection heat transfer coefficient to be h 1400
W/m2 · °C, determine how long it will take for the center of the
egg to reach 70°C. Egg
Ti = 8°C Transient Heat Conduction in Large Plane Walls,
Long Cylinders, and Spheres with Spatial Effects
4–26C What is an infinitely long cylinder? When is it proper
to treat an actual cylinder as being infinitely long, and when is
it not? For example, is it proper to use this model when finding
the temperatures near the bottom or top surfaces of a cylinder?
4–27C Can the transient temperature charts in Fig. 4–13 for
a plane wall exposed to convection on both sides be used for a
plane wall with one side exposed to convection while the other
side is insulated? Explain.
4–28C Why are the transient temperature charts prepared
using nondimensionalized quantities such as the Biot and
Fourier numbers instead of the actual variables such as thermal
conductivity and time?
4–29C What is the physical significance of the Fourier number? Will the Fourier number for a specified heat transfer problem double when the time is doubled? 97°C Boiling
water FIGURE P4–34
4–35 Reconsider Problem 4–34. Using EES (or other)
software, investigate the effect of the final center
temperature of the egg on the time it will take for the center to
reach this temperature. Let the temperature vary from 50°C
to 95°C. Plot the time versus the temperature, and discuss the
4–36 In a production facility, 3-cm-thick large brass plates
(k 110 W/m · °C,
8530 kg/m3, Cp 380 J/kg · °C, and
33.9 10 m /s) that are initially at a uniform temperature of 25°C are heated by passing them through an oven maintained at 700°C. The plates remain in the oven for a period of
10 min. Taking the convection heat transfer coefficient to be
h 80 W/m2 · °C, determine the surface temperature of the
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- Spring '10