9–1C What is natural convection? How does it differ from forced convection? What force causes natural convection currents
Get solution
9–2C
In which mode of heat transfer is the convection heat transfer
coefficient usually higher, natural convection or forced convection? Why
Get solution
9–3C Consider a hot boiled egg in a spacecraft that is filled with air at atmospheric pressure and temperature at all times.
Get solution
9–4C
What is buoyancy force? Compare the relative magnitudes of the buoyancy
force acting on a body immersed in these mediums: (a) air, (b) water,
(c) mercury, and (d) an evacuated chamber
Get solution
9–5C When will the hull of a ship sink in water deeper: when the ship is sailing in fresh water or in sea water? Why
Get solution
9–6C
Aperson weighs himself on a waterproof spring scale placed at the
bottom of a 1-m-deep swimming pool. Will the person weigh more or less
in water? Why
Get solution
9–7C
Consider two fluids, one with a large coefficient of volume expansion
and the other with a small one. In what fluid will a hot surface
initiate stronger natural convection currents? Why? Assume the viscosity
of the fluids to be the same
Get solution
9–8C
Consider a fluid whose volume does not change with temperature at
constant pressure. What can you say about natural convection heat
transfer in this medium
Get solution
9–9C What do the lines on an interferometer photograph represent? What do closely packed lines on the same photograph represent
Get solution
9–10C Physically, what does the Grashof number represent? How does the Grashof number differ from the Reynolds number
Get solution
9–11 Show that the volume expansion coefficient of an ideal gas is B=1/T, where T is the absolute temperature.
Get solution
9–12C How does the Rayleigh number differ from the Grashof number
Get solution
9–13C
Under what conditions can the outer surface of a vertical cylinder be
treated as a vertical plate in natural convection calculations
Get solution
9–14C
Will a hot horizontal plate whose back side is insulated cool faster or
slower when its hot surface is facing down instead of up
Get solution
9–15C
Consider laminar natural convection from a vertical hot plate. Will the
heat flux be higher at the top or at the bottom of the plate? Why
Get solution
9–16
A10-m-long section of a 6-cm-diameter horizontal hot water pipe passes
through a large room whose temperature is 22°C. If the temperature and
the emissivity of the outer surface of the pipe are 65°C and 0.8,
respectively, determine the rate of heat loss from the pipe by (a)
natural convection and (b) radiation
Get solution
9–17
Consider a wall-mounted power transistor that dissipates 0.18 Wof power
in an environment at 35°C. The transistor is 0.45 cm long and has a
diameter of 0.4 cm. The emissivity of the outer surface of the
transistor is 0.1, and the average temperature of the surrounding
surfaces is 25°C. Disregarding any heat transfer from the base surface,
determine the surface temperature of the transistor. Use air properties
at 100°C.
Get solution
9–18
Reconsider Problem 9–17. Using EES (or other) software, investigate the
effect of ambient temperature on the surface temperature of the
transistor. Let the environment temperature vary from 10˚C to 40˚C and
assume that the surrounding surfaces are 10˚C colder than the
environment temperature. Plot the surface temperature of the transistor
versus the environment temperature, and discuss the results
Get solution
9–19E
Consider a 2-ft 2-ft thin square plate in a room at 75°F. One side of
the plate is maintained at a temperature of 130°F, while the other side
is insulated. Determine the rate of heat transfer from the plate by
natural convection if the plate is (a) vertical, (b) horizontal with hot
surface facing up, and (c) horizontal with hot surface facing down
Get solution
9–20E
Reconsider Problem 9–19E. Using EES (or other) software, plot the rate
of natural convection heat transfer for different orientations of the
plate as a function of the plate temperature as the temperature varies
from 80˚F to 180˚F, and discuss the results
Get solution
9–21
A 400-W cylindrical resistance heater is 1 m long and 0.5 cm in
diameter. The resistance wire is placed horizontally in a fluid at 20°C.
Determine the outer surface temperature of the resistance wire in
steady operation if the fluid is (a) air and (b) water. Ignore any heat
transfer by radiation. Use properties at 500°C for air and 40°C for
water
Get solution
9–22
Water is boiling in a 12-cm-deep pan with an outer diameter of 25 cm
that is placed on top of a stove. The ambient air and the surrounding
surfaces are at a temperature of 25°C, and the emissivity of the outer
surface of the pan is 0.95. Assuming the entire pan to be at an average
temperature of 98°C, determine the rate of heat loss from the
cylindrical side surface of the pan to the surroundings by (a) natural
convection and (b) radiation. (c) If water is boiling at a rate of 2
kg/h at 100°C,determine the ratio of the heat lost from the side
surfaces of the pan to that by the evaporation of water. The heat of
vaporization of water at 100°C is 2257 kJ/kg.
Get solution
9–23 Repeat Problem 9–22 for a pan whose outer surface is polished and has an emissivity of 0.1
Get solution
9–24
In a plant that manufactures canned aerosol paints, the cans are
temperature-tested in water baths at 55°C before they are shipped to
ensure that they will withstand temperatures up to 55°C during
transportation and shelving. The cans, moving on a conveyor, enter the
open hot water bath, which is 0.5 m deep, 1 m wide, and 3.5 m long, and
move slowly in the hot water toward the other end. Some of the cans fail
the test and explode in the water bath. The water container is made of
sheet metal, and the entire container is at about the same temperature
as the hot water. The emissivity of the outer surface of the container
is 0.7. If the temperature of the surrounding air and surfaces is 20°C,
determine the rate of heat loss from the four side surfaces of the
container (disregard the top surface, which is open). The water is
heated electrically by resistance heaters, and the cost of electricity
is $0.085/kWh. If the plant operates 24 h a day 365 days a year and thus
8760 h a year, determine the annual cost of the heat losses from the
container for this facility.
Get solution
9–25
Reconsider Problem 9–24. In order to reduce the heating cost of the hot
water, it is proposed to insulate the side and bottom surfaces of the
container with 5-cm-thick fiberglass insulation (k 0.035 W/m · °C) and
to wrap the insulation with aluminum foil ( 0.1) in order to minimize
the heat loss by
radiation. An estimate is obtained from a local insulation contractor,
who proposes to do the insulation job for $350, including materials and
labor. Would you support this proposal? How long will it take for the
insulation to pay for itself from the energy it saves?
Get solution
9–26
Consider a 15-cm 20-cm printed circuit board (PCB) that has
electronic components on one side. The board is placed in a room at
20°C. The heat loss from the back surface of the board is negligible. If
the circuit board is dissipating 8 W of power in steady operation,
determine the average temperature of the hot surface of the board,
assuming the board is (a) vertical, (b) horizontal with hot surface
facing up, and (c) horizontal with hot surface facing down. Take the
emissivity of the surface of the board to be 0.8 and assume the
surrounding surfaces to be at the same temperature as the air in the
room
Get solution
9–27
Reconsider Problem 9–26. Using EES (or other) software, investigate the
effects of the room temperature and the emissivity of the board on the
temperature of the hot surface of the board for different orientations
of the board. Let the room temperature vary from 5˚C to 35˚C and the
emissivity from 0.1 to 1.0. Plot the hot surface temperature for
different orientations of the board as the functions of the room
temperature and the emissivity, and discuss the results
Get solution
9–28
A manufacturer makes absorber plates that are 1.2 m 0.8 m in size for
use in solar collectors. The back side of the plate is heavily
insulated, while its front surface is coated with black chrome, which
has an absorptivity of 0.87 for solar radiation and an emissivity of
0.09. Consider such a plate placed horizontally outdoors in calm air at
25°C. Solar radiation is incident on the plate at a rate of 700 W/m2.
Taking the effective sky temperature to be 10°C, determine the
equilibrium temperature of the absorber plate. What would your answer be
if the absorber plate is made of ordinary aluminum plate that has a
solar absorptivity of 0.28 and an emissivity of 0.07?
Get solution
9–29
Repeat Problem 9–28 for an aluminum plate painted flat black (solar
absorptivity 0.98 and emissivity 0.98) and also for a plate painted
white (solar absorptivity 0.26 and emissivity 0.90)
Get solution
9–30
The following experiment is conducted to determine the natural
convection heat transfer coefficient for a horizontal cylinder that is
80 cm long and 2 cm in diameter. A80-cm-long resistance heater is placed
along the centerline of the cylinder, and the surfaces of the cylinder
are polished to minimize the radiation effect. The two circular side
surfaces of the cylinder are well insulated. The resistance heater is
turned on, and the power dissipation is maintained constant at 40 W. If
the average surface temperature of the cylinder is measured to be 120°C
in the 20°C room air when steady operation is reached, determine the
natural convection heat transfer coefficient. If the emissivity of the
outer surface of the cylinder is 0.1 and a 5 percent error is
acceptable, do you think we need to do any correction for the radiation
effect? Assume the surrounding surfaces to be at 20°C also.
Get solution
9–31
Thick fluids such as asphalt and waxes and the pipes in which they flow
are often heated in order to reduce the viscosity of the fluids and
thus to reduce the pumping costs. Consider the flow of such a fluid
through a 100-m-long pipe of outer diameter 30 cm in calm ambient air at
0°C. The pipe is heated electrically, and a thermostat keeps the outer
surface temperature of the pipe constant at 25°C. The emissivity of the
outer surface of the pipe is 0.8, and the effective sky temperature is
-30°C, Determine the power rating of the electric resistance heater, in
kW, that needs to be used. Also, determine the cost of electricity
associated with heating the pipe during a 10-h period under the above
conditions if the price of electricity is $0.09/kWh.
Get solution
9–32
Reconsider Problem 9–31. To reduce the heating cost of the pipe, it is
proposed to insulate it with sufficiently thick fiberglass insulation (k
0.035 W/m · °C) wrapped with aluminum foil (E=0.1) to cut down the
heat losses by 85 percent. Assuming the pipe temperature to remain
constant at 25°C, determine the thickness of the insulation that needs
to be used. How much money will the insulation save during this 10-h
period?
Get solution
9–33E
Consider an industrial furnace that resembles a 13-ftlong horizontal
cylindrical enclosure 8 ft in diameter whose end surfaces are well
insulated. The furnace burns natural gas at a rate of 48 therms/h (1
therm 100,000 Btu). The combustion efficiency of the furnace is 82
percent (i.e., 18 percent of the chemical energy of the fuel is lost
through the flue gases as a result of incomplete combustion and the flue
gases leaving the furnace at high temperature). If the heat loss from
the outer surfaces of the furnace by natural convection and radiation is
not to exceed 1 percent of the heat generated inside, determine the
highest allowable surface temperature of the furnace. Assume the air and
wall surface temperature of the room to be 75°F, and take the
emissivity of the outer surface of the furnace to be 0.85. If the cost
of natural gas is $0.65/therm and the furnace operates 2800 h per year,
determine the annual cost of this heat loss to the plant.
Get solution
9–34
Consider a 1.2-m-high and 2-m-wide glass window with a thickness of 6
mm, thermal conductivity k 0.78 W/m · °C, and emissivity 0.9. The
room and the walls that face the window are maintained at 25°C, and the
average temperature of the inner surface of the window is measured to be
5°C. If the temperature of the outdoors is 5°C, determine (a) the
convection heat transfer coefficient on the inner surface of the window,
(b) the rate of total heat transfer through the window, and (c) the
combined natural convection and radiation heat transfer coefficient on
the outer surface of the window. Is it reasonable to neglect the thermal
resistance of the glass in this case?
Get solution
9–35
A 3-mm-diameter and 12-m-long electric wire is tightly wrapped with a
1.5-mm-thick plastic cover whose thermal conductivity and emissivity are
k 0.15 W/m · °C and E=0.9. Electrical measurements indicate that a
current of 10Apasses through the wire and there is a voltage drop of 8V
along the wire. If the insulated wire is exposed to calm atmospheric air
at T = 30°C, determine the temperature at the interface of the wire
and the plastic cover in steady operation. Take the surrounding surfaces
to be at about the same temperature as the air
Get solution
9–36
During a visit to a plastic sheeting plant, it was observed that a
60-m-long section of a 2-in. nominal (6.03-cm outer-diameter) steam pipe
extended from one end of the plant to the other with no insulation on
it. The temperature measurements at several locations revealed that the
average temperature of the exposed surfaces of the steam pipe was 170°C,
while the temperature of the surrounding air was 20°C. The outer
surface of the pipe appeared to be oxidized, and its emissivity can be
taken to be 0.7. Taking the temperature of the surrounding surfaces to
be 20°C also, determine the rate of heat loss from the steam pipe. Steam
is generated in a gas furnace that has an efficiency of 78 percent, and
the plant pays $0.538 per therm (1 therm 105,500 kJ) of natural gas.
The plant operates 24 h a day 365 days a year, and thus 8760 h a year.
Determine the annual cost of the heat losses from the steam pipe for
this facility.
Get solution
9–37
Reconsider Problem 9–36. Using EES (or other) software, investigate the
effect of the surface temperature of the steam pipe on the rate of heat
loss from the pipe and the annual cost of this heat loss. Let the
surface temperature vary from 100˚C to 200˚C. Plot the rate of heat loss
and the annual cost as a function of the surface temperature, and
discuss the results
Get solution
9–38
Reconsider Problem 9–36. In order to reduce heat losses, it is
proposedto insulate the steam pipe with 5-cm-thick fiberglass insulation
(k 0.038 W/m · °C) and to wrap it with aluminum foil (E=0.1) in order
to minimize the radiation losses. Also, an estimate is obtained from a
local insulation contractor, who proposed to do the insulation job for
$750, including materials and labor. Would you support this proposal?
How long will it take for the insulation to pay for itself from the
energy it saves? Assume the temperature of the steam pipe to remain
constant at 170°C
Get solution
9–39
A 30-cm x 30-cm circuit board that contains 121 square chips on one
side is to be cooled by combined natural convection and radiation by
mounting it on a vertical surface in a room at 25°C. Each chip
dissipates 0.05 Wof power, and the emissivity of the chip surfaces is
0.7. Assuming the heat transfer from the back side of the circuit board
to be negligible, and the temperature of the surrounding surfaces to be
the same as the air temperature of the room, determine the surface
temperature of the chips.
Get solution
9–40
Repeat Prob 9–35 assuming the circuit board to be positioned
horizontally with (a) chips facing up and (b) chips facing down
Get solution
9–41
The side surfaces of a 2-m-high cubic industrial furnace burning
natural gas are not insulated, and the temperature at the outer surface
of this section is measured to be 110°C. The temperature of the furnace
room, including its surfaces, is 30°C, and the emissivity of the outer
surface of the furnace is 0.7. It is proposed that this section of the
furnace wall be insulated with glass wool insulation (k = 0.038 W/m ·
°C) wrapped by a reflective sheet (E=0.2) in order to reduce the heat
loss by 90 percent. Assuming the outer surface temperature of the metal
section still remains at about 110°C, determine the thickness of the
insulation that needs to be used. The furnace operates continuously
throughout the year and has an efficiency of 78 percent. The price of
the natural gas is $0.55/therm (1 therm 105,500 kJ of energy content).
If the installation of the insulation will cost $550 for materials and
labor, determine how long it will take for the insulation to pay for
itself from the energy it saves.
Get solution
9–42
A1.5-m-diameter, 5-m-long cylindrical propane tank is initially filled
with liquid propane, whose density is 581 kg/m3. The tank is exposed to
the ambient air at 25°C in calm weather. The outer surface of the tank
is polished so that the radiation heat transfer is negligible. Now a
crack develops at the top of the tank, and the pressure inside drops to 1
atm while the temperature drops to -42°C, which is the boiling
temperature of propane at 1 atm. The heat of vaporization of propane at 1
atm is 425 kJ/kg. The propane is slowly vaporized as a result of the
heat transfer from the ambient air into the tank, and the propane vapor
escapes the tank at 42°C through the crack. Assuming the propane tank
to be at about the same temperature as the propane inside at all times,
determine how long it will take for the tank to empty if it is not
insulated.
Get solution
9–43E
An average person generates heat at a rate of 287 Btu/h while resting
in a room at 77°F. Assuming one-quarter of this heat is lost from the
head and taking the emissivity of the skin to be 0.9, determine the
average surface temperature of the head when it is not covered. The head
can be approximated as a 12-in.-diameter sphere, and the interior
surfaces of the room can be assumed to be at the room temperature.
Get solution
9–44
An incandescent lightbulb is an inexpensive but highly inefficient
device that converts electrical energy into light. It converts about 10
percent of the electrical energy it consumes into light while converting
the remaining 90 percent into heat. The glass bulb of the lamp heats up
very quickly as a result of absorbing all that heat and dissipating it
to the surroundings by convection and radiation. Consider an
8-cm-diameter 60-W light bulb in a room at 25°C. The emissivity of the
glass is 0.9. Assuming that 10 percent of the energy passes through the
glass bulb as light with negligible absorption and the rest of the
energy is absorbed and dissipated by the bulb itself by natural
convection and radiation, determine the equilibrium temperature of the
glass bulb. Assume the interior surfaces of the room to be at room
temperature.
Get solution
9–45
A 40-cm-diameter, 110-cm-high cylindrical hot water tank is located in
the bathroom of a house maintained at 20˚C. The surface temperature of
the tank is measured to be 44˚C and its emissivity is 0.4. Taking the
surrounding surface temperature to be also 20˚C, determine the rate of
heat loss from all surfaces of the tank by natural convection and
radiation
Get solution
9–46
A28-cm-high, 18-cm-long, and 18-cm-wide rectangular container suspended
in a room at 24˚C is initially filled with cold water at 2˚C. The
surface temperature of the container is observed to be nearly the same
as the water temperature inside. The emissivity of the container surface
is 0.6, and the temperature of the surrounding surfaces is about the
same as the air temperature. Determine the water temperature in the
container after 3 h, and the average rate of heat transfer to the water.
Assume the heat transfer coefficient on the top and bottom surfaces to
be the same as that on the side surfaces
Get solution
9–47
Reconsider Problem 9–46. Using EES (or other) software, plot the water
temperature in the container as a function of the heating time as the
time varies from 30 min to 10 h, and discuss the results
Get solution
9–48
Aroom is to be heated by a coal-burning stove, which is a cylindrical
cavity with an outer diameter of 32 cm and a height of 70 cm. The rate
of heat loss from the room is estimated to be 1.2 kW when the air
temperature in the room is maintained constant at 24˚C. The emissivity
of the stove surface is 0.85 and the average temperature of the
surrounding
wall surfaces is 17˚C. Determine the surface temperature of the stove.
Neglect the transfer from the bottom surface and take the heat transfer
coefficient at the top surface to be the same as that on the side
surface. The heating value of the coal is 30,000 kJ/kg, and the
combustion efficiency is 65 percent. Determine the amount of coal burned
a day if the stove operates 14 h a day
Get solution
9–49
The water in a 40-L tank is to be heated from 15˚C to 45˚C by a
6-cm-diameter spherical heater whose surface temperature is maintained
at 85˚C. Determine how long the heater should be kept on.
Get solution
9–50C
Why are finned surfaces frequently used in practice? Why are the finned
surfaces referred to as heat sinks in the electronics industry
Get solution
9–51C
Why are heat sinks with closely packed fins not suitable for natural
convection heat transfer, although they increase the heat transfer
surface area more
Get solution
9–52C
Consider a heat sink with optimum fin spacing. Explain how heat
transfer from this heat sink will be affected by (a) removing some of
the fins on the heat sink and (b) doubling the number of fins on the
heat sink by reducing the fin spacing. The base area of the heat sink
remains unchanged at all times
Get solution
9–53
Aluminum heat sinks of rectangular profile are commonly used to cool
electronic components. Consider a 7.62-cm-long and 9.68-cm-wide
commercially available heat sink whose cross section and dimensions are
as shown in Figure P9–53. The heat sink is oriented vertically and is
used to cool a power transistor that can dissipate up to 125 Wof power.
The back surface of the heat sink is insulated. The surfaces of the heat
sink are untreated, and thus they have a low emissivity (under 0.1).
Therefore, radiation heat transfer from the heat sink can be neglected.
During an experiment conducted in room air at 22°C, the base temperature
of the heat sink was measured to be 120°C when the power dissipation of
the transistor was 15 W. Assuming the entire heat sink to be at the
base temperature, determine the average natural convection heat transfer
coefficient for this case.
Get solution
9–54
Reconsider the heat sink in Problem 9–53. In order to enhance heat
transfer, a shroud (a thin rectangular metal plate) whose surface area
is equal to the base area of the heat sink is placed very close to the
tips of the fins such that the interfin spaces are converted into
rectangular channels. The base temperature of the heat sink in this case
was measured to be 108°C. Noting that the shroud loses heat to the
ambient air from both sides, determine the average natural convection
heat transfer coefficient in this shrouded case. (For complete details,
see Çengel and Zing, Re
f. 9).
Get solution
9–55E
A 6-in.-wide and 8-in.-high vertical hot surface in 78°F air is to be
cooled by a heat sink with equally spaced fins of rectangular profile.
The fins are 0.08 in. thick and 8 in. long in the vertical direction and
have a height of 1.2 in. from the base. Determine the optimum fin
spacing and the rate of heat transfer by natural convection from the
heat sink if the base temperature is 180°F
Get solution
9–56E
Reconsider Problem 9–55E. Using EES (or other) software, investigate
the effect of the length of the fins in the vertical direction on the
optimum fin spacing and the rate of heat transfer by natural convection.
Let the fin length vary from 2 in. to 10 in. Plot the optimum fin
spacing and the rate of convection heat transfer as a function of the
fin length, and discuss the results
Get solution
9–57
A12.1-cm-wide and 18-cm-high vertical hot surface in 25°C air is to be
cooled by a heat sink with equally spaced fins of rectangular profile.
The fins are 0.1 cm thick and 18 cm long in the vertical direction.
Determine the optimum fin height and the rate of heat transfer by
natural convection from the heat sink if the base temperature is 65°C.
Get solution
9–58C
The upper and lower compartments of a wellinsulated container are
separated by two parallel sheets of glass with an air space between
them. One of the compartments is to be filled with a hot fluid and the
other with a cold fluid. If it is desired that heat transfer between the
two compartments be minimal, would you recommend putting the hot fluid
into the upper or the lower compartment of the container? Why
Get solution
9–59C
Someone claims that the air space in a double-pane window enhances the
heat transfer from a house because of the natural convection currents
that occur in the air space and recommends that the double-pane window
be replaced by a single sheet of glass whose thickness is equal to the
sum of the thicknesses of the two glasses of the double-pane window to
save energy. Do you agree with this claim
Get solution
9–60C
Consider a double-pane window consisting of two glass sheets separated
by a 1-cm-wide air space. Someone suggests inserting a thin vinyl sheet
in the middle of the two glasses to form two 0.5-cm-wide compartments in
the window in order to reduce natural convection heat transfer through
the window. From a heat transfer point of view, would you be in favor of
this idea to reduce heat losses through the window
Get solution
9–61C
What does the effective conductivity of an enclosure represent? How is
the ratio of the effective conductivity to thermal conductivity related
to the Nusselt number
Get solution
9–62
Show that the thermal resistance of a rectangular enclosure can be
expressed as R =d/(Ak Nu), where k is the thermal conductivity of the
fluid in the enclosure
Get solution
9–63E
A vertical 4-ft-high and 6-ft-wide double-pane window consists of two
sheets of glass separated by a 1-in. air gap at atmospheric pressure. If
the glass surface temperatures across the air gap are measured to be
65°F and 40°F, determine the rate of heat transfer through the window by
(a) natural convection and (b) radiation. Also, determine the R-value
of insulation of this window such that multiplying the inverse of the
R-value by the surface area and the temperature difference gives the
total rate of heat transfer through the window. The effective emissivity
for use in radiation calculations between two large parallel glass
plates can be taken to be 0.82.
Get solution
9–64E
Reconsider Problem 9–63E. Using EES (or other) software, investigate
the effect of the air gap thickness on the rates of heat transfer by
natural convection and radiation, and the R-value of insulation. Let the
air gap thickness vary from 0.2 in. to 2.0 in. Plot the rates of heat
transfer by natural convection and radiation, and the R-value of
insulation as a function of the air gap thickness, and discuss the
results.
Get solution
9–65
Two concentric spheres of diameters 15 cm and 25 cm are separated by
air at 1 atm pressure. The surface temperatures of the two spheres
enclosing the air are T1 350 K and T2 275 K, respectively. Determine
the rate of heat transfer from the inner sphere to the outer sphere by
natural convection
Get solution
9–66
Reconsider Problem 9–65. Using EES (or other) software, plot the rate
of natural convection heat transfer as a function of the hot surface
temperature of the sphere as the temperature varies from 300 K to 500 K,
and discuss the results
Get solution
9–67
Flat-plate solar collectors are often tilted up toward the sun in order
to intercept a greater amount of direct solar radiation. The tilt angle
from the horizontal also affects the rate of heat loss from the
collector. Consider a 2-m-high and 3-mwide solar collector that is
tilted at an angle from the horizontal. The back side of the absorber
is heavily insulated. The absorber plate and the glass cover, which are
spaced 2.5 cm from each other, are maintained at temperatures of 80°C
and 40°C, respectively. Determine the rate of heat loss from the
absorber plate by natural convection for O=0°, 20°, and 90°.
Get solution
9–68
A simple solar collector is built by placing a 5-cmdiameter clear
plastic tube around a garden hose whose outer diameter is 1.6 cm. The
hose is painted black to maximize solar absorption, and some plastic
rings are used to keep the spacing between the hose and the clear
plastic cover constant. During a clear day, the temperature of the hose
is measured to be 65°C,
while the ambient air temperature is 26°C. Determine the rate of heat
loss from the water in the hose per meter of its length by natural
convection. Also, discuss how the performance of this solar collector
can be improved.
Get solution
9–69
Reconsider Problem 9–68. Using EES (or other) software, plot the rate
of heat loss from the water by natural convection as a function of the
ambient air temperature as the temperature varies from 4˚C to 40˚C, and
discuss the results
Get solution
9–70
A vertical 1.3-m-high, 2.8-m-wide double-pane window consists of two
layers of glass separated by a 2.2-cm air gap at atmospheric pressure.
The room temperature is 26˚C while the inner glass temperature is 18˚C.
Disregarding radiation heat transfer, determine the temperature of the
outer glass layer and the rate of heat loss through the window by
natural convection
Get solution
9–71
Consider two concentric horizontal cylinders of diameters 55 cm and 65
cm, and length 125 cm. The surfaces of the inner and outer cylinders are
maintained at 46˚C and 74˚C, respectively. Determine the rate of heat
transfer between the cylinders by natural convection if the annular
space is filled with (a) water and (b) air.
Get solution
9–72C When is natural convection negligible and when is it not negligible in forced convection heat transfer
Get solution
9–73C
Under what conditions does natural convection enhance forced
convection, and under what conditions does it hurt forced convection
Get solution
9–74C
When neither natural nor forced convection is negligible, is it correct
to calculate each independently and add them to determine the total
convection heat transfer
Get solution
9–75
Consider a 5-m-long vertical plate at 85°C in air at 30°C. Determine
the forced motion velocity above which natural convection heat transfer
from this plate is negligible.
Get solution
9–76
Reconsider Problem 9–75. Using EES (or other) software, plot the forced
motion velocity above which natural convection heat transfer is
negligible as a function of the plate temperature as the temperature
varies from 50˚C to 150˚C, and discuss the results
Get solution
9–77
Consider a 5-m-long vertical plate at 60°C in water at 25°C. Determine
the forced motion velocity above which natural convection heat transfer
from this plate is negligible. Take B=0.0004 K-1 for water
Get solution
9–78
In a production facility, thin square plates 2 m x 2 m in size coming
out of the oven at 270°C are cooled by blowing ambient air at 30°C
horizontally parallel to their surfaces. Determine the air velocity
above which the natural convection effects on heat transfer are less
than 10 percent and thus are negligible.
Get solution
9–79
A 12-cm-high and 20-cm-wide circuit board houses 100 closely spaced
logic chips on its surface, each dissipating 0.05 W. The board is cooled
by a fan that blows air over the hot surface of the board at 35°C at a
velocity of 0.5 m/s. The heat transfer from the back surface of the
board is negligible. Determine the average temperature on the surface of
the circuit board assuming the air flows vertically upwards along the
12cm-long side by (a) ignoring natural convection and (b) considering
the contribution of natural convection. Disregard any heat transfer by
radiation.
Get solution
9–80C
Why are the windows considered in three regions when analyzing heat
transfer through them? Name those regions and explain how the overall
U-value of the window is determined when the heat transfer coefficients
for all three regions are known
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9–81C
Consider three similar double-pane windows with air gap widths of 5,
10, and 20 mm. For which case will the heat transfer through the window
will be a minimum
Get solution
9–82C
In an ordinary double-pane window, about half of the heat transfer is
by radiation. Describe a practical way of reducing the radiation
component of heat transfer
Get solution
9–83C
Consider a double-pane window whose air space width is 20 mm. Now a
thin polyester film is used to divide the air space into two 10-mm-wide
layers. How will the film affect (a) convection and (b) radiation heat
transfer through the window
Get solution
9–84C
Consider a double-pane window whose air space is flashed and filled
with argon gas. How will replacing the air in the gap by argon affect
(a) convection and (b) radiation heat transfer through the window
Get solution
9–85C
Is the heat transfer rate through the glazing of a double-pane window
higher at the center or edge section of the glass area? Explain
Get solution
9–86C
How do the relative magnitudes of U-factors of windows with aluminum,
wood, and vinyl frames compare? Assume the windows are identical except
for the frames
Get solution
9–87
Determine the U-factor for the center-of-glass section of a double-pane
window with a 13-mm air space for winter
design conditions. The glazings are made of clear glass having an
emissivity of 0.84. Take the average air space temperature at design
conditions to be 10°C and the temperature difference across the air
space to be 15°C
Get solution
9–88
A double-door wood-framed window with glass glazing and metal spacers
is being considered for an opening that is 1.2 m high and 1.8 m wide in
the wall of a house maintained at 20°C. Determine the rate of heat loss
through the window and the inner surface temperature of the window glass
facing the room when the outdoor air temperature is 8°C if the window
is selected to be (a) 3-mm single glazing, (b) double glazing with an
air space of 13 mm, and (c) low-e-coated triple glazing with an air
space of 13 mm.
Get solution
9–89
Determine the overall U-factor for a double-door-type wood-framed
double-pane window with 13-mm air space and metal spacers, and compare
your result to the value listed in Table 9–6. The overall dimensions of
thewindow are 2.00 m x 2.40 m, and the dimensions of each glazing are
1.92 m x 1.14 m
Get solution
9–90
Consider a house in Atlanta, Georgia, that is maintained at 22°C and
has a total of 20 m2 of window area. The windows are double-door-type
with wood frames and metal spacers. The glazing consists of two layers
of glass with 12.7 mm of air space with one of the inner surfaces coated
with reflective film. The winter average temperature of Atlanta is
11.3°C. Determine the average rate of heat loss through the windows in
winter.
Get solution
9–91E
Consider an ordinary house with R-13 walls (walls that have an R-value
of 13 h · ft2 · °F/Btu). Compare this to the R-value of the common
double-door windows that are double pane with in. of air space and have
aluminum frames. If the windows occupy only 20 percent of the wall area,
determine if more heat is lost through the windows or through the
remaining 80 percent of the wall area. Disregard infiltration losses
Get solution
9–92
The overall U-factor of a fixed wood-framed window with double glazing
is given by the manufacturer to be U = 2.76 W/m2 · °C under the
conditions of still air inside and winds of 12 km/h outside. What will
the U-factor be when the wind velocity outside is doubled?
Get solution
9–93
The owner of an older house in Wichita, Kansas, is considering
replacing the existing double-door type wood-framed single-pane windows
with vinyl-framed double-pane windows with an air space of 6.4 mm. The
new windows are of doubledoor type with metal spacers. The house is
maintained at 22°C at all times, but heating is needed only when the
outdoor temperature drops below 18°C because of the internal heat gain
from people, lights, appliances, and the sun. The average winter
temperature of Wichita is 7.1°C, and the house is heated by electric
resistance heaters. If the unit cost of electricity is $0.07/kWh and the
total window area of the house is 12 m2, determine how much money the
new windows will save the home owner per month in winter.
Get solution
9–94E
A 0.1-W small cylindrical resistor mounted on a lower part of a
vertical circuit board is 0.3 in. long and has a diameter of 0.2 in. The
view of the resistor is largely blocked by another circuit board facing
it, and the heat transfer through the connecting wires is negligible.
The air is free to flow through the large parallel flow passages between
the boards as a result of natural convection currents. If the air
temperature at the vicinity of the resistor is 120°F, determine the
approximate surface temperature of the resistor.
Get solution
9–95
An ice chest whose outer dimensions are 30 cm x 40 cm x 40 cm is made
of 3-cm-thick styrofoam (k 0.033 W/m · °C). Initially, the chest is
filled with 30 kg of ice at 0°C, and the inner surface temperature of
the ice chest can be taken to be 0°C at all times. The heat of fusion of
water at 0°C is 333.7 kJ/kg, and the surrounding ambient air is at
20°C. Disregarding any heat transfer from the 40 cm x 40 cm base of the
ice chest, determine how long it will take for the ice in the chest to
melt completely if the ice chest is subjected to (a) calm air and (b)
winds at 50 km/h. Assume the heat transfer coefficient on the front,
back, and top surfaces to be the same as that on the side surfaces
Get solution
9–96
An electronic box that consumes 180 W of power is cooled by a fan
blowing air into the box enclosure. The dimensions of the electronic box
are 15 cm x 50 cm x 50 cm, and all surfaces of the box are exposed to
the ambient except the base surface. Temperature measurements indicate
that the box is at an average temperature of 32°C when the ambient
temperature and the temperature of the surrounding walls are 25°C. If
the emissivity of the outer surface of the box is 0.85, determine the
fraction of the heat lost from the outer surfaces of the electronic box.
Get solution
9–97
A 6-m-internal-diameter spherical tank made of 1.5cm-thick stainless
steel (k 15 W/m · °C) is used to store iced water at 0°C in a room at
20°C. The walls of the room are also at 20°C. The outer surface of the
tank is black (emissivity E=1), and heat transfer between the outer
surface of the tank and the surroundings is by natural convection and
radiation. Assuming the entire steel tank to be at 0°C and thus the
thermal resistance of the tank to be negligible, determine (a) the rate
of heat transfer to the iced water in the tank and (b) the amount of ice
at 0°C that melts during a 24-h period.
Get solution
9–98
Consider a 1.2-m-high and 2-m-wide double-pane window consisting of two
3-mm-thick layers of glass (k 0.78 W/m · °C) separated by a 3-cm-wide
air space. Determine the steady rate of heat transfer through this
window and the temperature of its inner surface for a day during which
the room is maintained at 20°C while the temperature of the outdoors is
0°C. Take the heat transfer coefficients on the inner and outer surfaces
of the window to be h1 10 W/m2 · °C and h2 25 W/m2 · °C and
disregard any heat transfer by radiation
Get solution
9–99
An electric resistance space heater is designed such that it resembles a
rectangular box 50 cm high, 80 cm long, and 15 cm wide filled with 45
kg of oil. The heater is to be placed against a wall, and thus heat
transfer from its back surface is negligible for safety considerations.
The surface temperature of the heater is not to exceed 45°C in a room at
25°C. Disregarding heat transfer from the bottom and top surfaces of
the heater in anticipation that the top surface will be used as a shelf,
determine the power rating of the heater in W. Take the emissivity of
the outer surface of the heater to be 0.8 and the average temperature of
the ceiling and wall surfaces to be the same as the room air
temperature. Also, determine how long it will take for the heater to
reach steady operation when it is first turned on (i.e., for the oil
temperature to rise from 25°C to 45°C). State your assumptions in the
calculations
Get solution
9–100
Skylights or “roof windows” are commonly used in homes and
manufacturing facilities since they let natural light in during day time
and thus reduce the lighting costs. However, they offer little
resistance to heat transfer, and large amounts of energy are lost
through them in winter unless they are equipped with a motorized
insulating cover that can be used in cold weather and at nights to
reduce heat losses. Consider a 1-m-wide and 2.5-m-long horizontal
skylight on the roof of a house that is kept at 20°C. The glazing of the
skylight is made of a single layer of 0.5-cm-thick glass (k 0.78 W/m
°C and E=0.9). Determine the rate of heat loss through the skylight
when the air temperature outside is 10°C and the effective sky
temperature is -30°C. Compare your result with the rate of heat loss
through an equivalent surface area of the roof that has a common R-5.34
construction in SI units (i.e., a
thickness–to–effectivethermal-conductivity ratio of 5.34 m2 · °C/W)
Get solution
9–101
Asolar collector consists of a horizontal copper tube of outer diameter
5 cm enclosed in a concentric thin glass tube of 9 cm diameter. Water
is heated as it flows through the tube, and the annular space between
the copper and glass tube is filled with air at 1 atm pressure. During a
clear day, the temperatures of the tube surface and the glass cover are
measured to be 60°C and 32°C, respectively. Determine the rate of heat
loss from the collector by natural convection per meter length of the
tube.
Get solution
9–102
A solar collector consists of a horizontal aluminum tube of outer
diameter 4 cm enclosed in a concentric thin glass tube of 7 cm diameter.
Water is heated as it flows through the aluminum tube, and the annular
space between the aluminum and glass tubes is filled with air at 1 atm
pressure. The pump circulating the water fails during a clear day, and
the water temperature in the tube starts rising. The aluminum tube
absorbs solar radiation at a rate of 20 W per meter length, and the
temperature of the ambient air outside is 30°C. Approximating the
surfaces of the tube and the glass cover as being black (emissivity E=1)
in radiation calculations and taking the effective sky temperature to
be 20°C, determine the temperature of the aluminum tube when equilibrium
is established (i.e., when the net heat loss from the tube by
convection and radiation equals the amount of solar energy absorbed by
the tube)
Get solution
9–103E
The components of an electronic system dissipating 180 W are located in
a 4-ft-long horizontal duct whose crosssection is 6 in. x 6 in. The
components in the duct are cooled by forced air, which enters at 85°F at
a rate of 22 cfm and leaves at 100°F. The surfaces of the sheet metal
duct are not painted, and thus radiation heat transfer from the outer
surfaces is negligible. If the ambient air temperature is 80°F,
determine (a) the heat transfer from the outer surfaces of the duct to
the ambient air by natural convection and (b) the average temperature of
the duct.
Get solution
9–104E Repeat Problem 9–103E for a circular horizontal duct of diameter 4 in
Get solution
9–105E
Repeat Problem 9–103E assuming the fan fails and thus the entire heat
generated inside the duct must be rejected to the ambient air by natural
convection through the outer surfaces of the duct
Get solution
9–106
Consider a cold aluminum canned drink that is initially at a uniform
temperature of 5°C. The can is 12.5 cm high and has a diameter of 6 cm.
The emissivity of the outer surface of the can is 0.6. Disregarding any
heat transfer from the bottom surface of the can, determine how long it
will take for the average temperature of the drink to rise to 7°C if the
surrounding air and surfaces are at 25°C.
Get solution
9–107
Consider a 2-m-high electric hot water heater that has a diameter of 40
cm and maintains the hot water at 60°C. The tank is located in a small
room at 20°C whose walls and the ceiling are at about the same
temperature. The tank is placed in a 46-cm-diameter sheet metal shell of
negligible thickness, and the space between the tank and the shell is
filled with foam insulation. The average temperature and emissivity of
the outer surface of the shell are 40°C and 0.7, respectively. The price
of electricity is $0.08/kWh. Hot water tank insulation kits large
enough to wrap the entire tank are available on the market for about
$30. If such an insulation is installed on this water tank by the home
owner himself, how long will it take for this additional insulation to
pay for itself? Disregard any heat loss from the top and bottom
surfaces, and assume the insulation to reduce the heat losses by 80
percent
Get solution
9–108
During a plant visit, it was observed that a 1.5-m-high and 1-m-wide
section of the vertical front section of a natural gas furnace wall was
too hot to touch. The temperature measurements on the surface revealed
that the average temperature of the exposed hot surface was 110°C, while
the temperature of the surrounding air was 25°C. The surface appeared
to be oxidized, and its emissivity can be taken to be 0.7. Taking the
temperature of the surrounding surfaces to be 25°C also, determine the
rate of heat loss from this furnace. The furnace has an efficiency of 79
percent, and the plant pays $0.75 per therm of natural gas. If the
plant operates 10 h a day, 310 days a year, and thus 3100 h a year,
determine the annual cost of the heat loss from this vertical hot
surface on the front section of the furnace wall.
Get solution
9–109
A group of 25 power transistors, dissipating 1.5 W each, are to be
cooled by attaching them to a black-anodized square aluminum plate and
mounting the plate on the wall of a room at 30°C. The emissivity of the
transistor and the plate surfaces is 0.9. Assuming the heat transfer
from the back side of the plate to be negligible and the temperature of
the surrounding surfaces to be the same as the air temperature of the
room, determine the size of the plate if the average surface temperature
of the plate is not to exceed 50°C.
Get solution
9–110
Repeat Problem 9–109 assuming the plate to be positioned horizontally
with (a) transistors facing up and (b) transistors facing down
Get solution
9–111E
Hot water is flowing at an average velocity of 4 ft/s through a cast
iron pipe (k 30 Btu/h · ft · °F) whose inner and outer diameters are
1.0 in. and 1.2 in., respectively. The pipe passes through a 50-ft-long
section of a basement whose temperature is 60°F. The emissivity of the
outer surface of the pipe is 0.5, and the walls of the basement are also
at about 60°F. If the inlet temperature of the water is 150°F and the
heat transfer coefficient on the inner surface of the pipe is 30 Btu/h ·
ft2 · °F, determine the temperature drop of water as it passes through
the basement
Get solution
9–112
Consider a flat-plate solar collector placed horizontally on the flat
roof of a house. The collector is 1.5 m wide and 6 m long, and the
average temperature of the exposed surface of the collector is 42°C.
Determine the rate of heat loss from the collector by natural convection
during a calm day when the ambient air temperature is 15°C. Also,
determine the heat loss by radiation by taking the emissivity of the
collector surface to be 0.9 and the effective sky temperature to be
-30°C.
Get solution
9–113
Solar radiation is incident on the glass cover of a solar collector at a
rate of 650 W/m2. The glass transmits 88 percent of the incident
radiation and has an emissivity of 0.90. The hot water needs of a family
in summer can be met completely by a collector 1.5 m high and 2 m wide,
and tilted 40° from the horizontal. The temperature of the glass cover
is measured to be 40°C on a calm day when the surrounding air
temperature is 20°C. The effective sky temperature for radiation
exchange between the glass cover and the open sky is -40°C. Water enters
the tubes attached to the absorber plate at a rate of 1 kg/min.
Assuming the back surface of the absorber plate to be heavily insulated
and the only heat loss occurs through the glass cover, determine (a) the
total rate of heat loss from the collector, (b) the collector
efficiency, which is the ratio of the amount of heat transferred to the
water to the solar energy incident on the collector, and (c) the
temperature rise of water as it flows through the collector.
Get solution
