12–1C What does the view factor represent? When is the view factor from a surface to itself not zero
Get solution
12–2C How can you determine the view factor F12 when the view factor F21 and the surface areas are available
Get solution
12–3C What are the summation rule and the superposition rule for view factors
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12–4C What is the crossed-strings method? For what kind of geometries is the crossed-strings method applicable
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12–5
Consider an enclosure consisting of six surfaces. How many view factors
does this geometry involve? How many of these view factors can be
determined by the application of the reciprocity and the summation
rules?
Get solution
12–6
Consider an enclosure consisting of five surfaces. How many view
factors does this geometry involve? How many of these view factors can
be determined by the application of the reciprocity and summation rules
Get solution
12–7
Consider an enclosure consisting of 12 surfaces. How many view factors
does this geometry involve? How many of these view factors can be
determined by the application of the reciprocity and the summation
rules?
Get solution
12–8 Determine the view factors F13 and F23 between the rectangular surfaces shown in Figure P12–8.
Get solution
12–9
Consider a cylindrical enclosure whose height is twice the diameter of
its base. Determine the view factor from the side surface of this
cylindrical enclosure to its base surface.
Get solution
12–10
Consider a hemispherical furnace with a flat circular base of diameter
D. Determine the view factor from the dome of this furnace to its base.
Get solution
12–11
Determine the view factors F12 and F21 for the very long ducts shown in
Figure P12–11 without using any view factor tables or charts. Neglect
end effects
Get solution
12–12
Determine the view factors from the very long grooves shown in Figure
P12–12 to the surroundings without using any view factor tables or
charts. Neglect end effects
Get solution
12–13 Determine the view factors from the base of a cube to each of the other five surfaces
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12–14
Consider a conical enclosure of height h and base diameter D. Determine
the view factor from the conical side surface to a hole of diameter d
located at the center of the base.
Get solution
12–15
Determine the four view factors associated with an enclosure formed by
two very long concentric cylinders of radii r1 and r2. Neglect the end
effects
Get solution
12–16 Determine the view factor F12 between the rectangular surfaces shown in Figure P12–16
Get solution
12–17
Two infinitely long parallel cylinders of diameter D are located a
distance s apart from each other. Determine the view factor F12 between
these two cylinders
Get solution
12–18
Three infinitely long parallel cylinders of diameter D are located a
distance s apart from each other. Determine the view factor between the
cylinder in the middle and the surroundings.
Get solution
12–19C
Why is the radiation analysis of enclosures that consist of black
surfaces relatively easy? How is the rate of radiation heat transfer
between two surfaces expressed in this case
Get solution
12–20C
How does radiosity for a surface differ from the emitted energy? For
what kind of surfaces are these two quantities identical
Get solution
12–21C
What are the radiation surface and space resistances? How are they
expressed? For what kind of surfaces is the radiation surface resistance
zero
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12–22C What are the two methods used in radiation analysis? How do these two methods differ
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12–23C What is a reradiating surface? What simplifications does a reradiating surface offer in the radiation analysis
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12–24E
Consider a 10-ft
10-ft
10-ft cubical furnace whose top and side surfaces closely approximate
black surfaces and whose base surface has an emissivity E=0.7. The base,
top, and side surfaces of the furnace are maintained at uniform
temperatures of 800 R, 1600 R, and 2400 R, respectively. Determine the
net rate of radiation heat transfer between (a) the base and the side
surfaces and (b) the base and the top surfaces. Also, determine the net
rate of radiation heat transfer to the base surface
Get solution
12–25E
Reconsider Problem 12–24E. Using EES (or other) software, investigate
the effect of base surface emissivity on the net rates of radiation heat
transfer between the base and the side surfaces, between the base and
top surfaces, and to the base surface. Let the emissivity vary from 0.1
to 0.9. Plot the rates of heat transfer as a function of emissivity, and
discuss the results
Get solution
12–26
Two very large parallel plates are maintained at uniform temperatures
of T1 600 K and T2 = 400 K and have emissivities E1 = 0.5 and E2 =
0.9, respectively. Determine the net rate of radiation heat transfer
between the two surfaces per unit area of the plates
Get solution
12–27
Reconsider Problem 12–26. Using EES (or other) software, investigate
the effects of the temperature and the emissivity of the hot plate on
the net rate of radiation heat transfer between the plates. Let the
temperature vary from 500 K to 1000 K and the emissivity from 0.1 to
0.9. Plot the net rate of radiation heat transfer as functions of
temperature and emissivity, and discuss the results
Get solution
12–28
Afurnace is of cylindrical shape with R = H = 2 m. The base, top, and
side surfaces of the furnace are all black and are maintained at uniform
temperatures of 500, 700, and 1200 K, respectively. Determine the net
rate of radiation heat transfer to or from the top surface during steady
operation.
Get solution
12–29
Consider a hemispherical furnace of diameter D = 5 m with a flat base.
The dome of the furnace is black, and the base has an emissivity of 0.7.
The base and the dome of the furnace are maintained at uniform
temperatures of 400 and 1000 K, respectively. Determine the net rate of
radiation heat transfer from the dome to the base surface during steady
operation.
Get solution
12–30
Two very long concentric cylinders of diameters D1 = 0.2 m and D2 = 0.5
m are maintained at uniform temperatures of T1 = 950 K and T2 = 500 K
and have emissivities
E1 = 1 and E2 = 0.7, respectively. Determine the net rate of radiation
heat transfer between the two cylinders per unit length of the cylinders
Get solution
12–31
This experiment is conducted to determine the emissivity of a certain
material. Along cylindrical rod of diameter D1 = 0.01 m is coated with
this new material and is placed in an evacuated long cylindrical
enclosure of diameter D2 = 0.1 m and emissivity E2 = 0.95, which is
cooled externally and maintained at a temperature of 200 K at all times.
The rod is heated by passing electric current through it. When steady
operating conditions are reached, it is observed that the rod is
dissipating electric power at a rate of 8 W per unit of its length and
its surface temperature is 500 K. Based on these measurements, determine
the emissivity of the coating on the rod
Get solution
12–32E
Afurnace is shaped like a long semicylindrical duct of diameter D = 15
ft. The base and the dome of the furnace have emissivities of 0.5 and
0.9 and are maintained at uniform temperatures of 550 and 1800 R,
respectively. Determine the net rate of radiation heat transfer from the
dome to the base surface per unit length during steady operation.
Get solution
12–33
Two parallel disks of diameter D = 0.6 m separated by L = 0.4 m are
located directly on top of each other. Both disks are black and are
maintained at a temperature of 700 K. The back sides of the disks are
insulated, and the environment that the disks are in can be considered
to be a blackbody at T∞ = 300 K. Determine the net rate of radiation
heat transfer from the disks to the environment.
Get solution
12–34
Afurnace is shaped like a long equilateral-triangular duct where the
width of each side is 2 m. Heat is supplied from the base surface, whose
emissivity is E1 = 0.8, at a rate of 800 W/m2 while the side surfaces,
whose emissivities are 0.5, are maintained at 500 K. Neglecting the end
effects, determine the temperature of the base surface. Can you treat
this geometry as a two-surface enclosure
Get solution
12–35
Reconsider Problem 12–34. Using EES (or other) software, investigate
the effects of the rate of the heat transfer at the base surface and the
temperature of the side surfaces on the temperature of the base
surface. Let the rate of heat transfer vary from 500 W/m2 to 1000 W/m2
and the temperature from 300 K to 700 K. Plot the temperature of the
base surface as functions of the rate of heat transfer and the
temperature of the side surfaces, and discuss the results
Get solution
12–36
Consider a 4-m x 4-m x 4-m cubical furnace whose floor and ceiling are
black and whose side surfaces are reradiating. The floor and the
ceiling of the furnace are maintained at temperatures of 550 K and 1100
K, respectively. Determine the net rate of radiation heat transfer
between the floor and the ceiling of the furnace
Get solution
12–37
Two concentric spheres of diameters D1 = 0.3 m and D2 = 0.8 m are
maintained at uniform temperatures T1 = 700K and T2 = 400 K and have
emissivities
E1 = 0.5 and E2 = 0.7, respectively. Determine the net rate of radiation
heat transfer between the two spheres. Also, determine the convection
heat transfer coefficient at the outer surface if both the surrounding
medium and the surrounding surfaces are at 30°C. Assume the emissivity
of the outer surface is 0.35
Get solution
12–38
A spherical tank of diameter D = 2 m that is filled with liquid
nitrogen at 100 K is kept in an evacuated cubic enclosure whose sides
are 3 m long. The emissivities of the spherical tank and the enclosure
are
E1 = 0.1 and E2 = 0.8, respectively. If the temperature of the cubic
enclosure is measured to be 240 K, determine the net rate of radiation
heat transfer to the liquid nitrogen.
Get solution
12–39 Repeat Problem 12–38 by replacing the cubic enclosure by a spherical enclosure whose diameter is 3 m
Get solution
12–40
Reconsider Problem 12–38. Using EES (or other) software, investigate
the effects of the side length and the emissivity of the cubic
enclosure, and the emissivity of the spherical tank on the net rate of
radiation heat transfer. Let the side length vary from 2.5 m to 5.0 m
and both emissivities from 0.1 to 0.9. Plot the net rate of radiation
heat transfer as functions of side length and emissivities, and discuss
the results
Get solution
12–41
Consider a circular grill whose diameter is 0.3 m. The bottom of the
grill is covered with hot coal bricks at 1100 K, while the wire mesh on
top of the grill is covered with steaks initially at 5°C. The distance
between the coal bricks and the steaks is 0.20 m. Treating both the
steaks and the coal bricks as blackbodies, determine the initial rate of
radiation heat transfer from the coal bricks to the steaks. Also,
determine the initial rate of radiation heat transfer to the steaks if
the side opening of the grill is covered by aluminum foil, which can be
approximated as a reradiating surface.
Get solution
12–42E
A19–ft-high room with a base area of 12 ft x 12 ft is to be heated by
electric resistance heaters placed on the ceiling, which is maintained
at a uniform temperature of 90°F at all times. The floor of the room is
at 65°F and has an emissivity of 0.8. The side surfaces are well
insulated. Treating the ceiling as a blackbody, determine the rate of
heat loss from the room through the floor
Get solution
12–43
Consider two rectangular surfaces perpendicular to each other with a
common edge which is 1.6 m long. The horizontal surface is 0.8 m wide
and the vertical surface is 1.2 m high. The horizontal surface has an
emissivity of 0.75 and is maintained at 400 K. The vertical surface is
black and is maintained at 550 K. The back sides of the surfaces are
insulated. The surrounding surfaces are at 290 K, and can be considered
to have an emissivity of 0.85. Determine the net rate of radiation heat
transfers between the two surfaces, and between the horizontal surface
and the surroundings.
Get solution
12–44
Two long parallel 16-cm-diameter cylinders are located 50 cm apart from
each other. Both cylinders are black, and are maintained at
temperatures 425 K and 275 K. The surroundings can be treated as a
blackbody at 300 K. For a 1-m-long section of the cylinders, determine
the rates of radiation heat transfer between the cylinders and between
the hot cylinder and the surroundings.
Get solution
12–45
Consider a long semicylindrical duct of diameter 1.0 m. Heat is
supplied from the base surface, which is black, at a rate of 1200 W/m2,
while the side surface with an emissivity of 0.4 are is maintained at
650 K. Neglecting the end effects, determine the temperature of the base
surface
Get solution
12–46
Consider a 20-cm-diameter hemispherical enclosure. The dome is
maintained at 600 K and heat is supplied from the dome at a rate of 50
Wwhile the base surface with an emissivity is 0.55 is maintained at 400
K. Determine the emissivity of the dome.
Get solution
12–47C What is a radiation shield? Why is it used
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12–48C What is the radiation effect? How does it influence the temperature measurements
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12–49C Give examples of radiation effects that affect human comfort
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12–50
Consider a person whose exposed surface area is 1.7 m2, emissivity is
0.85, and surface temperature is 30°C. Determine the rate of heat loss
from that person by radiation in a large room whose walls are at a
temperature of (a) 300 K and (b) 280 K
Get solution
12–51
Athin aluminum sheet with an emissivity of 0.15 on both sides is placed
between two very large parallel plates, which are maintained at uniform
temperatures T1 = 900 K and T2 = 650 K and have emissivities
E1 = 0.5 and E2 = 0.8, respectively. Determine the net rate of radiation
heat transfer between the two plates per unit surface area of the
plates and compare the result with that without the shield.
Get solution
12–52
Reconsider Problem 12–51. Using EES (or other) software, plot the net
rate of radiation heat transfer between the two plates as a function of
the emissivity of the aluminum sheet as the emissivity varies from 0.05
to 0.25, and discuss the results
Get solution
12–53
Two very large parallel plates are maintained at uniform temperatures
of T1 = 1000 K and T2 = 800 K and have emissivities of
E1 = E2 = 0.2, respectively. It is desired to reduce the net rate of
radiation heat transfer between the two plates to one-fifth by placing
thin aluminum sheets with an emissivity of 0.15 on both sides between
the plates. Determine the number of sheets that need to be inserted
Get solution
12–54
Five identical thin aluminum sheets with emissivities of 0.1 on both
sides are placed between two very large parallel plates, which are
maintained at uniform temperatures of T1 = 800 K and T2 = 450 K and have
emissivities of
E1 = E2 = 0.1, respectively. Determine the net rate of radiation heat
transfer between the two plates per unit surface area of the plates and
compare the result to that without the shield
Get solution
12–55
Reconsider Problem 12–54. Using EES (or other) software, investigate
the effects of the number of the aluminum sheets and the emissivities of
the plates on the net rate of radiation heat transfer between the two
plates. Let the number of sheets vary from 1 to 10 and the emissivities
of the plates from 0.1 to 0.9. Plot the rate of radiation heat transfer
as functions of the number of sheets and the emissivities of the plates,
and discuss the results
Get solution
12–56E
Two parallel disks of diameter D = 3 ft separated by L = 2 ft are
located directly on top of each other. The disks are separated by a
radiation shield whose emissivity is 0.15. Both disks are black and are
maintained at temperatures of 1200 R and 700 R, respectively. The
environment that the disks are in can be considered to be a blackbody at
540 R. Determine the net rate of radiation heat transfer through the
shield under steady conditions.
Get solution
12–57
A radiation shield that has the same emissivity
3 on both sides is placed between two large parallel plates, which are
maintained at uniform temperatures of T1 = 650 K and T2 = 400 K and have
emissivities of
E1 = 0.6 and E2 = 0.9, respectively. Determine the emissivity of the
radiation shield if the radiation heat transfer between the plates is to
be reduced to 15 percent of that without the radiation shield
Get solution
12–58
Reconsider Problem 12–57. Using EES (or other) software, investigate
the effect of the percent reduction in the net rate of radiation heat
transfer between the plates on the emissivity of the radiation shields.
Let the percent reduction vary from 40 to 95 percent. Plot the
emissivity versus the percent reduction in heat transfer, and discuss
the results
Get solution
12–59
Two coaxial cylinders of diameters D1 = 0.10 m and D2 = 0.30 m and
emissivities
E1 = 0.7 and E2 = 0.4 are maintained at uniform temperatures of T1 = 750
K and T2 = 500 K, respectively. Now a coaxial radiation shield of
diameter D3 = 0.20 m and emissivity
E3 = 0.2 is placed between the two cylinders. Determine the net rate of
radiation heat transfer between the two cylinders per unit length of the
cylinders and compare the result with that without the shield
Get solution
12–60
Reconsider Problem 12–59. Using EES (or other) software, investigate
the effects of the diameter of the outer cylinder and the emissivity of
the radiation shield on the net rate of radiation heat transfer between
the two cylinders. Let the diameter vary from 0.25 m to 0.50 m and the
emissivity from 0.05 to 0.35. Plot the rate of radiation heat transfer
as functions of the diameter and the emissivity, and discuss the
results.
Get solution
12–61C How does radiation transfer through a participating medium differ from that through a nonparticipating medium
Get solution
12–62C
Define spectral transmissivity of a medium of thickness L in terms of
(a) spectral intensities and (b) the spectral absorption coefficient
Get solution
12–63C Define spectral emissivity of a medium of thickness L in terms of the spectral absorption coefficient
Get solution
12–64C How does the wavelength distribution of radiation emitted by a gas differ from that of a surface at the same temperature
Get solution
12–65
Consider an equimolar mixture of CO2 and O2 gases at 500 K and a total
pressure of 0.5 atm. For a path length of 1.2 m, determine the
emissivity of the gas
Get solution
12–66
A cubic furnace whose side length is 6 m contains combustion gases at
1000 K and a total pressure of 1 atm. The composition of the combustion
gases is 75 percent N2, 9 percent H2O, 6 percent O2, and 10 percent CO2.
Determine the effective emissivity of the combustion gases.
Get solution
12–67
Acylindrical container whose height and diameter are 8 m is filled with
a mixture of CO2 and N2 gases at 600 K and 1 atm. The partial pressure
of CO2 in the mixture is 0.15 atm. If the walls are black at a
temperature of 450 K, determine the rate of radiation heat transfer
between the gas and the container walls
Get solution
12–68 Repeat Problem 12–67 by replacing CO2 by the H2O gas
Get solution
12–69
A2-m-diameter spherical furnace contains a mixture of CO2 and N2 gases
at 1200 K and 1 atm. The mole fraction of CO2 in the mixture is 0.15. If
the furnace wall is black and its temperature is to be maintained at
600 K, determine the net rate of radiation heat transfer between the gas
mixture and the furnace walls
Get solution
12–70
A flow-through combustion chamber consists of 15-cm diameter long tubes
immersed in water. Compressed air is routed to the tube, and fuel is
sprayed into the compressed air. The combustion gases consist of 70
percent N2, 9 percent H2O, 15 percent O2, and 6 percent CO2, and are
maintained at 1 atm and 1500 K. The tube surfaces are near black, with
an emissivity of 0.9. If the tubes are to be maintained at a temperature
of 600 K, determine the rate of heat transfer from combustion gases to
tube wall by radiation per m length of tube
Get solution
12–71 Repeat Problem 12–70 for a total pressure of 3 atm
Get solution
12–72
In a cogeneration plant, combustion gases at 1 atm and 800 K are used
to preheat water by passing them through 6-m-long 10-cm-diameter tubes.
The inner surface of the tube is black, and the partial pressures of CO2
and H2O in combustion gases are 0.12 atm and 0.18 atm, respectively. If
the tube temperature is 500 K, determine the rate of radiation heat
transfer from the gases to the tube
Get solution
12–73
Agas at 1200 K and 1 atm consists of 10 percent CO2, 10 percent H2O, 10
percent N2, and 70 percent N2 by volume. The gas flows between two
large parallel black plates maintained at 600 K. If the plates are 20 cm
apart, determine the rate of heat transfer from the gas to each plate
per unit surface area.
Get solution
12–74C
Consider a person who is resting or doing light work. Is it fair to say
that roughly one-third of the metabolic heat generated in the body is
dissipated to the environment by convection, one-third by evaporation,
and the remaining onethird by radiation
Get solution
12–75C
What is sensible heat? How is the sensible heat loss from a human body
affected by (a) skin temperature, (b) environment temperature, and (c)
air motion
Get solution
12–76C
What is latent heat? How is the latent heat loss from the human body
affected by (a) skin wettedness and (b) relative humidity of the
environment? How is the rate of evaporation from the body related to the
rate of latent heat loss?
Get solution
12–77C
How is the insulating effect of clothing expressed? How does clothing
affect heat loss from the body by convection, radiation, and
evaporation? How does clothing affect heat gain from the sun
Get solution
12–78C Explain all the different mechanisms of heat transfer from the human body (a) through the skin and (b) through the lungs
Get solution
12–79C
What is operative temperature? How is it related to the mean ambient
and radiant temperatures? How does it differ from effective temperature
Get solution
12–80
The convection heat transfer coefficient for a clothed person while
walking in still air at a velocity of 0.5 to 2 m/s is given by h =
8.6V0.53, where V is in m/s and h is in W/m2 · °C. Plot the convection
coefficient against the walking velocity, and compare the convection
coefficients in that range to the average radiation coefficient of about
5 W/m2 · °C
Get solution
12–81
Aclothed or unclothed person feels comfortable when the skin
temperature is about 33°C. Consider an average man wearing summer
clothes whose thermal resistance is 0.7 clo. The man feels very
comfortable while standing in a room maintained at 20°C. If this man
were to stand in that room unclothed, determine the temperature at which
the room must be maintained for him to feel thermally comfortable.
Assume the latent heat loss from the person to remain the same.
Get solution
12–82E
An average person produces 0.50 lbm of moisture while taking a shower
and 0.12 lbm while bathing in a tub. Consider a family of four who
shower once a day in a bathroom that is not ventilated. Taking the heat
of vaporization of water to be 1050 Btu/lbm, determine the contribution
of showers to the latent heat load of the air conditioner in summer per
day
Get solution
12–83
An average (1.82 kg or 4.0 lbm) chicken has a basal metabolic rate of
5.47 W and an average metabolic rate of 10.2 W (3.78 W sensible and 6.42
W latent) during normal activity. If there are 100 chickens in a
breeding room, determine the rate of total heat generation and the rate
of moisture production in the room. Take the heat of vaporization of
water to be 2430 kJ/kg
Get solution
12–84
Consider a large classroom with 150 students on a hot summer day. All
the lights with 4.0 kWof rated power are kept on. The room has no
external walls, and thus heat gain through the walls and the roof is
negligible. Chilled air is available at 15°C, and the temperature of the
return air is not to exceed 25°C. Determine the required flow rate of
air, in kg/s, that needs to be supplied to the room.
Get solution
12–85
Aperson feels very comfortable in his house in light clothing when the
thermostat is set at 22°C and the mean radiation temperature (the
average temperature of the surrounding surfaces) is also 22°C. During a
cold day, the average mean radiation temperature drops to 18°C. To what
level must the indoor air temperature be raised to maintain the same
level of comfort in the same clothing
Get solution
12–86 Repeat Problem 12–85 for a mean radiation temperature of 12°C
Get solution
12–87
A car mechanic is working in a shop whose interior space is not heated.
Comfort for the mechanic is provided by two radiant heaters that
radiate heat at a total rate of 10 kJ/s. About 5 percent of this heat
strikes the mechanic directly. The shop and its surfaces can be assumed
to be at the ambient temperature, and the emissivity and absorptivity of
the mechanic can be taken to be 0.95 and the surface area to be 1.8 m2.
The mechanic is generating heat at a rate of 350 W, half of which is
latent, and is wearing medium clothing with a thermal resistance of 0.7
clo. Determine the lowest ambient temperature in which the mechanic can
work comfortably.
Get solution
12–88
A thermocouple used to measure the temperature of hot air flowing in a
duct whose walls are maintained at Tw = 500 K shows a temperature
reading of Tth = 850 K. Assuming the emissivity of the thermocouple
junction to be E=0.6 and the convection heat transfer coefficient to be h
= 60 W/m2 ·°C, determine the actual temperature of air.
Get solution
12–89
A thermocouple shielded by aluminum foil of emissivity 0.15 is used to
measure the temperature of hot gases flowing in a duct whose walls are
maintained at Tw = 380 K. The thermometer shows a temperature reading of
Tth = 530 K. Assuming the emissivity of the thermocouple junction to be
E=0.7 and the convection heat transfer coefficient to be h = 120 W/m2 ·
°C, determine the actual temperature of the gas. What would the
thermometer reading be if no radiation shield was used
Get solution
12–90E
Consider a sealed 8-in.-high electronic box whose base dimensions are
12 in. x 12 in. placed in a vacuum chamber. The emissivity of the outer
surface of the box is 0.95. If the electronic components in the box
dissipate a total of 100 W of power and the outer surface temperature of
the box is not to exceed 130°F, determine the highest temperature at
which the surrounding surfaces must be kept if this box is to be cooled
by radiation alone. Assume the heat transfer from the bottom surface of
the box to the stand to be negligible.
Get solution
12–91
A2-m-internal-diameter double-walled spherical tank is used to store
iced water at 0°C. Each wall is 0.5 cm thick, and the 1.5-cm-thick air
space between the two walls of the tank is evacuated in order to
minimize heat transfer. The surfaces surrounding the evacuated space are
polished so that each surface has an emissivity of 0.15. The
temperature of the outer wall of the tank is measured to be 20°C.
Assuming the inner wall of the steel tank to be at 0°C, 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
12–92
Two concentric spheres of diameters D1 = 15 cm and D2 = 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,
and their emissivities are 0.5. Determine the rate of heat transfer from
the inner sphere to the outer sphere by (a) natural convection and (b)
radiation
Get solution
12–93
Consider a 1.5-m-high and 3-m-wide solar collector that is tilted at an
angle 20° from the horizontal. The distance between the glass cover and
the absorber plate is 3 cm, and the back side of the absorber is
heavily insulated. The absorber plate and the glass cover are maintained
at temperatures of 80°C and 32°C, respectively. The emissivity of the
glass surface is 0.9 and that of the absorber plate is 0.8. Determine
the rate of heat loss from the absorber plate by natural convection and
radiation.
Get solution
12–94E
A solar collector consists of a horizontal aluminum tube having an
outer diameter of 2.5 in. enclosed in a concentric thin glass tube of
diameter 5 in Water is heated as it flows through the tube, and the
annular space between the aluminum and the glass tube is filled with air
at 0.5 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 30 Btu/h per foot
length, and the temperature of the ambient air outside is 75°F. The
emissivities of the tube and the glass cover are 0.9. Taking the
effective sky temperature to be 60°F, determine the temperature of the
aluminum tube when thermal equilibrium is established (i.e., when the
rate of heat loss from the tube equals the amount of solar energy gained
by the tube)
Get solution
12–95
A vertical 2-m-high and 3-m-wide double-pane window consists of two
sheets of glass separated by a 5-cm-thick air gap. In order to reduce
heat transfer through the window, the air space between the two glasses
is partially evacuated to 0.3 atm pressure. The emissivities of the
glass surfaces are 0.9. Taking the glass surface temperatures across the
air gap to be 15°C and 5°C, determine the rate of heat transfer through
the window by natural convection and radiation.
Get solution
12–96
A simple solar collector is built by placing a 6-cm-diameter clear
plastic tube around a garden hose whose outer diameter is 2 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. The emissivities of the hose surface and the glass cover
are 0.9, and the effective sky temperature is estimated to be 15°C. The
temperature of the plastic tube is measured to be 40°C, while the
ambient air temperature is 25°C. Determine the rate of heat loss from
the water in the hose by natural convection and radiation per meter of
its length under steady conditions.
Get solution
12–97
Asolar collector consists of a horizontal copper tube of outer diameter
5 cm enclosed in a concentric thin glass tube of diameter 9 cm. Water
is heated as it flows through the tube, and the annular space between
the copper and the glass tubes is filled with air at 1 atm pressure. The
emissivities of the tube surface and the glass cover are 0.85 and 0.9,
respectively. During a clear day, the temperatures of the tube surface
and the glass cover are measured to be 60°C and 40°C, respectively.
Determine the rate of heat loss from the collector by natural convection
and radiation per meter length of the tube
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12–98
A furnace is of cylindrical shape with a diameter of 1.2 m and a length
of 1.2 m. The top surface has an emissivity of 0.70 and is maintained
at 500 K. The bottom surface has an emissivity of 0.50 and is maintained
at 650 K. The side surface has an emissivity of 0.40. Heat is supplied
from the base surface at a net rate of 1400 W. Determine the temperature
of the side surface and the net rates of heat transfer between the top
and the bottom surfaces, and between the bottom and side surfaces.
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12–99
Consider a cubical furnace with a side length of 3 m. The top surface
is maintained at 700 K. The base surface has an emissivity of 0.90 and
is maintained at 950 K. The side surface is black and is maintained at
450 K. Heat is supplied from the base surface at a rate of 340 kW.
Determine the emissivity of the top surface and the net rates of heat
transfer between the top and the bottom surfaces, and between the bottom
and side surfaces.
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12–100
Athin aluminum sheet with an emissivity of 0.12 on both sides is placed
between two very large parallel plates maintained at uniform
temperatures of T1 = 750 K and T2 = 550 K. The emissivities of the
plates are E1 = 0.8 and E2 = 0.9. Determine the net rate of radiation
heat transfer between the two plates per unit surface area of the
plates, and the temperature of the radiation shield in steady operation
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12–101
Two thin radiation shields with emissivities of
E3 = 0.10 and E4 = 0.15 on both sides are placed between two very large
parallel plates, which are maintained at uniform temperatures T1 = 600 K
and T2 = 300 K and have emissivities
E1 = 0.6 and E2 = 0.7, respectively. Determine the net rates of
radiation heat transfer between the two plates with and without the
shields per unit surface area of the plates, and the temperatures of the
radiation shields in steady operation.
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12–102
In a natural-gas fired boiler, combustion gases pass through 6-m-long
15-cm-diameter tubes immersed in water at 1 atm pressure. The tube
temperature is measured to be 105°C, and the emissivity of the inner
surfaces of the tubes is estimated to be 0.9. Combustion gases enter the
tube at 1 atm and 1200 K at a mean velocity of 3 m/s. The mole
fractions of CO2 and H2O in combustion gases are 8 percent and 16
percent, respectively. Assuming fully developed flow and using
properties of air for combustion gases, determine (a) the rates of heat
transfer by convection and by radiation from the combustion gases to the
tube wall and (b) the rate of evaporation of water
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12–103 Repeat Problem 12–102 for a total pressure of 3 atm for the combustion gases.
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