6. M. Planck. The Theory of Heat Radiarion. New york:
Dover, 1959.
7. W. Sieber. Zeitschrift
pp. 130-135.
fiir
Technische physics 22
9. Y. S. Touloukian and D. P. DeWitt. ..Nonmetallic Solids."
In Thermal Radiative Properties. Vol. 8. New york:
(lg4l),
10. Y. S. Touloukian and D. P. DeWitt. "Metallic Elements
and Alloys." In Thermal Radiative properties, Vol. 7.
8. R. Siegel and J. R. Howell. Thermal Radiation Heat
Transfer.3rd ed. Washington, DC: Hemisphere, 1992.
New York: IFI/Plenum. 1970.
Electromagnetic and Thermal Radiation
I
c
IFVPlenum, 1970.
12-12 A radio station is broadcasting radio waves at
By what properties is an electromagnetic
wave
erized? How are these properties related to each other?
a
wavelength of 200 m. Determine the frequency of these waves.
12-13 A microwave oven is designed to operare ar
a
l2-2C
frequency of 2.2 x l}e Hz. Determine the wavelensth of these
microwaves and the energy of each microwave.
12-3C How does microwave cooking differ from conven_
tional cooking?
12-14
Whatis thermal radiation? How does it differ from the
other forms of electromagnetic radiation?
other forms of electromagnetic radiation?
Consider a radio wave with a wavelength of 107 pm
y-ray with a wavelength of 10-7 pm. Determine the photon energies ofthe radio wave and the y-ray, and the photon
energy ratio of the 7-ray to the radio wave.
What is the cause of color? Why do some objects
blue to the eye while others appear red? Is the color of
a surface at room temperature related to the radiation it emits?
12-6C Why do skiers get sunburned so easily?
0.5 pm is being propagated in different mediums: air, water,
and glass. The refractive index of air, water, and glass are 1,
1.33, and 1.5 respectively. Determine the photon energy, in
eV, of the electromagnetic wave in each medium (1 eV :
l2-4C
l2-7C
What is visible light? How does
it differ from
the
How do ultraviolet and infrared radiation differ? Do
and, a
12-15 An electromagnetic wave with a
1.6022
x
l0-re
wavelength of
J).
you think your body emits any radiation in the ultraviolet
12-16
range? Explain.
and 0.76 pm is what we call visible tight. Within this spectrum,
the color violet has the shortest wavelength while the color red
l2-8C Why is radiation usually treated as a surface
phenomenon?
cordless telephone is designed to operate at a
of 8.5 X 108 Hz. Determine the wavelensth of these
waves.
Electricity is generated and transmitted in power
a frequency of 60Hz (1 Hz : I cycle per second).
ine the wavelength of the electromagnetic waves
The electromagnetic spectrum that lies between 0.40
has the longest wavelength. Determine which of these colors,
violet (z\ 0.40 pm) or red (,\ 0.76 pm), propagates more
photon energy.
:
:
Blackbody Radiation
l2-l7c
What is a blackbody? Does a blackbody actually exist?
12-18C Dehne the total and spectral blackbody emissive
generated by the passage of electricity in power lines.
powers. How are they related to each other? How do they differ?
12.
l2-19C Why did we dehne the blackbody radiation function?
What does it represent? For what is it used?
The speed of light in vacuum is given to be 3.0 x
lOE s. Determine the speed of light in air (n: 1), in water
(n : 1.33), and in glass (n : 1.5).
"Problems designated by a "C" are concept questions, ano
students are encouraged to answer them all. problems with the
rcon e? are solved using EES, and complete solutions together with
parametric studies are included on the text website. problems with
the rcon are comprehensive in nature, and are intended to be
lved with an equation solver such as ESS. problems with the icon
are Prevention through Design problems.
I
l2-20C Consider two identical bodies, one at 1000 K and
the other at 1500 K. Which body emits more radiation in the
shorter-wavelength region? Which body emits more radiation
at a wavelength of 20 pm?
12-21 Consider a surface at a uniform temperature of g00 K.
Determine the maximum rate of thermal raiiation that can be
emitted by this surface, in Wm2.
12-22 Consider a 20-cm X 20-cm X 20-cm cubical body
at 750 K suspended in the air. Assuming the body closely
approximates a blackbody, determine (a) the rate at which
the cube emits radiation energy, in W and (b) the spectral
blackbody emissive power at a wavelength of 4 pm.
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range, (b) at wavelengths shorter than the visible range, and (c)
at wavelengths longer than the visible range.
by
A'
strikes 42 directly. What would your answer be
if
A2
were directly above A, at a distance of 80 cm?
Radiation Intensity
l2-39C What does a solid angle represent,
and how does
it
Az= 8 cmz
differ from a plane angle? What is the value of a solid angle
associated with a sphere?
1240C For a surface, how is irradiation defined? For diffusely incident radiation, how is irradiation on a surface related
to the intensity of incident radiation?
l24lc For a surface, how is radiosity dehned? For diffusely
emitting and reflecting surfaces, how is radiosity related to the
intensities of emitted and reflected radiation?
At=8cm2
7r=800K
l2-42C When the variation of
spectral radiation quantity
with wavelength is known, how is the corresponding total
quantity determined?
l2-43C How is the intensity of emitted radiation defrned?
For a diffusely emitting surface, how is the emissive power
related to the intensity of emitted radiation?
12-44 A small surface of area Ar : 3 cm2 emits radiation as a blackbody, and part of the radiation emiued by Ar
strikes another small surface of area Az : 8 cm2 oriented as
shown in the figure. If the rate at which radiation emitted by
Athat strikes A, is measured tobe 214 X l0i determine the
intensity of the radiation emitted by A,, and the temperature
of
A,.
P1247
FIGURE
A small surface of area A : 7 cm2 emits radiation as
blackbody at 1800 K. Determine the rate at which radiation
energy is emitted through a band defined by 0 < Q
= 2n and
45 < 0 s 60o, where d is the angle a radiation beam makes
with the normal of the surface and @ is the azimuth angle.
l?48
a
12-49 Consider the intensity of solar radiation incident on
earth's surface can be expressed as d l00cos0,where I has
the units of Wm2.sr. Determine the peak value for the intensity of incident solar radiation, and the solar irradiation on
earth's surface.
:
12-50 A small surface of area A, 3 cm2 emits radiation as
a blackbody with total emissive power of
5.67 x Wml
Part of the radiation emitted by A, strikes another small surface
of area
8 cm2 oriented as shown in the frgure. Determine
Az= 8 cmz
4=
Ar:
the rate at which radiation emitted by
irradiation on Ar.
Az= 8 cm2
At =3 cm2
FIGURE
P12-4
12-45 A small circular surface of area Ar : 2 cm2 located
at the center of a 2-m-diameter sphere emits radiation as a
blackbody atTl : 1000 K. Determine the rate at which radiation energy is streaming through a D2 : l-cm-diameter hole
located (a) on top of the sphere directly above A, and (b) on
the side of sphere such that the line that connects the centers of
At and, A, makes 45' with surface A,.
1246 RepeatProb. 1245 for a 4-m-diameter sphere.
1247 A small surface of area Ar : 8 cm2 emits radiation
as
blackbody at T1 : 800 K. Part of the radiation emitted by A,
strikes another small surface of area Az : 8 cm2 oriented as
shown in the figure. Determine the solid angle subtendedby A,
when viewed from A,, and the rate at which radiation emitted
a
A, strikes A,. and the
At=3cmz
FIGURE
P12-50
:
12-51 A small surface of area Ar 3 cm2 emits radiation
as a blackbody at T1
1000 K. A radiation detector (Ar) is
placed normal to the direction of viewing from surface A, at a
distance I, as shown in the figure. If the radiation detector is
measuring an irradiation of 100 Wm2, determine the distance
between the radiation detector and surface A,.
:
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12-61
A radiometer is employed to monitor the
temperature of manufactured parts (A r : 10 cm2)
on a conveyor. The radiometer is placed at a distance of I m
from and normal to the manufactured parts. When a part moves
to the position normal to the radiometer, the sensor measures
the radiation emitted from the part. In order to prevent thermal
burn on people handling the manufactured parts at the end of
the conveyor, the temperature of the parts should be below
45'C. An array of spray heads is programmed to discharge mist
to cool the parts when the radiometer detects a temperature of
45"C or higher on a par1. If the manufactured parts can be
approximated as blackbody, determine the irradiation on the
radiometer that should tdgger the spray heads to release cooling
mist when the temperature is not below 45'C.
it differ from a
l2-64C Define the properties emissivity and absorptivity.
When are these two properties equal to each other?
12-65C Define the properties reflectivity and transmissivity
and discus the different forms of reflection.
l2-66C What is the greenhouse effect? Why is
great concern among atmospheric scientists?
it a matter of
l2-67C We can see the inside of a microwave oven during
operation through its glass door, which indicates that visible
radiation is escaping the oven. Do you think that the harmful
microwave radiation might also be escaping?
13-cm-diameter spherical ball is known to emit radia-
tion at a rate of 160 W when its surface temperature is 530 K.
T
Determine the average emissivity of the ball ai this temperature.
i
f
Convevor
:
/
A long metal bar (c, :
450 J/kg.K,
:
12-69 A small surface of area At 5 cm2 emits radiation as
a blackbody ar T1
1000 K. A radiation sensor of area 42
3 cm2 is placed normal to the direction of viewing from surface
At at a distance L. An optical filter with the following spectral
transmissivity is placed in front of the sensor:
Manufactured Part
rrcunt P12-61
12-62
12-63C What is a graybody? How does
blackbody? What is a diffuse gray surface?
12-68 A
Radiometer
@-
Radiation Properties
_'^ _lr,
- I",
p:
7900 kg/m3) is being conveyed through a water
bath to be quenched. The metal bar has a cross section of
30 mm X 15 mm, and it enters the water bath at 700.C.
During the quenching process, 500 kW of heat is released
from the bar in the water bath. In order to prevent thermal
burn on people handling the metal bar, it must exit the water
bath at a temperature below 45'C. A radiometer is placed
normal to and at a distance of 1 m from the bar to monitor the
exit temperature. The radiometer receives radiation from a
target area of 1 cm2 of the bar surface. Irradiation signal
detected by the radiometer is used to control the speed of the
bar being conveyed through the water bath so that the exit
temperature is safe for handling. If the radiometer detects an
irradiation of 0.015 Wm2, determine the speed of the bar
being conveyed through the water bath. Assume that the metal
bar can be approximated as a blackbody.
:
0, 0<),<2pm
0.5, 2p.m',\ { o
If the distance
I:
between the radiation sensor and surface A, is
0.5 m, determine the irradiation measured by the sensor.
I 2-7
0
ffii I
iil*l Ji:::,,:f fff TJ:1,il",H,""iT ;:
tank wall, and to prevent thermal bum on individuals, the tank's
outer surface temperature should be below 45'C. The emissivity
of the tank surface is 0.85, and irradiation on the tank surface
from the surroundings is estimated to be 390
W/m2.
A radiometer is placed normal to and at a distance of 0.5 m
from the tank surface to monitor the surface temperature. The
radiometer receives radiation from a target area of 1 cm2 of the
tank surface. If the irradiation measured by the radiometer is
0.085 Wm2, determine whether or not the tank surface is safe
to touch.
72-71 A furnace that has a 40-cm X 40-cm glass window
can be considered to be a blackbody at 1200 K. If the transmissivity of the glass is 0.7 for radiation at wavelengths less
than 3 pm and zero for radiation at wavelengths greater than
3 pm, determine the fraction and the rate of radiation coming
from the furnace and transmitted through the window.
12-72 The spectral emissivity function of an opaque surface
at 1000 K is approximated as
FIGURE
P12-62
:0.4, 0<.tr<2pm
: 0.7. 2 pm <,,\ < 6 pm
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over the surface providing a uniform convection heat transfer
coefficient of 40 Wm2.K. Under steady state conditions the
surface has a radiosity of 4000 Wm2, and the plate temperature is maintained uniformly at 350 K. If the total absorptivity of the plate is 0.40, determine (a) the irradiation on the
plate, (b) the total reflectivity of the plate, (c) the emissive
power of the plate, and (4 the total emissivity of the plate.
.l
Air, 300 K
h=40.W/m2.K
fb/
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FIGURE
P12_82
12-83 Consider
an opaque plate that is well insulated on the
edges and it is heated at the bottom with an electric heater. The
plate has an emissivity of 0.6'7, and is situated in an ambient
surrounding temperature of 7"C where the natural convection
heat transfer coefficient is 7 Wm2.K. To maintain a surface
temperature of 80"C, the electric heater supplies 1000 Wm2 of
uniform heat flux to the plate. Determine the radiosity of the
plate under these conditions.
12-84 A horizontal plate is experiencing uniform irradiation
on the both upper and lower surfaces. The ambient air
temperature surrounding the plate is 290 K with a convection heat transfer coefficient of 30 Wm2.K. Both upper and
lower surfaces of the plate have a radiosity of 4000 Wm2, and
the plate temperature is maintained uniformly at 390 K. If the
plate is not opaque and has an absorptivity of 0.527, determine
the irradiation and emissivity of the plate.
the plate is uniform at 350 K, determine the irradiation that the
radiometer would detect.
Atmospheric and Solar Radiation
l2-86C
When the earth is closest to the sun, we have winter
in the northern hemisphere. Explain why. Also explain why
we have surlmer in the northem hemisphere when the earth is
farthest away from the sun.
12-87C Explain why surfaces usually have quite different
absorptivities for solar radiation and for radiation originating
from the surrounding bodies.
12-88C You have probably noticed warning signs on
the
highways stating that bridges may be icy even when the roads
are not. Explain how this can happen.
12-89C What changes would you notice if the sun emitted
radiation at an effective temperature of 2000 K insteadof 5162K?
l2-90C What is the solar constant? How is it used to determine the effective surface temperature of the sun? How would
the value of the solar constant change if the distance between
the earth and the sun doubled?
l2-9lc Explain why the sky is blue and the sunser
is
yellow-orange.
l2-92C
What is the effective sky temperature?
12-93
Solar radiation is incident on the outer suface of a soaceof 1260 Wm2. The surface has an absorptivity of a.
: 0.10 for solar radiation and an emissivity of e : 0.6 at room
temperature. The outer surface radiates heat into space at 0 K. If
there is no net heat transfer into the spaceship, determine the equiship at a rate
fibrium temperature of the surface. Answer: 247
K
12-94 The air temperature on a clear night is observed
to
remain at about 4'C. Yet water is reported to have frozen
that night due to radiation effect. Taking the convection heat
transfer coefficient to be l8 Wm2.K, determine the value of
the maximum effective sky temperature that night.
Air, 290 K
h = 30 Wm2.K
r"=390r
,/
Air, 290 K
J
h=30Wlm2.K
FIGURE
P12_84
12-85 A semi-transparent plate (At : 2 cm2) has an irradiation
of 500 Wm2, where 307o of the irradiation is reflected away
from the plate and 50Vo of the irradiation is transmitted rhrough
the plate. A radiometer is placed 0.5 m above the plate normal
to the direction of viewing from the plate. If the temperature of
temperature. The surface temperature is observed to be 350 K
when the direct and the diffuse components of solar radiation
arc Gp: 350 and Ga : 400 Wm2, respecrively, and the direct
radiation makes a 30o angle with the normal of the surface.
Taking the effective sky temperature to be 280 K, determine the
net rate ofradiation heat transfer to the surface at that time.
12-96 The absorber surface of a solar collector is made of
aluminum coated with black chrome (a, : 0.87 and e : 0.09).
Solar radiation is incident on the surface at a rate of 600 Wm2.
The air and the effective sky temperatures are 25oC and 15"C,
respectively, and the convection heat transfer coefficient is
10 W/m2-K. For an absorber surface temperature of 70'C,
determine the net rate of solar energy delivered by the absorber
plate to the water circulating behind it.
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12-107 Repeat Prob. 12-106 for
a south window.
12-108 Consider
a building located near 40o N latitude that
has equal window areas on all four sides. The building owner is
considering coating the south-facing windows with reflective
film to reduce the solar heat gain and thus the cooling load.
But someone suggests that the owner will reduce the cooling
load even more if she coats the west-facins windows instead.
What do you think?
12-109 Determine
the rate of net heat gain (or loss) through
a 3-m-high, 5-m-wide, fixed 3-mm single-glass window with
aluminum frames on the west wall at 3 prr.l solar time during a typical day in January at a location near 40" N latitude
when the indoor and outdoor temperatures are 20oC and -7.C,
respectively.
l2-ll0 A manufacturing facility located at 32o N latitude
has a glazing area of 60 m2 facing west that consists of
double-pane windows made of clear glass (SHGC : 0.766).
To reduce the solar heat gain in summer, a reflective film that
will reduce the SHGC to 0.35 is considered. The cooling season consists of June, July, August, and September, and the
heating season, October through April. The average daily
solar heat fluxes incident on the west side at this latitude are
2.35, 3.03, 3.62, 4.00, 4.20, 4.24, 4.16, 3.93, 3.48, 2.94, 2.33,
and2.0l kWh/day.m2 for January through December, respectively. Also, the unit costs of electricity and natural gas are
$0.09/kwh and $0.45ltherm (l therm : 105,500 kJ), respectively. If the coefficient ofperformance ofthe cooling system
is 3.2 and the efficiency of the furnace is 0.90, determine the
net annual cost savings due to installing reflective coating on
the windows. Also, determine the simple payback period if
the installation cost of reflective film is $20lm2.
l2-lll A house located in Boulder,
l2-ll5
The human skin is "selective" when it comes to the
absorption of the solar radiation that strikes it perpendicularly.
The skin absorbs only 50 percent of the incident radiation with
wavelengths between i r 0.5 17 pm and 12
0.552 pr,m. The
radiation with wavelengths shorter than ,\, and longer than 12
is fully absorbed. The solar surface may be modeled as a blackbody with effective surface temperature of 5800 K. Calculate
the fraction of the incident solar radiation that is absorbed bv
the human skin.
:
12-116 Consider a small black surface of area A 3.5 cm2
maintained at 600 K. Determine the rate at which radiation
energy is emitted by the surface through a ring-shaped opening defined by 0 Q - 2r and40
=
= I = 50", where { is the
azimuth angle and d is the angle a radiation beam makes with
the normal of the surface.
l2-ll7 A small surface of area A : 3.5 cm2 emits radiation
with an intensity ofradiation that can be expressed as I.(0, $)
: 100 d cos9, where 1, has the units of Wm2.sr. Determine
the emissive power from the surface into the hemisphere surrounding it, and the rate of radiation emission from the surface.
lLllS A radiation sensor and a small surface of area A r that
emits radiation as a blackbody are oriented as shown in the
figure. Determine the distance Z at which the sensor is measuring
two-thirds of the radiation rate emitted from surface A, corresponding to the position directly under the sensor at Z
0.
:
Colorado (40" N
latitude), has ordinary double-pane windows with 6-mm-thick
glasses and the total window areas are 8,6,6, and 4 m2 on
the south, west, east, and north walls, respectively. Determine
the total solar heat gain ofthe house at 9:00, 12:00, and 15:00
solar time in July. Also, determine the total amount of solar
heat gain per day for an average day in January.
l2-ll2
Repeat Prob.
l1-lll
H=50cm
Al
L
for double-pane windows that
FTGURE
are gray-tinted.
Review Problems
l2-ll3 A l-m-diameter
spherical cavity is maintained at a
uniform temperature of 600 K. Now a 5-mm-diameter hole
is drilled. Determine the maximum rate of radiation energy
streaming through the hole. What would your answer be if the
diameter of the cavity were 3 m?
l2-ll4
Daylight and incandescent light may be approxi-
mated as a blackbody at the effective surface temperatures of
5800 K and 2800 K, respectively. Determine the wavelength
at maximum emission of radiation for each of the lighting
sources.
:
Pl2-1 18
l2-ll9
The spectral emissivity ofan opaque surface at 1500 K
is approximated as
sr:0
ez : 0.85
e::0
for
for
for
z\<2pm
2=,\<6pm
i>6pm
Determine the total emissivity and the emissive flux of thesurface.
12-120 The spectral absorptivity of
an opaque surface is as
shown on the graph. Determine the absorptivity of the surface for radiation emitted by a source at (a) 1000 K and (b)
3000 K.
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rulos szl-zl
If the surface is exposed to atmosphere with an
effective sky temperature of 250 K, the equilibrium temperature of the surface is
(c) 303 K
(b) 298 K
(a) 28rK
12-130 A surface absorbs 10 percent of radiation at wavelengths less than 3 pm and 50 percent of radiation at wavelengths greater than 3 pm. The average absorptivity of this
surface for radiation emitted by a source at 3000 K is
(a) 0.\4 (b) 0.22 (c) 0.30 (d) 0.38 (e) 0.42
6 W/m2'K.
l2-l3l A surface at 300"C has an emissivity of 0.7 in the
wavelength range of 0-4.4 pm and 0.3 over the rest of the
wavelength range. At a temperature of 300'C, 19 percent of
the blackbody emissive power is in wavelength range uP to
4.4 um. The total emissivitv of this surface is
(c) 0.624
(b) 0.316
(a) 0.300
12-135 A surface is exposed to solar radiation. The direct and
diffuse components of sola.r radiation are 350 and 250 W/m2, and
the direct radiation makes a 35' angle with the normal of the
surface. The solar absorptivity and the emissivity of the surface are 0.24 and 0.41, respectively. If the surface is observed
to be at 315 K and the effective sky temperature is 256 K, the
net rate of radiation heat transfer to the surface is
h) -129W1m2 (b) -44Wlm2 (c) 0 wm2
(a
(e) 0.50
0.10
12-132 Consider a 4-cm-diameter and 6-cm-long cylindrical
rod at 1000 K. If the emissivity of the rod surface is 0.75, the
total amount of radiation emitted by all surfaces of the rod in
20 min is
(c) 434 kJ
(a) 43kI
(b) 385 kJ
(e) 684 kJ
(d) s13 kJ
12-133 Solar radiation is incident on a semi-transparent body
at a rate of 500 Wm2. If 150 W/m2 of this incident radiation
is reflected back and 225 W lm2 is transmitted across the bodv,
the absorptivity ofthe body is
(a') o
(b)
0.2s
(c)
0.30
(A
0.45
(e)
I
12-134 Solar radiation is incident on an opaque surface at a
rate of 400 Wm2. The emissivity of the surface is 0.65 and
the absorptivity to solar radiation is 0.85. The convection coefficient between the surface and the environment at 25oC is
(a 3t1K
(A
t29Wlm2
(e) 339 K
(el5)7'V,llmz
Design and Essay Problems
12-136 Write an essay on the radiation properties of selective surfaces used on the absorber plates of solar collectors.
Find out about the various kinds of such surfaces, and discuss the performance and cost of each type. Recommend a
selective surface that optimizes cost and performance.
12-137 According to an Atomic Energy Commission report,
a hydrogen bomb can be approximated as a large fireball at a
temperature of 1200 K. You are to assess the impact if such a
bomb exploded 5 km above a city. Assume the diameter of the
hreball to be 1 km, and the blast to last 15 s. Investigate the level
of radiation energy people, plants, and houses will be exposed
to, and how adversely they will be affected by the blast.