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Fundamentals of Thermal-Fluid Sciences
4th Edition in SI Units
Yunus A. Çengel, John M. Cimbala, Robert H. Turner
McGraw-Hill, 2012
Chapter 21
RADIATION HEAT TRANSFER
Lecture slides by
Mehmet Kanoğlu
Copyright © 2012 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Objectives
•
Classify electromagnetic radiation, and identify thermal radiation
•
Understand the idealized blackbody, and calculate the total and
spectral blackbody emissive power
•
Calculate the fraction of radiation emitted in a specified
wavelength band using the blackbody radiation functions
•
Develop a clear understanding of the properties emissivity,
absorptivity, reflectivity, and transmissivity on spectral and total
basis
•
Apply Kirchhoff law’s to determine the absorptivity of a surface
when its emissivity is known
•
Define view factor, and understand its importance in radiation
heat transfer calculations
•
Calculate radiation heat transfer between black surfaces
•
Obtain relations for net rate of radiation heat transfer between the
surfaces of a two-zone enclosure, including two large parallel
plates, two long concentric cylinders, and two concentric spheres
•
Understand radiation heat transfer in three-surface enclosures
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21-1 INTRODUCTION
The hot object in vacuum
chamber will eventually cool
down and reach thermal
equilibrium with its
surroundings by a heat transfer
mechanism: radiation.
Radiation differs from conduction and
convection in that it does not require the
presence of a material medium to take place.
Radiation transfer occurs in solids as well as
liquids and gases.
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Accelerated charges or changing electric currents give rise to electric and
magnetic fields. These rapidly moving fields are called electromagnetic waves or
electromagnetic radiation, and they represent the energy emitted by matter as a
result of the changes in the electronic configurations of the atoms or molecules.
Electromagnetic waves transport energy just like other waves and they are
characterized by their frequency  or wavelength . These two properties in a
medium are related by
c = c0 /n
c, the speed of propagation of a wave in that medium
c0 = 2.9979108 m/s, the speed of light in a vacuum
n, the index of refraction of that medium
n =1 for air and most gases, n = 1.5 for glass, and n = 1.33 for water
It has proven useful to view electromagnetic radiation as the propagation
of a collection of discrete packets of energy called photons or quanta.
In this view, each photon of frequency n is considered to have an energy of
The energy of a photon is inversely
proportional to its wavelength.
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21-2 THERMAL RADIATION
The type of electromagnetic radiation that is pertinent
to heat transfer is the thermal radiation emitted as a
result of energy transitions of molecules, atoms, and
electrons of a substance.
Temperature is a measure of the strength of these
activities at the microscopic level, and the rate of
thermal radiation emission increases with increasing
temperature.
Thermal radiation is continuously emitted by all matter
whose temperature is above absolute zero.
Everything
around us
constantly
emits thermal
radiation.
The
electromagnetic
wave spectrum.
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Light is simply the visible portion of
the electromagnetic spectrum that
lies between 0.40 and 0.76 m.
A body that emits some radiation in the
visible range is called a light source.
The sun is our primary light source.
The electromagnetic radiation emitted by
the sun is known as solar radiation, and
nearly all of it falls into the wavelength
band 0.3–3 m.
Almost half of solar radiation is light (i.e.,
it falls into the visible range), with the
remaining being ultraviolet and infrared.
The radiation emitted by bodies at room temperature falls into the
infrared region of the spectrum, which extends from 0.76 to 100 m.
The ultraviolet radiation includes the low-wavelength end of the thermal
radiation spectrum and lies between the wavelengths 0.01 and 0.40 m.
Ultraviolet rays are to be avoided since they can kill microorganisms and
cause serious damage to humans and other living beings.
About 12 percent of solar radiation is in the ultraviolet range. The ozone
(O3) layer in the atmosphere acts as a protective blanket and absorbs
most of this ultraviolet radiation.
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In heat transfer studies, we are interested in
the energy emitted by bodies because of their
temperature only. Therefore, we limit our
consideration to thermal radiation.
The electrons, atoms, and molecules of
all solids, liquids, and gases above
absolute zero temperature are constantly
in motion, and thus radiation is
constantly emitted, as well as being
absorbed or transmitted throughout the
entire volume of matter.
That is, radiation is a volumetric
phenomenon.
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21-3 BLACKBODY RADIATION
•
•
•
•
•
Different bodies may emit different amounts of radiation per unit surface area.
A blackbody emits the maximum amount of radiation by a surface at a given
temperature.
It is an idealized body to serve as a standard against which the radiative
properties of real surfaces may be compared.
A blackbody is a perfect emitter and absorber of radiation.
A blackbody absorbs all incident radiation, regardless of wavelength and
direction.
The radiation energy
emitted by a blackbody:
Blackbody emissive power
Stefan–Boltzmann constant
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Spectral blackbody emissive Power:
The amount of radiation energy emitted
by a blackbody at a thermodynamic
temperature T per unit time, per unit
surface area, and per unit wavelength
about the wavelength .
Planck’s
law
Boltzmann’s constant
9
The wavelength at which the
peak occurs for a specified
temperature is given by
Wien’s displacement law:
10
Observations from the figure
• The emitted radiation is a continuous function of wavelength.
At any specified temperature, it increases with wavelength,
reaches a peak, and then decreases with increasing
wavelength.
• At any wavelength, the amount of emitted radiation increases
with increasing temperature.
• As temperature increases, the curves shift to the left to the
shorter wavelength region. Consequently, a larger fraction of
the radiation is emitted at shorter wavelengths at higher
temperatures.
• The radiation emitted by the sun, which is considered to be a
blackbody at 5780 K (or roughly at 5800 K), reaches its peak
in the visible region of the spectrum. Therefore, the sun is in
tune with our eyes.
• On the other hand, surfaces at T < 800 K emit almost entirely
in the infrared region and thus are not visible to the eye
unless they reflect light coming from other sources.
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The radiation energy emitted by a blackbody per unit
area over a wavelength band from  = 0 to  is
Blackbody radiation function f:
The fraction of radiation emitted from a
blackbody at temperature T in the
wavelength band from  = 0 to .
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21-4 RADIATIVE PROPERTIES
Most materials encountered in practice, such as metals, wood,
and bricks, are opaque to thermal radiation, and radiation is
considered to be a surface phenomenon for such materials.
Radiation through semitransparent materials such as glass and
water cannot be considered to be a surface phenomenon since
the entire volume of the material interacts with radiation.
A blackbody can serve as a convenient reference in describing
the emission and absorption characteristics of real surfaces.
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Emissivity
•
Emissivity: The ratio of the radiation emitted by the surface at a given
temperature to the radiation emitted by a blackbody at the same temperature.
0    1.
•
Emissivity is a measure of how closely a surface approximates a blackbody (
= 1).
•
The emissivity of a real surface varies with the temperature of the surface as
well as the wavelength and the direction of the emitted radiation.
•
The emissivity of a surface at a specified wavelength is called spectral
emissivity . The emissivity in a specified direction is called directional
emissivity  where  is the angle between the direction of radiation and the
normal of the surface.
spectral
hemispherical
emissivity
total
hemispherical
emissivity
The ratio of the total radiation energy
emitted by the surface to the radiation
emitted by a blackbody of the same
surface area at the same temperature
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A surface is said to be diffuse if its properties are independent of
direction, and gray if its properties are independent of wavelength.
The gray and diffuse approximations are often utilized in radiation
calculations.
 is the
angle
measured
from the
normal of
the surface
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20
The variation of normal emissivity with (a)
wavelength and (b) temperature for various
materials.
In radiation analysis, it is
common practice to assume
the surfaces to be diffuse
emitters with an emissivity
equal to the value in the
normal ( = 0) direction.
Typical ranges
of emissivity
for various
materials.
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Irradiation, G:
Radiation flux
incident on a
surface.
Absorptivity,
Reflectivity, and
Transmissivity
for opaque surfaces
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spectral
hemispherical
absorptivity
spectral
hemispherical
reflectivity
spectral
hemispherical
transmissivity
spectral directional
absorptivity
spectral directional
reflectivity
G: the spectral irradiation, W/m2m
Average absorptivity, reflectivity, and
transmissivity of a surface:
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In practice, surfaces are assumed to reflect in a perfectly specular or diffuse manner.
Specular (or mirrorlike) reflection: The angle of reflection equals the angle of
incidence of the radiation beam.
Diffuse reflection: Radiation is reflected equally in all directions.
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Kirchhoff’s Law
Kirchhoff’s law
The total hemispherical emissivity of
a surface at temperature T is equal
to its total hemispherical absorptivity
for radiation coming from a
blackbody at the same temperature.
spectral form of
Kirchhoff’s law
The emissivity of a surface at a specified wavelength,
direction, and temperature is always equal to its absorptivity
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at the same wavelength, direction, and temperature.
The Greenhouse Effect
Glass has a transparent window in the wavelength range 0.3 m <  < 3 m in which
over 90% of solar radiation is emitted. The entire radiation emitted by surfaces at room
temperature falls in the infrared region ( > 3 m).
Glass allows the solar radiation to enter but does not allow the infrared radiation from the
interior surfaces to escape. This causes a rise in the interior temperature as a result of
the energy buildup in the car.
This heating effect, which is due to the nongray characteristic of glass (or clear plastics),
is known as the greenhouse effect.
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21-5 THE VIEW FACTOR
View factor is a purely geometric quantity
and is independent of the surface
properties and temperature.
It is also called the shape factor,
configuration factor, and angle factor.
The view factor based on the assumption
that the surfaces are diffuse emitters and
diffuse reflectors is called the diffuse view
factor, and the view factor based on the
assumption that the surfaces are diffuse
emitters but specular reflectors is called
the specular view factor.
Fij the fraction of the radiation leaving
surface i that strikes surface j directly
The view factor ranges between 0 and 1.
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28
The view factor has proven to be very useful in radiation analysis
because it allows us to express the fraction of radiation leaving a
surface that strikes another surface in terms of the orientation of
these two surfaces relative to each other.
The underlying assumption in this process is that the radiation a
surface receives from a source is directly proportional to the
angle the surface subtends when viewed from the source.
This would be the case only if the radiation coming off the
source is uniform in all directions throughout its surface and the
medium between the surfaces does not absorb, emit, or scatter
radiation.
That is, it is the case when the surfaces are isothermal and
diffuse emitters and reflectors and the surfaces are separated by
a nonparticipating medium such as a vacuum or air.
View factors for hundreds of common geometries are evaluated
and the results are given in analytical, graphical, and tabular
form.
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View factor between two aligned parallel rectangles of equal size.
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View factor between two perpendicular rectangles with a common edge.
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View factor between two coaxial parallel disks.
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View factors for two concentric cylinders of finite length: (a) outer
cylinder to inner cylinder; (b) outer cylinder to itself.
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View Factor Relations
Radiation analysis on an enclosure consisting of N
surfaces requires the evaluation of N2 view factors.
Once a sufficient number of view factors are available,
the rest of them can be determined by utilizing some
fundamental relations for view factors.
1 The Reciprocity Relation
reciprocity
relation (rule)
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2 The Summation Rule
The sum of the view factors from surface i of an enclosure to all
surfaces of the enclosure, including to itself, must equal unity.
The total number of view factors that need to be
evaluated directly for an N-surface enclosure is
The remaining view factors can be
determined from the equations that are
obtained by applying the reciprocity and
the summation rules.
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3 The Superposition Rule
The view factor from a surface i to
a surface j is equal to the sum of
the view factors from surface i to
the parts of surface j.
multiply by A1
apply the reciprocity relation
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4 The Symmetry Rule
Two (or more) surfaces that possess symmetry about a third
surface will have identical view factors from that surface.
If the surfaces j and k are symmetric about the surface i then
Fi  j = Fi  k and Fj  i = Fk  i
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View Factors between
Infinitely Long Surfaces: The
Crossed-Strings Method
Channels and ducts that are very
long in one direction relative to the
other directions can be considered
to be two-dimensional.
These geometries can be modeled
as being infinitely long, and the view
factor between their surfaces can be
determined by simple crossedstrings method.
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21-6 RADIATION HEAT TRANSFER: BLACK SURFACES
When the surfaces involved can be
approximated as blackbodies because of the
absence of reflection, the net rate of radiation
heat transfer from surface 1 to surface 2 is
reciprocity relation
emissive power
A negative value for Q1 → 2 indicates that net
radiation heat transfer is from surface 2 to surface 1.
The net radiation
heat transfer from
any surface i of an N
surface enclosure is
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21-7 RADIATION HEAT TRANSFER:
DIFFUSE, GRAY SURFACES
• Most enclosures encountered in practice involve nonblack
surfaces, which allow multiple reflections to occur.
• Radiation analysis of such enclosures becomes very
complicated unless some simplifying assumptions are made.
• It is common to assume the surfaces of an enclosure to be
opaque, diffuse, and gray.
• Also, each surface of the enclosure is isothermal, and both
the incoming and outgoing radiation are uniform over each
surface.
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Radiosity
For a surface i that is gray and
opaque (i = i and i + i = 1)
Radiosity J: The total
radiation energy leaving
a surface per unit time
and per unit area.
For a blackbody  = 1
The radiosity of a blackbody is
equal to its emissive power since
radiation coming from a blackbody
is due to emission only.
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Net Radiation Heat Transfer to or from a Surface
The net rate of
radiation heat transfer
from a surface i
surface resistance
to radiation.
The surface resistance to radiation for a
blackbody is zero since i = 1 and Ji = Ebi.
Reradiating surface: Some surfaces are
modeled as being adiabatic since their back sides
are well insulated and the net heat transfer
through them is zero.
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Net Radiation Heat Transfer between Any Two Surfaces
The net rate of
radiation heat transfer
from surface i to
surface j is
Apply the reciprocity relation
space resistance
to radiation
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In an N-surface enclosure, the conservation of energy principle requires
that the net heat transfer from surface i be equal to the sum of the net heat
transfers from surface i to each of the N surfaces of the enclosure.
The net radiation flow from a
surface through its surface
resistance is equal to the sum of
the radiation flows from that surface
to all other surfaces through the
corresponding space resistances.
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Methods of Solving Radiation Problems
In the radiation analysis of an enclosure, either the temperature or the net rate
of heat transfer must be given for each of the surfaces to obtain a unique
solution for the unknown surface temperatures and heat transfer rates.
The equations above give N linear algebraic equations for the determination
of the N unknown radiosities for an N-surface enclosure. Once the radiosities
J1, J2, . . . , JN are available, the unknown heat transfer rates and the
unknown surface temperatures can be determined from the above equations.
Direct method: Based on using the above procedure. This method is
suitable when there are a large number of surfaces.
Network method: Based on the electrical network analogy. Draw a
surface resistance associated with each surface of an enclosure and
connect them with space resistances. Then solve the radiation problem
by treating it as an electrical network problem. The network method is not
practical for enclosures with more than three or four surfaces.
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Radiation Heat Transfer in Two-Surface Enclosures
This important result is
applicable to any two gray,
diffuse, and opaque surfaces
that form an enclosure.
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Radiation Heat
Transfer in ThreeSurface Enclosures
When Qi is specified at
surface i instead of the
temperature, the term
(Ebi − Ji)/Ri should be
replaced by the
specified Qi.
The algebraic
sum of the
currents (net
radiation heat
transfer) at each
node must equal
zero.
These equations are to be solved for J1, J2, and J3.
Draw a surface
resistance
associated with
each of the three
surfaces and
connect them
with space
resistances.
Schematic of a
three-surface
enclosure and the
radiation network
51
associated with it.
Summary
• Thermal Radiation
• Blackbody Radiation
• Radiative Properties




Emissivity
Absorptivity, Reflectivity, and Transmissivity
Kirchhoff’s Law
The Greenhouse Effect
• The View Factor
• Radiation Heat Transfer: Black Surfaces
• Radiation Heat Transfer: Diffuse, Gray Surfaces






Radiosity
Net Radiation Heat Transfer to or from a Surface
Net Radiation Heat Transfer between Any Two Surfaces
Methods of Solving Radiation Problems
Radiation Heat Transfer in Two-Surface Enclosures
Radiation Heat Transfer in Three-Surface Enclosures
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