This document discusses fundamentals of thermal radiation. It begins by defining radiation and distinguishing it from conduction and convection. Radiation transfer occurs via electromagnetic waves and is characterized by frequency and wavelength. Thermal radiation emitted by all objects above absolute zero is within the spectrum of 0.1 to 100 micrometers. The document then covers blackbody radiation, spectral emissive power, radiation intensity, radiative properties of materials including emissivity and absorptivity, and Kirchhoff's law relating emissivity and absorptivity.

1. Chapter 12: Fundamentals of
Thermal Radiation

2. 2
INTRODUCTION 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.
The hot object in vacuum
chamber will eventually cool
down and reach thermal
equilibrium with its
surroundings by a heat transfer
mechanism: radiation.

3. • Unlike conduction and convection, radiation does not
require the presence of a material medium to take place.
• Electromagnetic waves or electromagnetic radiation
─ represent the energy emitted by matter as a result of
the changes in the electronic configurations of the atoms
or molecules.
• Electromagnetic waves are characterized by their
frequency n or wavelength l
• c ─ the speed of propagation of a wave in that medium.
c
l
n
 (12-1)

4. THERMAL RADIATION
Electromagnetic
wave spectrum
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.
Thermal radiation is defined as the spectrum that
extends from about 0.1 to 100 mm.
Thermal radiation is continuously emitted by all matter
whose temperature is above absolute zero.
Everything
around us
constantly
emits thermal
radiation.

5. 5
Light is simply the visible portion of
the electromagnetic spectrum that
lies between 0.40 and 0.76 mm.
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 mm.
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 mm.
The ultraviolet radiation includes the low-wavelength end of the thermal
radiation spectrum and lies between the wavelengths 0.01 and 0.40 mm.
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.

6. Blackbody Radiation
• A body at a thermodynamic (or absolute)
temperature above zero emits radiation in
all directions over a wide range of
wavelengths.
• The amount of radiation energy emitted
from a surface at a given wavelength
depends on:
– the material of the body and the condition of its surface,
– the surface temperature.
• A blackbody ─ the maximum amount of radiation that can be
emitted by a surface at a given temperature.
• At a specified temperature and wavelength, no surface can emit
more energy than a blackbody.
• A blackbody absorbs all incident radiation, regardless of
wavelength and direction.
• A blackbody emits radiation energy uniformly in all directions
per unit area normal to direction of emission.

7. • The radiation energy emitted by a blackbody per unit
time and per unit surface area (Stefan–Boltzmann law)
s=5.67 X 10-8 W/m2·K4.
• Examples of approximate blackbody:
– snow,
– white paint,
– a large cavity with a small opening.
• The spectral blackbody emissive power
   
4 2
W/m
b
E T T
s
 (12-3)
 
 
 
 
 
2
1
5
2
2 8 4 2
1 0
4
2 0
, W/m μm
exp 1
2 3.74177 10 W μm m
/ 1.43878 10 μm K
b
C
E T
C T
C hc
C hc k
l l
l l

 
 

 
   
   
(12-4)

8. • The variation of the spectral blackbody emissive power with
wavelength is plotted in Fig. 12–9.
• Several observations can be made
from this figure:
– at any specified temperature there is a
maximum emissive power,
– at any wavelength, the amount of
emitted radiation increases with
increasing temperature,
– as temperature increases, the curves
shift to the shorter wavelength,
– the radiation emitted by the sun
(5780 K) reaches its peak in the visible spectrum.
• The wavelength at which the peak occurs is given by Wien’s
displacement law as
   
max power
2897.8 m K
T
l m
  (12-5)

12. • We are often interested in the
amount of ration emitted over
some wavelength band.

13. 13
The radiation energy emitted by a blackbody per unit
area over a wavelength band from l = 0 to l is
Blackbody radiation function fl:
The fraction of radiation emitted from a
blackbody at temperature T in the
wavelength band from l = 0 to l.

14. 14

19. RADIATION INTENSITY
Radiation is emitted by all parts of a
plane surface in all directions into the
hemisphere above the surface, and
the directional distribution of emitted
(or incident) radiation is usually not
uniform.
Therefore, we need a quantity that
describes the magnitude of radiation
emitted (or incident) in a specified
direction in space.
This quantity is radiation intensity,
denoted by I.
19
Zenith Angle = θ
Azimuth Angle = φ

20. Solid Angle

22. Intensity of Emitted Radiation
22

23. 23

24. • Intensity of incident radiation
Ii(q,f) ─ the rate at which radiation
energy dG is incident from the (q,f)
direction per unit area of the
receiving surface normal to this
direction and per unit solid angle
about this direction.
• The radiation flux incident on a surface from all
directions is called irradiation G
• When the incident radiation is diffuse:
   
2 / 2
2
0 0
, cos sin W m
i
hemisphere
G dG I d d
 
f q
q f q q q f
 
 
  
(12-19)
i
G I

 (12-20)

25. • Radiosity (J )─ the rate at
which radiation energy leaves
a unit area of a surface in all
directions:
• For a surface that is both a diffuse emitter and a
diffuse reflector, Ie+r≠f(q,f):
   
2 / 2
2
0 0
, cos sin W m
e r
J I d d
 
f q
q f q q q f

 
   (12-21)
2
( W m )
e r
J I
 
 (12-22)

26. • Spectral Quantities ─ the
variation of radiation with
wavelength.
• The spectral radiation
intensity Il(l,q,f), for
example, is simply the total radiation intensity I(q,f)
per unit wavelength interval about l.
• The spectral intensity for emitted radiation Il,e(l,q,f)
• Then the spectral emissive power becomes
 
, 2
W
, ,
cos m sr μm
e
e
dQ
I
dA d d
l l q f
q  l
 
  
   
 
(12-23)
 
2 / 2
,
0 0
, , cos sin
e
E I d d
 
l l
f q
l q f q q q f
 
   (12-24)

27. • The spectral intensity of radiation emitted by a
blackbody at a thermodynamic temperature T
at a wavelength l has been determined by Max
Planck, and is expressed as
• Then the spectral blackbody emissive power is
 
 
 
2
2
0
5
0
2
, W/m sr μm
exp 1
b
hc
I T
hc kT
l l
l l
  
 

 
(12-28)
   
, ,
b b
E T I T
l l
l  l
 (12-29)

41. 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.
• In these materials thermal radiation is emitted or
absorbed within the first few microns of the surface.
• Some materials like glass and water exhibit different
behavior at different wavelengths:
– Visible spectrum ─ penetrate to depths before absorption,
– Infrared spectrum ─ opaque.

42. Emissivity
• Emissivity of a surface ─ the ratio of the radiation
emitted by the surface at a given temperature to the
radiation emitted by a blackbody at the same
temperature.
• The emissivity of a surface is denoted by e, and it
varies between zero and one, 0≤e ≤1.
• The emissivity of real surfaces varies with:
– the temperature of the surface,
– the wavelength, and
– the direction of the emitted radiation.
• Spectral directional emissivity ─ the most elemental
emissivity of a surface at a given temperature.

43. • Spectral directional emissivity
• The subscripts l and q are used to designate
spectral and directional quantities, respectively.
• The total directional emissivity (intensities
integrated over all wavelengths)
• The spectral hemispherical emissivity
 
 
 
,
,
, , ,
, , ,
,
e
b
I T
T
I T
l
l q
l
l q f
e l q f
l
 (12-30)
 
 
 
, ,
, , e
b
I T
T
I T
q
q f
e q f  (12-31)
 
 
 
,
,
,
b
E T
T
E T
l
l
l
l
e l
l
 (12-32)

44. • The total hemispherical emissivity
• Since Eb(T)=sT4 the total hemispherical
emissivity can also be expressed as
• To perform this integration, we need to know
the variation of spectral emissivity with
wavelength at the specified temperature.
 
 
 
b
E T
T
E T
e  (12-33)
 
 
 
   
0
4
, ,
b
b
T E T d
E T
T
E T T
l l
e l l l
e
s

 
 (12-34)

45. Gray and Diffuse Surfaces
• Diffuse surface ─ a surface whose properties are
independent of direction.
• Gray surface ─ surface properties are independent of
wavelength.
• Therefore, the emissivity of a gray, diffuse surface is
simply the total hemispherical emissivity of that
surface because of independence of direction and
wavelength

49. Absorptivity, Reflectivity, and
Transmissivity
• When radiation strikes a surface,
part of it:
– is absorbed (absorptivity, a),
– is reflected (reflectivity, r),
– and the remaining part, if any, is
transmitted (transmissivity, t).
• Absorptivity:
• Reflectivity:
• Transmissivity:
Absorbed radiation
Incident radiation
abs
G
G
a   (12-37)
Reflected radiation
Incident radiation
ref
G
G
r   (12-38)
Transmitted radiation
Incident radiation
tr
G
G
t   (12-39)

50. • The first law of thermodynamics requires that
the sum of the absorbed, reflected, and
transmitted radiation be equal to the incident
radiation.
• Dividing each term of this relation by G yields
• For Black Bodies: r   & t  , thus α  
• For Opaque surfaces ( most solid & liquid),
t = 0, and thus
• For most Gases: r  , thus α  t  
abs ref tr
G G G G
   (12-40)
1
a r t
   (12-41)
1
a r
  (12-42)

51. Kirchhoff’s Law
• Consider a small body of surface area
As, emissivity e, and absorptivity a at
temperature T contained in a large
isothermal enclosure at the same
temperature.
• Recall that a large isothermal enclosure forms a
blackbody cavity regardless of the radiative properties
of the enclosure surface.
• The body in the enclosure is too small to interfere with
the blackbody nature of the cavity.
• Therefore, the radiation incident on any part of the
surface of the small body is equal to the radiation
emitted by a blackbody at temperature T.
G=Eb(T)=sT4.

52. • The radiation absorbed by the small body per
unit of its surface area is
• The radiation emitted by the small body is
• Considering that the small body is in thermal
equilibrium with the enclosure, the net rate of
heat transfer to the body must be zero.
• Thus, we conclude that
4
abs
G G T
a as
 
4
emit
E T
es

4 4
s s
A T A T
es as

(12-47)
   
T T
e a


53. • 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.
• The restrictive conditions inherent in the derivation of
Eq. 12-47 should be remembered:
– Surface temperature is equal to the temperature of the
source of irradiation