mec 520 f15 lecture 3
DESCRIPTION
Stony Brook MEC 520 Third LectureTRANSCRIPT
04/21/2023 MEC 520 – Energy Technology Thermodynamics 1
LECTURE 3MEC 520
SEPTEMBER 13, 2015
Thermal Radiation
continued
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Radiative heat transfer is the transfer of heat from one body to another by the emission and absorption of radiationDifferent 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 idealized body to serve as a standard to serve as a standard against which the radiative 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.
WHAT WE HAVE COVERED SO FAR
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The amount of radiation energy emitted by a blackbody at a temperature T per unit time, per unit surface area, and per unit wavelength about the wavelength .
SPECTRAL BLACKBODY EMISSIVE POWER
12
51
T
Cb
e
CE
C1 = 3.743 × 108 [W·mm4/m2]C2 = 1.4387 × 104 [mm·K]
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BLACKBODY SPECTRUM
0 1 2 3 4 5 60
20
40
60
80
100
120
3000 K4000 K5000 K6000 K
Wavelength [microns]
Pow
er/m
2 p
er u
nit W
avel
engt
h
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NORMALIZED BLACKBODY SPECTRUM
0 1 2 3 4 5 60
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
3000 K
4000 K
5000 K
6000 K
Wavelength [microns]
Nor
mal
ized
Pow
er p
er u
nit
wav
e-le
ngt
h
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BLACKBODY SPECTRUM
0 5 10 15 20 250
0.002
0.004
0.006
0.008
0.01
0.012
0.014
1000 K500 K310 K
Wavelength [microns]
Pow
er/m
2 p
er u
nit
Wav
elen
gth
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NORMALIZED BLACKBODY SPECTRUM
0 5 10 15 20 250
0.05
0.1
0.15
0.2
0.25
1000 K500 K310 K
Wavelength [microns]
Nor
mal
ized
Pow
er/m
2 pe
r w
avel
engt
h
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STEFAN BOLTZNANN LAW
4
0TEdEE bbb
The area under the chart represents the total radiation energy emitted by a black body at a given temperature
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STEFAN-BOLTZMANN LAW
100 200 300 400 500 600 700 800 900 1000 11000
10000
20000
30000
40000
50000
60000
T [K]
Bla
ckbo
dy R
adia
tion
[W
/m2]
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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
00, ),()( dTETE bb
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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BLACKBODY RADIATION FUNCTION
Graphical representation of the fraction of the radiation emitted in a wavelength band from l1 to l2
It is not possible to evaluate this integral analytically, therefore tables are provided.
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BLACKBODY RADIATION FUNCTION
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What fraction of total solar emission falls into the visible spectrum (0.4 to 0.7 mm)?
What fraction of total solar emission falls into the infrared spectrum (0.7 to 14 mm)?
Compare these values
EXAMPLE 1
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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.
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.
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DIRECTIONAL CONSIDERATIONS SOLID ANGLE
2r
dAd n
The amount of radiation emitted from a surface, and propagating in a particular direction, is quantified in terms of a differential solid angle associated with the direction.
1dA , , ,
dAn is unit element of surface on a hypothetical sphere and normal to the q, f direction.
2 sinndA r d d
2 sinndAd d d
r
– The solid angle has units of steradians (sr).
– The solid angle associated with a complete hemisphere is2 2
0 0 2hemi d d sr
/
sin
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DIFFERENTIAL SOLID ANGLE
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Determine the solid angle with which the sun is seen from Earth.
What is the solid angle with which the narrow strip shown in the figure below is seen from point "0"?
EXAMPLE 2
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RADIATION INTENSITY
• Spectral Intensity: A quantity used to specify the radiant heat flux within a unit solid angle about a prescribed direction and within a unit wavelength interval about a prescribed wavelength
2W/m 2W/m sr
2W/m sr m .
• The spectral intensity associated with emission from a surface element in the solid angle about and the wavelength interval about is defined as:
,eI 1dAd , d
1, , ,
cosedq
IdA d d
• The rationale for defining the radiation flux in terms of the projected surface area stems from the existence of surfaces for which, to a good approximation, is independent of direction. Such surfaces are termed diffuse, and the radiation is said to be isotropic.
,eI 1 cosdA
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SPECTRAL HEAT FLUX
The projected area is how would appear if observed along .
1dA,
– What is the projected area for ?0
– What is the projected area for ?2/ • The spectral heat rate and heat flux associated with emission from are, respectively,
1dA
1, , , cosedq
dq I dA dd
, ,, , cos , , cos sine edq I d I d d
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EMISSIVE POWER
• The spectral emissive power corresponds to spectral emission over all possible directions.
2W/m m
2 2
0 0
/
, , , cos sineE I d d
• The total emissive power corresponds to emission over all directions and wavelengths.
2W/m
0E E d
• For a diffuse surface, emission is isotropic and
,eE I eE I
• The spectral intensity of radiation incident on a surface, , is defined in terms of the unit solid angle about the direction of incidence, the wavelength interval about , and the projected area of the receiving surface,
,iI
d
1 cos .dA
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IRRADIATION
• The spectral irradiation is then: 2W/m m
2 2
0 0 iG I d d
/
, , , cos sin
and the total irradiation is 2W/m
0G G d
How may and G be expressed if the incident radiation is diffuse?G
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RADIOSITY
• With designating the spectral intensity associated with radiation emitted by the surface and the reflection of incident radiation, the spectral radiosity is:
,e rI
2W/m m
2 2
0 0 e rJ I d d
/
, , , cos sin
and the total radiosity is 2W/m
0J J d
How may and J be expressed if the surface emits and reflects diffusely?
J
• The radiosity of an opaque surface accounts for all of the radiation leaving the surface in all directions and may include contributions to both reflection and emission.
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The net heat flux from the surface may be calculated by adding both contributions, or
The total radiative heat flux at the surface is
NET RADIATIVE HEAT FLUX
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A solar collector mounted on a satellite orbiting Earth is directed at the sun (i.e., normal to the sun's rays). Determine the total solar heat flux incident on the collector per unit area.
EXAMPLE 3
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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.
THE VIEW FACTOR
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VIEW FACTOR DERIVATION
Differential view factor
View factor
Net heat transfer rate
Reciprocity relation
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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.
VIEW FACTOR
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Fij the fraction of the radiation leaving surface i that strikes surface j directlyThe view factor ranges between 0 and 1.
RADIATED ENERGY AND TEMPERATURE
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COMMON GEOMETRIES
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COMMON 2D GEOMETRIES
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COMMON 2D GEOMETRIES
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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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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.
VIEW FACTOR RELATIONS
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THE RECIPROCITY RELATION
reciprocity relation (rule)
Relates the view factors from (i) to (j) and that from (j) to (i) as follows
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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 SUMMATION RULE
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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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
THE SUPERPOSITION RULE
apply the reciprocity relation
multiply by A1
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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
THE SYMMETRY RULE
Fi j = Fi k and Fj i = Fk i
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THE CROSSED-STRINGS METHOD
View Factors b/n Infinitely Long Surfaces
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 crossed-strings method.
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RADIATION HEAT TRANSFER: BLACK SURFACES
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
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
Two general black surfaces maintained at uniform temperature T1 and T2
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Consider a very long duct as shown below. The duct is 30 cm x 40 cm in cross-section, and all surfaces are black. The top and bottom walls are at temperature T1 = 1000 K, while the side walls are at temperature T2 = 600 K. Determine the net radiative heat transfer rate (per unit duct length) on each surface.
EXAMPLE 4
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NET RADIATION HEAT TRANSFER TO OR FROM A SURFACE
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
resistance to radiation
The net rate of radiation heat transfer from
surface i to surface j is
Apply the reciprocity relation
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RADIATION HEAT TRANSFER IN TWO-SURFACE ENCLOSURES
Schematic of a two-surface enclosure and the radiation network associated with it
This important result is applicable to any two gray, diffuse, and opaque surfaces that form an enclosure.
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RADIATION HEAT TRANSFER FOR TWO SURFACE ARRANGEMENTS
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PARALLEL PLATES
Radiation heat transfer between two large parallel plates
Radiation heat transfer between two large parallel plates with one shield
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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 ceiling of the furnace are maintained at temperature 500 K and 1100 K, respectively. Determine the net rate of radiation heat transfer between the floor and the ceiling of the furnace.
EXAMPLE 5
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RADIATION EFFECT ON TEMPERATURE MEASUREMENTS
The last term in the equation is due to the radiation effect and represents the radiation correction.
The radiation correction term is most significant when the convection heat transfer coefficient is small and the emissivity of the surface of the sensor is large.
Therefore, the sensor should be coated with a material of high reflectivity (low emissivity) to reduce the radiation effect.
A thermometer used to measure the temperature in a fluid channel