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Heat Transfer
Radiation between a small body in a large
enclosure
Introduction
Black-body (Small-body) radiation is the thermal
electromagnetic radiation within or surrounding a body in
thermodynamic equilibrium with its environment, emitted
by a black body (an idealized opaque, non-reflective
body). It has a specific spectrum of wavelengths, inversely
related to intensity that depend only on the body's
temperature, which is assumed for the sake of calculations
and theory to be uniform and constant.
2
Planks law
Planck's law describes the
spectral density of
electromagnetic radiation
emitted by a black body in
thermal equilibrium at a
given temperature T, when
there is no net flow of
matter or energy between
the body and its
environment.
3
Wiens displacement law
Wien's displacement law
states that the black-body
radiation curve for
different temperatures
will peak at different
wavelengths that are
inversely proportional to
the temperature.
4
Stefan-Boltzmann law
Stefan-Boltzmann law,
statement that the total
radiant heat power emitted
from a surface is
proportional to the fourth
power of its absolute
temperature
5
Black-body radiation partition function
Partition Function and
BlackBody Radiation.
Where T is the temperature
of a system. Where s is an
index over all
distinguishable microstates
of the system (in the case of
discrete states) and ϵ is the
energy of each of the
microstates. In the
continuous case, D(ϵ) is the
density of states.
6
Intensity of radiation
The intensity of radiation is
defined as the rate of
emission of radiation in a
given direction from a
surface per unit solid angle
and per unit projected area
of a radiating surface on a
plane perpendicular to the
direction of radiation. Eb is
the energy emitted and Ib is
the intensity of radiations.
7
Intensity of emitted radiation.
Intensity of radiation
emitted by a blackbody is
proportional to the fourth
power of its temperature
(Stefan's law). The
wavelength at which the
emitted radiation has the
maximum intensity is
inversely proportional to its
temperature (Wien's law)
8
Radiative properties on surface
 Absorptivity.
 Reflectivity.
 Transmissivity.
 Radiosity.
 Irradiation.
9
Absorptivity
Absorptivity (α) is a
measure of how much of
the radiation is absorbed by
the body. Reflectivity (ρ) is
a measure of how much is
reflected, and
transmissivity (τ) is a
measure of how much
passes through the object.
... Emissivity (ε) is a
measure of how much
thermal radiation a body
emits to its environment.
10
Reflectivity
Reflectivity (ρ) is a
measure of how much is
reflected, and
transmissivity (τ) is a
measure of how much
passes through the object.
Each of these parame- ters
is a number that ranges
from 0 to 1, and f or any
given wavelength (λ ),
αλ+ρλ+τλ=1
11
Transmissivity
Transmissivity. The
radiation model supports
radiative heat transfer
through transparent solid
media. ... Radiative heat
transfer through a
transparent solid object that
is completely surrounded
by fluid can be simulated
by assigning a non-zero
transmissivity property to
the material.
12
Radiosity
In radiometry, radiosity is
the radiant flux leaving a
surface per unit area, and
spectral radiosity is the
radiosity of a surface per
unit frequency or
wavelength, depending on
whether the spectrum is
taken as a function of
frequency or of wavelength.
13
Irradiation.
Irradiation is the process by
which an object is exposed
to radiation. The exposure
can originate from various
sources, including natural
sources.
14
Applications of Gears
• Emits thermal radiation.
• Incoming radiation can be absorbed.
• Properties are independent.
• Intensities can be studied.
• Used in thermal power plants.
• Used ti industrial applications.
15
16

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Relation between a small body in a large enclosure

  • 1. Heat Transfer Radiation between a small body in a large enclosure
  • 2. Introduction Black-body (Small-body) radiation is the thermal electromagnetic radiation within or surrounding a body in thermodynamic equilibrium with its environment, emitted by a black body (an idealized opaque, non-reflective body). It has a specific spectrum of wavelengths, inversely related to intensity that depend only on the body's temperature, which is assumed for the sake of calculations and theory to be uniform and constant. 2
  • 3. Planks law Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T, when there is no net flow of matter or energy between the body and its environment. 3
  • 4. Wiens displacement law Wien's displacement law states that the black-body radiation curve for different temperatures will peak at different wavelengths that are inversely proportional to the temperature. 4
  • 5. Stefan-Boltzmann law Stefan-Boltzmann law, statement that the total radiant heat power emitted from a surface is proportional to the fourth power of its absolute temperature 5
  • 6. Black-body radiation partition function Partition Function and BlackBody Radiation. Where T is the temperature of a system. Where s is an index over all distinguishable microstates of the system (in the case of discrete states) and ϵ is the energy of each of the microstates. In the continuous case, D(ϵ) is the density of states. 6
  • 7. Intensity of radiation The intensity of radiation is defined as the rate of emission of radiation in a given direction from a surface per unit solid angle and per unit projected area of a radiating surface on a plane perpendicular to the direction of radiation. Eb is the energy emitted and Ib is the intensity of radiations. 7
  • 8. Intensity of emitted radiation. Intensity of radiation emitted by a blackbody is proportional to the fourth power of its temperature (Stefan's law). The wavelength at which the emitted radiation has the maximum intensity is inversely proportional to its temperature (Wien's law) 8
  • 9. Radiative properties on surface  Absorptivity.  Reflectivity.  Transmissivity.  Radiosity.  Irradiation. 9
  • 10. Absorptivity Absorptivity (α) is a measure of how much of the radiation is absorbed by the body. Reflectivity (ρ) is a measure of how much is reflected, and transmissivity (τ) is a measure of how much passes through the object. ... Emissivity (ε) is a measure of how much thermal radiation a body emits to its environment. 10
  • 11. Reflectivity Reflectivity (ρ) is a measure of how much is reflected, and transmissivity (τ) is a measure of how much passes through the object. Each of these parame- ters is a number that ranges from 0 to 1, and f or any given wavelength (λ ), αλ+ρλ+τλ=1 11
  • 12. Transmissivity Transmissivity. The radiation model supports radiative heat transfer through transparent solid media. ... Radiative heat transfer through a transparent solid object that is completely surrounded by fluid can be simulated by assigning a non-zero transmissivity property to the material. 12
  • 13. Radiosity In radiometry, radiosity is the radiant flux leaving a surface per unit area, and spectral radiosity is the radiosity of a surface per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. 13
  • 14. Irradiation. Irradiation is the process by which an object is exposed to radiation. The exposure can originate from various sources, including natural sources. 14
  • 15. Applications of Gears • Emits thermal radiation. • Incoming radiation can be absorbed. • Properties are independent. • Intensities can be studied. • Used in thermal power plants. • Used ti industrial applications. 15
  • 16. 16