Relation between a small body in a large enclosure

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

Relation between a small body in a large enclosure

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