Download - Radiation Fundamental Concepts
RadiationFundamental Concepts
EGR 4345
Heat Transfer
Thermal Radiation
Occurs in solids, liquids, and gases Occurs at the speed of light Has no attenuation in a vacuum Can occur between two bodies with a colder
medium in between
Fundamental Concepts
Ts > Tsur
q rad,net
Types of Radiation
Two categories– Volumetric phenomenon – gases, transparent solids– Surface phenomenon – most solids and liquids
Thermal radiation – emitted by all substances above absolute zero
Includes visible & infrared radiation & some UV radiation.
Fundamental Concepts
Background
Electromagnetic radiation – energy emitted due to changes in electronic configurations of atoms or molecules
where =wavelength (usually in m), =frequency In a vacuum c=co=2.998x108 m/s
Other media: c= co /n where n=index of refraction
c
Background, cont.
Radiation – photons or waves? Max Planck (1900): each photon has an
energy of
h=Planck’s constant=6.625 x 10-34 Js Shorter wavelengths have higher energy
hche
Radiation Spectrum
Radiation Properties
Magnitude of radiation varies with wavelength – it’s spectral.
Radiation is made up of a continuous, nonuniform distribution of monochromatic (single-wavelength) components.
Magnitude & spectral distribution vary with temp & type of emitting surface.
Emission Variation with Wavelength
Radiation Properties
Directional distribution – a surface doesn’t emit the same in all directions.
Nomenclature
Nomenclature
Nomenclature
Spectral Intensity
Spectral Intensity of the Emitted Radiation, I,e
– Rate at which radiant energy is emitted at the wavelength, , in the (, ) direction, per unit solid angle about this direction, and per unit wavelength interval d about
Spectral Intensity
Spectral Intensity
Heat Flux
Emissive Power
Spectral, hemispherical emissive power – E
– Rate at which radiation of wavelength is emitted in all directions from a surface per unit wavelength d about and per unit surface area
– Flux based on actual surface area (not projected)– Hemispherical often not used as emission is in all
directions from surface
Total emissive power, E
Emissive Power
Emissive Power
Diffuse emitter – intensity of the emitted radiation independent of direction
ee II ,, ,,
Spectral Irradiation
Spectral Irradiation, G – Rate at which radiation of wavelength is incident
on a surface per unit area of the surface and per unit wavelength d about
Total Irradiation, G
Spectral Irradiation
Spectral Radiosity
Spectral Radiosity, J – Rate at which radiation of wavelength is leaves a
unit area of surface, per unit wavelength interval d about
Total Radiosity, J
Spectral Radiosity
Blackbody Radiation
Blackbody – a perfect emitter & absorber of radiation Emits radiation uniformly in all directions – no
directional distribution – it’s diffuse Joseph Stefan (1879)– total radiation emission per
unit time & area over all wavelengths and in all directions:
=Stefan-Boltzmann constant =5.67 x10-8 W/m2K4
24 mW TEb
Planck’s Distribution Law
Sometimes we’re interested in radiation at a certain wavelength
Spectral blackbody emissive power (Eb) = “amount of radiation energy emitted by a blackbody at an absolute temperature T per unit time, per unit surface area, and per unit wavelength about the wavelength .”
Planck’s Distribution Law
Emitted radiation varies continuously with At any the magnitude of the emitted radiation
increases with increasing temperature The spectral region in which the radiation is
concentrated depends on temperature, with comparatively more radiation appearing at the shorter as the temperature increases
Sun – approximated as a blackbody at 5800 K, radiation is mostly in the visible region
Planck’s Distribution Law
For a surface in a vacuum or gas
Other media: replace C1 with C1/n2
Integrating this function over all gives us the equation for Eb.
constant sBoltzmann'J/K 1038051
Kμm 104391
mμmW 1074232
where
μmmW 1
23
42
24821
2
25
1
-
o
o
b
x.k
x.khcC
x.hcC
TCexp
CTE
Radiation Distribution
Radiation is a continuous function of wavelength
Radiation increases with temp.
At higher temps, more radiation is at shorter wavelengths.
Solar radiation peak is in the visible range.
Wien’s Displacement Law
Peak can be found for different temps using Wien’s Displacement Law:
Note that color is a function of absorption & reflection, not emission
Km 52897 .T powermax
Blackbody Radiation Function
We often are interested in radiation energy emitted over a certain wavelength.
This is a tough integral to do!
Blackbody Radiation Function
Use blackbody radiation function, F
If we want radiation between 1 & 2,
40
T
dTE
TF
b
TFTFTF1221