Radiation Intro ME 114 Powerpoint

8/7/2019 Radiation Intro ME 114 Powerpoint

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Introduction to Thermal Radiation

Figures except for the McDonnell Douglas figures come from Incorpera &

DeWitt, Introduction to Heat and Mass Transfer or Cengel, Heat Transfer: APractical Approach


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Thermal Radiation

Occurs in solids, liquids, and gases

Occurs at the speed of light

Has no attenuation in a vacuumCan occur between two bodies with a colder medium inbetween

Applications: satellite temperature management, taking

accurate temperature measurements, designing heatersfor manufacturing, estimating heat gains throughwindows, infrared cameras, metal cooling duringmanufacturing, Greenhouse effect, lasers, insulatingcryogenic tanks, thermos design, ice skating rink ceiling

design


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Background

Electromagnetic radiation energy emitted dueto changes in electronic configurations of atoms

or molecules

where P=wavelength (usually in Qm),

R=frequencyIn a vacuum c=co=2.998x10

8m/s

Other media: c=co/n where n=index of refraction

R!P c


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Background, cont.

Radiation photons or waves?

Max Planck (1900): each photon has an energy

of

h=Plancks constant=6.625 x 10-34 Js

Shorter wavelengths have higher energy

P!R! hhe


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Radiation Spectrum


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Types of Radiation

Two categories

Volumetric phenomenon radiation emitted or absorbed

throughout gases, transparent solids, some fluids Surface phenomenon radiation to/from solid or liquid

surface

Thermal radiation emitted by all substances above

absolute zeroIncludes visible & infrared radiation & some UV

radiation.


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Radiation Properties

Magnitude of radiation varies with wavelength itsspectral.

The wavelength of the radiation is a major factor in what itseffects will be.

Earth/sun example

Radiation is made up of a continuous, nonuniformdistribution of monochromatic (single-wavelength)components.

Magnitude & spectral distribution (how the radiationvaries with wavelength) vary with temp & type ofemitting surface.


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Emission Variation with Wavelength


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Blackbody Radiation

Blackbody a perfect emitter & absorber of radiation; itabsorbs all incident radiation, and no surface can emitmore for a given temperature and wavelength

Emits radiation uniformly in all directions nodirectional distribution its diffuse

Example of a blackbody: large cavity with a small holeJoseph Stefan (1879) total radiation emission per unittime & area over all wavelengths and in all directions:

W=Stefan-B

oltzmann constant =5.67 x10-8

W/m2

K4

24 mWTEb W!


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Plancks Distribution Law

Sometimes we care about the radiation in a certain wavelength interval

For a surface in a vacuum or gas

Integrating this function over allP gives us

? A

constantsBoltzmann'J/K1038051

Km104391

mmW1074232

where

mmW1

23

42

24821

2

25

1

!!!!

!T!

PP!P

-

o

o

b

x.k

x.khcC

x.hcC

TCexp

C

TE

4bE TW!


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Radiation

DistributionRadiation is a continuousfunction of wavelength

Magnitude increaseswith temp.

At higher temps, moreradiation is at shorter

wavelengths.Solar radiation peak is inthe visible range.


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Wiens Displacement Law

Wavelength of radiation with the largest

magnitude can be found for different temps

using Wiens Displacement Law:

Note that color is a function of absorption &

reflection, not emission

max

2897.8 m Kpower

TP Q!


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Blackbody Radiation Function

We often are interested in radiation energy emitted overa certain wavelength interval.

This is a tough integral to do!


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Blackbody Radiation Function

Use blackbody radiation function,

FP(often called the fractional

function)

If we want radiation between P1 &

P2,

4

0

T

dTE

TF

b

W

TFTFTF1221 PPPP

!


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More Radiation Properties

Directional distribution a surface doesnt emit

the same in all directions.

Hemispherical refers to all directions


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Angle definitions

zenith angle Uup and down)

azimuthal angle Jside to side)


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Solid Angle

differential solid angle d[!dAn/r2= dA1cosU/r

2=sinU dU dJ

A solid angle is for a sphere what an angle is for a circle

Units: steradians (sr); For a sphere [=4T sr


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Solid Angle, cont.


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Spectral Intensity

IP,e: rate at which radiant energy is emitted at the

wavelength P in the (UJ) direction, per unit area of the

emitting surface normal to this direction, per unit solidangle about this direction, and per unit wavelength

interval dP aboutP

Translation: rate of emission at a given wavelength, in a

given direction, per unit area, solid angle, andwavelength interval

Units: W/(m2srQm)


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Spectral Intensity

, , ,en

dqI

dA d d P P U J

Z P!

1 cosnd d U!


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To solve for dq

Sometimes we know the intensity Ie rather thanthe spectral intensity (i.e., the rate of emission in

a given direction, per unit area and solid angle).

This is IP,e integrated over all wavelengths. Then

, 1, ,edQ I dA d d P P U J U P! &

1,ed I dA d U J U Z ! &


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Total heat flux

To find the total heat flux, we must integrate over

both angles and wavelength.

2 2

,

0 0

0

, ,eq I cos sin d d

q q d

P

P

TT

PP P U J U U U J

P P

g

!

!

&

& &

2 2

,

0 0 0

, ,eq I cos sin d d d

TT

P P U J U U U J Pg

!&OR

spectral heat flux

total heat flux

total heat flux


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Emissive Power

E: amount of radiation emitted per unit area

Spectral hemispherical emissive power EP (often leave

out the word hemispherical) W/m

2

P Rate of emission per unit area of radiation of a given

wavelength P in all directions per unit wavelength interval

Total (hemisperical) emissive power E (W/m2)

Rate of emission per unit area of radiation of all wavelengthsand in all directions; this is emittedq&


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Diffuse emitters

Diffuse emitter: intensity is the same in all

directions; integration is easy!

,

,0

e e

e e

E I and E I

where I I d

P P

P

P T P T

Pg

! !

!


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Irradiation, G

Irradiation: radiation incident on (hitting) a

surface per unit area

Use subscript i

Same equations as E except replace E with G

and IP,e with IP,i(intensity of incident radiation)


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Radiosity, J

Radiosity: all radiation leaving a surface per unit

area, both emitted and reflected

Use subscript e+r

Same equations as E except replace E with J

and IP,e with IP,e+r(intensity of emitted+reflected

radiation)


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Example 1

A small surface of area A1=3 cm2diffusely emits

radiation with an emissive power of 7350 W/m2.Part of the radiation strikes another small surface

of area A2=5 cm2oriented as shown on the board.

a) Find the intensity of the emitted radiation.

b) Find the solid angle subtended by A2

whenviewed from A1.

c) Find the rate of radiation emitted by A1 thatstrikes A2.

Radiation Intro ME 114 Powerpoint

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