Radiation(Chapter14)

8/6/2019 Radiation(Chapter14)

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RADIATION

HEAT TRANSFER


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Radiation

Thermal radiation is the energy emitted by matteras a result of its finite temperature. Any matter

with temperature above absolute zero (0 K) emits

electromagnetic radiation. Electromagnetic

radiation can be visualized as waves traveling at

the speed of light, thus, radiation is a surface

phenomenon.

Electromagnetic radiation is categorized into

types by their wavelengths.


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Types of Radiation

The type of radiation emitted by a body depends on its

temperature. The hotter the object is, the shorter the

wavelength and the greater its amount.


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1. The thermal energy of the hot source at T1 isconverted into energy in the form of

electromagnetic waves.

2. These waves travel through intervening spacein straight lines and strike a cold object at T2.

3. The electromagnetic waves that stikes the

body are absorbed by the body and convertedback to thermal energy or heat.

Mechanism of Radiation


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The amount of radiation emitted by a bodydepends on its temperature, and is proportional to

T4. when this radiation strikes a surface, a portion

of it is reflected, and the rest enters the surface.

On the portion that enters, some are absorbedby

the material, and the remaining radiation is

transmittedthrough.

Blackbody emissive power (W/m2) depends ontemperature (T) of surface


E Tb

!W 4


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The ratio of reflected energy to the incidentenergy is called reflectivity, . Similarly,

transmitivity () and absorptivity () are defined

as the fraction of the incident energy that istransmitted through or absorbed by the object.

Irradiation = the total amount of incident

radiation that strikes a surfaceRadiosity = the sum of the radiation emitted by

a surface and the fraction of irradiation that is

reflected by the surface.



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e = emissive power

G = total irradiation

J = total radiosity

1! XVE

In general:

Opaque material:

1! VE

E = absorptivity

V = reflectivity

X= transmissivity

I = emissivity

E!I



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P

eP

T1

T2

T3

Energy

e

Ideal EmitterSchematicT3> T2> T1


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A body that is assumed to absorb all radiant energyand does not reflect any is called a black body.

Such a body also emits radiation. The ratio of the

emissive power of a surface to that of a black body

is called emissivity () and is equal to 1.0 for a

black body. According to Kirchhoffs law,

emissivity and absorptivity of a surface in

surroundings at its own temperature are the samefor both monochromatic and total radiation; thus

for a given surface at thermal radiation

=

Black Body


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At thermal equilibrium

emissivity of surface = absorptivity

EI

transmissivity of solid surfaces = 0

emissivity is the only significant parameter

emissivities vary from 0.1 (polished surfaces) to0.95 (blackboard)

=

Black Body


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The black body is an idealized surface having thefollowing properties:

Perfect absorber: it absorbs all incident radiation of

wavelength and direction

Perfect emitter: for a prescribed temperature andwavelength, no surface can emit more than a black body.

Although the radiation emitted by a black body is a

function of wavelength and temperature, it is independent

of direction. That is, the black body is a diffuse emitter.

Black Body

INTENSITY FOR DIFFUSE

BLACKBODY RADIATION


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Black Body absorptivity = E!

emissivity = I!

ideal emissive power = eb

4Teb W!

1!! IE

PE f{

PI f{

4Te gray WI!

bgray ee I!

Gray Body

absorptivity < 1

emissivity < 1

emissive power


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P

eP Gray

Body

Black

Body

Energy

RealBody

black

gray

ee!I

IE !

I f{

Schematic


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All Real Surfaces are Grey

IRRADIATION, INCIDENT

RADIATION


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The total energy emittedby a body, regardlessof the wavelengths, is given by:

Where: = emissivity

A = surface area exposed

T = absolute temperature = Stefan-Boltzmann constant

= 5.67 x10-8 W/m2.K4 = 0.1714 x 10-8 Btu/hr.ft2.OR4

Emissive Power

44111 SS

TTAq !WI


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The total energy absorbed a body, regardless ofthe wavelengths, is given by:

Where: = absorptivity

A = surface area exposed

T = absolute temperature = Stefan-Boltzmann constant

= 5.67 x10-8 W/m2.K4 = 0.1714 x 10-8 Btu/hr.ft2.OR4

Emissive Power

41

aSS

TAq W!


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If two surfaces are arranged so that radiant energycan be exchanged, a net flow of energy will occur

from the hotter surface to the colder surface. The

size, shape and orientation of the two radiating

surfaces or a system of surfaces are factors in

determining the heat transfer rate between them.

View Factor, F12= fraction of radiation leaving

the surface 1 in all directions which is intercepted

by surface 2.

Radiant Transfer between Surfaces


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Surface and View Factor Resistance


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For two black planes radiating to each other, the

net radiation is expressed as

q12 = 12A1(T1

4-T24)

Where F1

2

is the view factor of surface 1 to surface

2, also

q21 = 21A2(T14-T2

4)

For view factor cannot exceed unity. Such thatA

1F

12 = A2F21

and is independent of temperature

Radiant Transfer between Black Bodies


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1 !j

ijF 1...... 111211 ! nj FFFF

jijiji FAFA ! Thermal Equilibrium

View Factor: Fij = fraction of radiation fromsurface i intercepted by surface j.

1 2



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In the case of infinite parallel planes, F12=F21=1.0,the geometric factor is omitted.

q12 = A1(T1

4-T24)

When surfaces are connected by nonconductingbut reradiating walls, the reradiating view factor

is 12, is used instead of 12 and is treated

similarly.



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For two gray planes radiating to each other, the net

radiation is expressed as

q12 = 12A1(T1

4-T24)

Where F12 is the new view factor and defined as

Radiant Transfer between Gray Bodies

12 = 1

1 + A1 1 1 + 1 -1F

12 A2 2 1


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1be1J 2J

RJ11

11

I

I

A

22

21

I

I

A

RFA 11

1

121

1

FA

RFA 22

1No net heat flux wall

Analog

circuit

12Q 11212

AqQ !Find:

2be

X

1 2

R

R



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1be1J 2J

2be

RJ11

11II

A

22

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ARFA 11

1

121

1

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RFA 22

1

RR FAFA 2211

11

1be1J 2J

2be

11

1

1

I

I

A

22

2

1

I

I

A

121

1

FA



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11

11

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22

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I

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A

RR FAFA 2211

11

121

1

FA

1be 1J 2J 2be

11

11

I

I

A

22

21

I

I

A

RR FAFA

FA

2211

121 111

1

RR FAFA

FAFA

2211

121121 11

1

!



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1be 1J 2J 2be

11

1

1

I

I

A

22

2

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I

A

121

1

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RR FAFA

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1

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2

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I

I

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AFAA

1be

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22

2

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1

121 111

1

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A

!F



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1be 2be

121

1

FA

4241112 TTAQ ! W12F

21112 bb eeAQ ! 12F

121tanF

AceConduc !

RR FAFA

FAFA

2211

121121 11

1

!

22

2

12111

1

121 111

1

I

I

I

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AFAA

A

!F



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12

netq ,12

2be1be 1J 2J

22

21

I

I

A

11

11

I

I

A

121

1

FA

21 AA !

22

2

12111

1

21112 111

I

I

I

I

AFAA

eeAq bb

!

111

21

2112

!

II

bbee

q

1


12112 !! FF

Radiation heat transfer between two infinite parallel plates


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1

S

netSq ,1 bSe1be1J SJ

SS

S

A I

I1

11

11

I

I

A

SFA 11

1

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A

SS

bSb

S

AFAA

eeAq

I

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2

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1111

1

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11 111

!

bSbS eeq ! 111 I

1

0

1!! SS IE

44111 SS

TTq !WI


Radiation heat transfer between small objects and infinite surrounding


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The total incident radiant energy upon a body which

partially reflects, absorbs and transmits radiant energy is

2200 W/m2. of this amount, 450 W/m2 is reflected and900 W/m2 is absorbed by the body. Find the transmitivity.

= 1 = 1 450/2200 900/2200 = 0.386

Determine the total emissive power of a blackbody at

1000OC

Eb = T4 = 5.67 x 10-8 (1273.15K) = 149 kW/m2


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Two black body rectangles, 1.8 m by 3.6 m are parallel

and directly opposed and are 3.6 m apart. If surface 1 is at

T1 = 95OC and surface 2 is at T2 = 315OC, determine a)the net rate of heat transfer b) the net energy loss rate

from the 95OC surface if the surrounding other than

surface 2 behave as black body at 295 K.


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Radiation(Chapter14)

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