Introduction to Thermal Radiation and Radiation 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• Occurs in combination with conduction and

convection, and significant where large temperature differences occur

• Applications: Furnace with boiler tubes, radiant dryers, oven baking, designing heaters for manufacturing, estimating heat gains through windows, infrared cameras, metal cooling during manufacturing, Greenhouse effect, thermos design, among others.

Background

• Electromagnetic radiation – energy emitted due to changes in electronic configurations of atoms or molecules

• where l=wavelength (usually in mm), n=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

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 zero

• Includes visible & infrared radiation & some UV radiation.

Radiation Properties

• Magnitude of radiation varies with wavelength – it’s spectral.– The wavelength of the radiation is a major factor in

what its effects will be.– Earth/sun example

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

• Magnitude & spectral distribution (how the radiation varies with wavelength) vary with temp & type of emitting surface.

Emission Variation with Wavelength

Blackbody Radiation• Blackbody – a perfect emitter & absorber of

radiation; it absorbs all incident radiation, and no surface can emit more for a given temperature and wavelength

• Emits radiation uniformly in all directions – no directional distribution – it’s diffuse

• Example of a blackbody: large cavity with a small hole

Stefan-Boltzmann Law

• Joseph Stefan (1879)– total radiation emission per unit time & area over all wavelengths and in all directions:

s =Stefan-Boltzmann constant

=5.67 x10-8 W/m2K4

T must be in absolute scale.

24 mW TEb

Planck’s 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 all l gives us

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

4 bE T

Radiation Distribution

• Radiation is a continuous function of wavelength

• Magnitude increases with temp.

• At higher temps, more radiation is at shorter wavelengths.

• Solar radiation peak is in the visible range.

Wien’s Displacement Law

• Wavelength of radiation with the largest magnitude can be found for different temps using Wien’s Displacement Law:

• Note that color is a function of absorption & reflection, not emission.

max2897.8 m K

powerT

What is your favorite wavelength?

More Radiation Properties

• Directional distribution – a surface doesn’t emit the same in all directions.

• Hemispherical – refers to all directions

Emissive Power• E: amount of radiation emitted per unit area• Spectral hemispherical emissive power El

(often leave out the word “hemispherical”) W/m2l– Rate of emission per unit area of radiation of a

given wavelength l in all directions per unit wavelength interval

• Total (hemisperical) emissive power E (W/m2)– Rate of emission per unit area of radiation of all

wavelengths and in all directions; this is

emittedq

Diffuse emitters

• Diffuse emitter: intensity is the same in all directions

Irradiation

• Irradiation: radiation incident on (hitting) a surface per unit area

Radiosity

• Radiosity: all radiation leaving a surface per unit area, both emitted and reflected

Emmisivity and Kirchoff’s law

e = E/Eb

Kirchoffs’ Law

( 1)= ( 1)a T e T

l

El

T1

T2

T3

Energy

e

Ideal EmitterSchematic

T3> T2> T1

1 In general:

Opaque material:

1

a = absorptivity

r = reflectivity

t = transmissivity

Mechanism of Radiation Heat Transfer

• Thermal energy of hot source ( furnace wall at T1) is converted into radiant energy.

• These waves travel through the intervening space in straight lines and strike a cold object at T2 such as a furnace tube

• The electromagnetic waves that strike the body are absorbed and converted back to thermal energy.

Black Body and Gray Body

• Black Body– absorptivity = =1a– emissivity = =1e– ideal emissive power = Eb

4bE T

1

4grayE T

gray bE E

• Gray Body– absorptivity < 1– emissivity < 1

(independent of wavelength)

– emissive power<1

Radiation of a small object from surrounding

A1

4 412 1 1 1 1 12 2q A T A T

T2

T1

T2 > T1

4 412 1 1 2( )q A T T

Combined radiation and convection heat transfer

1 1 2 1 1 2

convection radiation

c r

q q q

q h A T T h A T T

4 41 2

1 2r

T Th

T T

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

1 2

Summation rule (View factor)

1 j

ijF

1...... 111211 nj FFFF

Reciprocity rule (View factor)

jijiji FAFA

Superposition rule

Symmetry rule

Radiation heat transfer between black surfaces

Radiation heat transfer between black surfaces

(surfaces forming anenclosure)

Net radiation from heat transfer to or from a surface

Electrical analogy

Surface resistance

Net Radiation Transfer between two surfaces

space resistance

Radiation heat transfer in two-surface enclosures

Consider the radiation heat transfer between

two infinite parallel plates

1 2

netq ,12

2be1be1J 2J

22

21

A

11

11

A

121

1

FA

12112 FF 21 AA

22

2

12111

1

21112 111

AFAA

eeAq bb

1

11

21

2112

bb eeq

1

Application:Radiation shield

• Highly reflective thin plate to reduce radiation heat transfer between two surfaces

Radiation effect on temperature measurement