Fundamentals of Thermal Radiationmazlan/?download=Heat Transfer... · • The dual nature of radiation: – In some cases, the physical manifestations of radiation may be explained

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CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER

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SME SME 44463 463 HEAT TRANSFERHEAT TRANSFER

LECTURER:

ASSOC. PROF. DR. MAZLAN ABDUL WAHIDhttp://www.fkm.utm.my/~mazlan

Faculty of Mechanical EngineeringUniversiti Teknologi Malaysiawww.fkm.utm.my/~mazlan

FACULTY OF MECHANICAL ENGINEERINGUNIVERSITI TEKNOLOGI MALAYSIASKUDAI, JOHOR, MALAYSIA HEAT TRANSFER INTERNAL FLOW CONVECTIONINTERNAL FLOW CONVECTIONINTERNAL FLOW CONVECTIONINTERNAL FLOW CONVECTIONINTERNAL FLOW CONVECTIONINTERNAL FLOW CONVECTIONINTERNAL FLOW CONVECTIONINTERNAL FLOW CONVECTION

DR MAZLAN


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Chapter 12Fundamentals of Thermal

Radiation

FACULTY OF MECHANICAL ENGINEERINGUNIVERSITI TEKNOLOGI MALAYSIASKUDAI, JOHOR, MALAYSIA HEAT TRANSFER DR MAZLAN

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ObjectivesWhen you finish studying this chapter, you should be able to:• Classify electromagnetic radiation, and identify thermal

radiation,• Understand the idealized blackbody, and calculate the total and

spectral blackbody emissive power,• Calculate the fraction of radiation emitted in a specified

wavelength band using the blackbody radiation functions,• Understand the concept of radiation intensity, and define

spectral directional quantities using intensity,• Develop a clear understanding of the properties emissivity,

absorptivity, relflectivity, and transmissivity on spectral, directional, and total basis,

• Apply Kirchhoff law’s law to determine the absorptivity of a surface when its emissivity is known,

• Model the atmospheric radiation by the use of an effective sky temperature, and appreciate the importance of greenhouse effect.


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Chapter 10 : Thermal Radiation

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Radiation phenomena:

A hot object in a vacuum chamber will eventually cool down and reach thermal equilibrium with its surroundings by a heat transfer mechanism: radiation .

� Radiation differs from conduction and convection in that it does not require the presence of a material medium to take place.

� Radiation transfer occurs in solids as well as liquids and gases.

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General Considerations• Attention is focused on thermal radiation, whose origins are associated

with emission from matter at an absolute temperature (K)

• Emission is due to oscillations and transitions of the many electrons that comprisematter, which are, in turn, sustained by the thermal energy of the matter.

• Emission corresponds to heat transfer from the matter and hence to a reductionin thermal energy stored by the matter.

• Radiation may also be intercepted and absorbed by matter.

• Absorption results in heat transfer to the matter and hence an increase in thermal energy stored by the matter.

• Consider a solid of temperaturein an evacuated enclosure whose wallsare at a fixed temperature

sT

surT :

� What changes occur if Ts > Tsur ?


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• Emission from a gas or a semitransparent solid or liquid is a volumetricphenomenon. Emission from an opaque solid or liquid is a surface

phenomenon.

*For an opaque solid or liquid, emission originates from atoms and moleculeswithin 1 µm of the surface.

• The dual nature of radiation:– In some cases, the physical manifestations of radiation may be explained

by viewing it as particles (aka photons or quanta).

– In other cases, radiation behaves as an electromagnetic wave.

An opaquesolid transmits no light, and therefore reflects, scatters, or absorbs all of it. E.g. mirrors and carbon black.

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• Unlike conduction and convection, radiation does not require the presence of a material medium to take place.

• Electromagnetic waves or electromagnetic radiation─ represent the energy emitted by matter as a result of the changes in the electronic configurations of the atoms or molecules.

• Electromagnetic waves are characterized by their frequency ν or wavelength λ

• c─ the speed of propagation of a wave in that medium.

cλν

= (12-1)


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Thermal Radiation

• Engineering application concerning electromagnetic radiation covers a wide range of wavelengths.

• Of particular interest in the study of heat transfer is the thermal radiation emitted as a result of energy transitions of molecules, atoms, and electrons of a substance.

• Temperature is a measure of the strength of these activities at the microscopic level.

• Thermal radiation is defined as the spectrum that extends from about 0.1 to 100µm.

• Radiation is a volumetric phenomenon. However, frequently it is more convenient to treat it as a surface phenomenon.

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Thermal Radiation

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Everything around us constantly emits thermal radiation.

� Temperature is a measure of the strength of these activities at the microscopic level, and the rate of thermal radiation emission increases with increasing temperature.

� Thermal radiation is continuously emitted by all matter whose temperature is above absolute zero.

Radiation phenomena:

� In all cases, radiation is characterized by a wavelength, λ and frequency, ν which are related through the speed at which radiation propagates in the medium of interest:

c = c0 /nc, the speed of propagation of a wave in that medium c0 = 2.9979 × 108 m/s, the speed of light in a vacuum n, the index of refraction of that mediumn = 1 for air and most gases, n = 1.5 for glass, and n = 1.33 for water


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The Electromagnetic Spectrum

• Thermal radiation is confined to the infrared, visible and ultraviolet regions of thespectrum 0.1 < λ < 100 µm .

• The amount of radiation emitted by an opaque surface varies with wavelength, and we may speak of the spectral distribution over all wavelengths or of monochromatic/spectral components associated with particular wavelengths.

* Thermal radiation is confined to the infrared, visible and ultraviolet regions.

Light is simply the visibleportion of the electromagneticspectrum that lies between 0.4 and 0.7 µm.

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Thermal Radiation

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The electromagnetic wave spectrum

� Light is simply the visibleportion of the electromagnetic spectrum that lies between 0.40 and 0.76 µm.

� A body that emits some radiation in the visible range is called a light source.

� The sun is our primary light source.

� The electromagnetic radiation emitted by the sun is known as solar radiation, and nearly all of it falls into the wavelength band 0.3–3 µm.

� Almost half of solar radiation islight (i.e., it falls into the visible range), with the remaining being ultravioletand infrared.

Brief About Light:

Short wavelength – Interest of high energy physicist/nuclear engineer

Long and radio wavelength –Interest of electrical engineer

Thermal Radiation


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Blackbody Radiation• A body at a thermodynamic (or absolute)

temperature above zero emits radiation in all directions over a wide range ofwavelengths.

• The amount of radiation energy emitted from a surface at a given wavelength depends on:– the material of the body and the condition of its surface,– the surface temperature.

• A blackbody─ the maximum amount of radiation that can be emitted by a surface at a given temperature.

• At a specified temperature and wavelength, no surface can emit more energy than a blackbody.

• A blackbody absorbs all incident radiation, regardless of wavelength and direction.

• A blackbody emits radiation energy uniformly in all directionsper unit area normal to direction of emission.

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• The radiation energy emitted by a blackbody per unit time and per unit surface area (Stefan–Boltzmann law)

σ = 5.67 X 10-8 W/m2·K4.

• Examples of approximate blackbody:– snow,

– white paint,

– a large cavity with a small opening.

• The spectral blackbody emissive power

( ) ( )4 2 W/mbE T Tσ= (12-3)

( ) ( ) ( )

( )( )

215

2

2 8 4 21 0

42 0

, W/m µmexp 1

2 3.74177 10 Wµm m

/ 1.43878 10 µm K

b

CE T

C T

C hc

C hc k

λ λλ λ

π

= ⋅ −

= = × ⋅

= = × ⋅

(12-4)


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• The variation of the spectral blackbody emissive power with wavelength is plotted in Fig. 12–9.

• Several observations can be made

from this figure:– at any specified temperature a

maximum exists,

– at any wavelength, the amount of

emitted radiation increases with

increasing temperature,

– as temperature increases, the curves

shift to the shorter wavelength,

– the radiation emitted by the sun

(5780 K) is in the visible spectrum.

• The wavelength at which the peak occurs is given by Wien’s displacement lawas

( ) ( )max power

2897.8 m KTλ µ= ⋅ (12-5)

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• We are often interested in the amount of radiation emitted over some wavelength band.

• The radiation energy emitted by a blackbody per unit area over a wavelength band from λ=0 to λ= λ1 is determined from

• This integration does not have a simple closed-form solution. Therefore a dimensionless quantity fλ called the blackbody radiation function is defined:

• The values of fλ are listed in Table 12–2.

( ) ( ) ( )1

1

2,0 0

, W/mb bE T E T dλ

λ λ λ λ→ = ∫ (12-7)

( )( )

04

, ; 1 or 2

n

n

bE T df T n

T

λ

λλ

λ λσ

= =∫ (12-8)


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Table 12-2 ─ Blackbody Radiation Functions fλ

( )( )1

1

04

,bE T df T

T

λ

λλ

λ λσ

= ∫

(12-8)

( )( ) ( )

1 2

2 1

f T

f T f T

λ λ

λ λ

− =

−

(12-9)

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Thermal Radiation

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� An electrical heater starts radiating heat soon after is plugged, we can feel the heat but cannot be sensed by our eyes (within infrared region)

� When temp reaches 1000K, heater starts emitting a detectable amount of visible red radiation (heater appears bright red)

� When temp reaches 1500K, heater emits enough radiation and appear almost white to the eye (called white hot).

� Although infrared radiation cannot be sensed directly by human eye, but it can be detected by infrared cameras.


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Thermal Radiation

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Radiation Intensity & Directional Consideration

� Radiation is emitted by all parts of a plane surface in all directions into thehemisphere above the surface, and the directional distribution of emitted (orincident) radiation is usually not uniform.

� Therefore, we need a quantity thatdescribes the magnitude of radiation emitted (or incident) in a specified direction in space.

� This quantity is radiation intensity,denoted by I.

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Thermal Radiation

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Thermal Radiation

20�� Eq. (12.4)

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Thermal Radiation

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Relation of Intensity to Emissive Power, E, Irradiation, G and Radiosity, J

Ie : total intensity of the emitted radiation

�� Eq. (12.9)

�� Eq. (12.14)

�� Eq. (12.17)


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Relation of Intensity to Emissive Power, E, Irradiation, G and Radiosity, J

Thermal Radiation

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Thermal Radiation

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�� Eq. (12.19)

�� Eq. (12.22)


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Radiation Intensity

• The direction of radiation passing through a point is best described in spherical coordinates in terms of the zenith angle θ and the azimuth angleφ.

• Radiation intensity is used to describe how the emitted radiation varies with the zenith and azimuth angles.

• A differentially small surface in space dAn, through which this radiation passes, subtends a solid angledω when viewed from a point on dA.

dAn

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• The differential solid angle dω subtended by a differential area dSon a sphere of radius r can be expressed as

• Radiation intensity─ the

rate at which radiation energy

is emitted in the(θ,φ) direction

per unit area normal to this

direction and per unit solid angle about this direction.

2sin

dSd d d

rω θ θ φ= = (12-11)

( ) 2

W,

cos cos sin m sre e

e

dQ dQI

dA d dA d dθ φ

θ ω θ θ θ φ = = ⋅ ⋅

& &(12-13)


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• The radiation fluxfor emitted radiation is the emissive powerE

• The emissive power from the surface into the hemisphere surrounding it can be determined by

• For a diffusely emittingsurface, the intensity of the emitted radiation is independent of direction and thus Ie=constant:

( ), cos sinee

dQdE I d d

dAθ φ θ θ θ φ= =

&

(12-14)

( ) ( )2 / 2 2

0 0, cos sin W me

hemisphere

E dE I d dπ π

φ θθ φ θ θ θ φ

= == =∫ ∫ ∫ (12-15)( )2 / 2

0 0, cos sine

hemisphere

E dE I d dπ π


= == =∫ ∫ ∫ (12-1)( )2W m

2 / 2

0 0cos sine e

hemisphere

E dE I d d Iπ π

φ θ

π

θ θ θ φ π= =

= = =∫ ∫ ∫14444244443

(12-12)

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• For a blackbody, which is a diffuse emitter, Eq. 12–16 can be expressed as

• where Eb=σT4 is the blackbody emissive power. Therefore, the intensity of the radiation emitted by a blackbody at absolute temperature T is

b bE Iπ= (12-17)

( ) ( )4

2 W m ×srbb

E TI T

σπ π

= = (12-18)


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• Intensity of incident radiation

I i(θ,φ) ─ the rate at which radiation

energy dG is incident from the (θ,φ)

direction per unit area of the

receiving surface normal to this

direction and per unit solid angle

about this direction.

• The radiation flux incident on a surface from all directions is called irradiation G

• When the incident radiation is diffuse:

( ) ( )2 / 2 2

0 0, cos sin W mi

hemisphere

G dG I d dπ π


= == =∫ ∫ ∫

(12-19)

iG Iπ= (12-20)

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• Radiosity (J )─ the rate at

which radiation energy leaves

a unit area of a surface in all

directions:

• For a surface that is both a diffuse emitter and a diffuse reflector, Ie+r≠f(θ,φ):

( ) ( )2 / 2 2

0 0, cos sin W me rJ I d d

π π

φ θθ φ θ θ θ φ+= =

= ∫ ∫ (12-21)

2 ( W m )e rJ Iπ += (12-22)


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• Spectral Quantities─ the

variation of radiation with

wavelength.

• The spectral radiation

intensity Iλ(λ,θ,φ), for

example, is simply the total radiation intensity I(θ,φ) per unit wavelength interval about λ.

• The spectral intensityfor emitted radiation Iλ,e(λ,θ,φ)

• Then the spectral emissive powerbecomes

( ), 2

W, ,

cos m srµme

e

dQI

dA d dλ λ θ φθ ω λ

= ⋅ ⋅ ⋅ ⋅

&(12-23)

( )2 / 2

,0 0, , cos sineE I d d

π π

λ λφ θλ θ φ θ θ θ φ

= == ∫ ∫ (12-24)

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• The spectral intensity of radiation emitted by a blackbody at a thermodynamic temperature Tat a wavelength λ has been determined by Max Planck, and is expressed as

• Then the spectral blackbody emissive power is

( ) ( ) ( )2

205

0

2, W/m sr µm

exp 1b

hcI T

hc kTλ λ

λ λ= ⋅ ⋅

− (12-23)

( ) ( ), ,b bE T I Tλ λλ π λ= (12-24)


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Radiative Properties

• Many materials encountered in practice, such as metals, wood, and bricks, are opaqueto thermal radiation, and radiation is considered to be a surface phenomenonfor such materials.

• In these materials thermal radiation is emitted or absorbed within the first few microns of the surface.

• Some materials like glass and water exhibit different behavior at different wavelengths:– Visible spectrum─ semitransparent,

– Infrared spectrum─ opaque.

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1. Emissivity

• Emissivity of a surface─ the ratio of the radiation emitted by the surface at a given temperature to the radiation emitted by a blackbody at the same temperature.

• The emissivity of a surface is denoted by ε, and it varies between zero and one, 0≤ε ≤1.

• The emissivity of real surfaces varies with:– the temperatureof the surface, – the wavelength, and – the directionof the emitted radiation.

• Spectral directional emissivity─ the most elemental emissivity of a surface at a given temperature.


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Thermal Radiation

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Emissivity, εεεε• The ratio of the radiation emitted by the surface at a given

temperature to the radiation emitted by a blackbody at the same temperature. 0 ≤ ε ≤ 1.

• Emissivity is a measure of how closely a surface approximates a blackbody (ε = 1).

• The emissivity of a real surface varies with thetemperatureof the surface as well as the wavelengthand the directionof the emitted radiation.

• The emissivity of a surface at a specified wavelength is called spectral emissivityελ. The emissivity in a specified direction is called directional emissivityεθ where θ is the angle between the direction of radiation and the normal of the surface.

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• Spectral directional emissivity

• The subscripts λ and θ are used to designate spectraland directionalquantities, respectively.

• The total directional emissivity (intensities integrated over all wavelengths)

• The spectral hemispherical emissivity

( ) ( )( )

,,

, , ,, , ,

,e

b

I TT

I Tλ

λ θλ

λ θ φε λ θ φ

λ= (12-30)

( ) ( )( ), ,

, , e

b

I TT

I Tθθ φ

ε θ φ = (12-31)

( ) ( )( )

,,

,b

E TT

E Tλ

λλ

λε λ

λ= (12-32)


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• The total hemispherical emissivity

• Since Eb(T)=σT4 the total hemisphericalemissivity can also be expressed as

• To perform this integration, we need to know the variation of spectral emissivity with wavelength at the specified temperature.

( ) ( )( )b

E TT

E Tε = (12-33)

( ) ( )( )

( ) ( )0

4

, ,b

b

T E T dE TT

E T T

λ λε λ λ λε

σ

∞

= = ∫ (12-34)

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Gray and Diffuse Surfaces

• Diffuse surface─ a surface which properties are independent of direction.

• Gray surface─ surface properties are independent of wavelength.


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2. Absorptivity 3. Reflectivityand 4. Transmissivity

• When radiation strikes a surface, part of it:– is absorbed (absorptivity , α), – is reflected (reflectivity , ρ),– and the remaining part, if any, is

transmitted (transmissivity, τ).

• Absorptivity:

• Reflectivity:

• Transmissivity:

Absorbed radiation

Incident radiationabsG

Gα = = (12-37)

Reflected radiation

Incident radiationrefG

Gρ = = (12-38)

Transmitted radiation

Incident radiationtrG

Gτ = = (12-39)


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• The first law of thermodynamics requires that the sum of the absorbed, reflected, and transmitted radiation be equal to the incident radiation.

• Dividing each term of this relation by G yields

• For opaque surfaces, τ=0, and thus

• These definitions are for total hemispherical properties.

abs ref trG G G G+ + = (12-40)

1α ρ τ+ + = (12-41)

1α ρ+ = (12-42)

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• Like emissivity, these properties can also be defined for a specific wavelength and/or direction.

• Spectral directional absorptivity

• Spectral directional reflectivity

( ) ( )( )

,,

,

, ,, ,

, ,abs

i

I

Iλ

λ θλ

λ θ φα λ θ φ

λ θ φ= (12-43)

( ) ( )( )

,,

,

, ,, ,

, ,ref

i

I

Iλ

λ θλ

λ θ φρ λ θ φ

λ θ φ= (12-43)


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• Spectral hemispherical absorptivity

• Spectral hemispherical reflectivity

• Spectral hemispherical transmissivity

( ) ( )( )

,absG

Gλ

λλ

λα λ

λ= (12-44)

( ) ( )( )

,refG

Gλ

λλ

λρ λ

λ= (12-44)

( ) ( )( )

,trG

Gλ

λλ

λτ λ

λ= (12-44)

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• The average absorptivity, reflectivity, and transmissivity of a surface can also be defined in terms of their spectral counterparts as

• The reflectivity differs somewhat from the other properties in that it is bidirectionalin nature.

• For simplicity, surfaces are assumed to reflect in a perfectly specularor diffusemanner.

0 0 0

0 0 0

, , G d G d G d

G d G d G d

λ λ λ λ λ λ

λ λ λ

α λ ρ λ τ λα ρ τ

λ λ λ

∞ ∞ ∞

∞ ∞ ∞= = =∫ ∫ ∫

∫ ∫ ∫(12-46)


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Kirchhoff’s Law• Consider a small body of surface area

As, emissivity ε, and absorptivity α at temperature T contained in a large isothermal enclosure at the same temperature.

• Recall that a large isothermal enclosure forms a blackbody cavity regardless of the radiative properties of the enclosure surface.

• The body in the enclosure is too small to interfere with the blackbody nature of the cavity.

• Therefore, the radiation incident on any part of the surface of the small body is equal to the radiation emitted by a blackbody at temperature T.

G=Eb(T)=σT4.

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• The radiation absorbed by the small body per unit of its surface area is

• The radiation emitted by the small body is

• Considering that the small body is in thermal equilibrium with the enclosure, the net rate of heat transfer to the body must be zero.

• Thus, we conclude that

4absG G Tα ασ= =

4emitE Tεσ=

4 4s sA T A Tεσ ασ=

(12-47)( ) ( )T Tε α=


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• The restrictive conditions inherent in the derivation of Eq. 12-47 should be remembered:– the surface irradiation correspond to emission from a

blackbody,– Surface temperature is equal to the temperature of the source

of irradiation,– Steady state.

• The derivation above can also be repeated for radiation at a specified wavelength to obtain the spectral form of Kirchhoff’s law:

• This relation is valid when the irradiation or the emitted radiation is independent of direction.

• The form of Kirchhoff’s law that involves no restrictions is the spectral directional form

(12-48)( ) ( )T Tλ λε α=

( ) ( ), ,T Tλ θ λ θε α=

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Atmospheric and Solar Radiation• The energy coming off the sun, called solar energy,

reaches us in the form of electromagnetic waves after experiencing considerable interactions with the atmosphere.

• The sun:– is a nearly spherical body.– diameter of D≈1.39X109 m, – mass of m≈2X1030 kg, – mean distance of L=1.5X1011 m from the earth,– emits radiation energy continuously at a rate of

Esun≈3.8X1026W,– about 1.7X1017 W of this energy strikes the earth,– the temperature of the outer region of the sun is about 5800

K.


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• The solar energy reaching the earth’s atmosphere is called the total solar irradianceGs, whose value is

• The total solar irradiance (the solar constant) represents the rate at which solar energy is incident on a surface normal to the sun’s rays at the outer edge of the atmosphere when the earth is at its mean distance from the sun.

• The value of the total solar irradiance can be used to estimate the effective surface temperature of the sun from the requirement that

(12-49)21373 W/msG =

(12-50)( ) ( )2 2 44 4s sunL G r Tπ π σ=

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• The solar radiation undergoes considerable attenuationas it passes through the atmosphere as a result of absorption and scattering.

• The several dips on the spectral distribution of radiation on the earth’s surface are due to absorption by various gases:– oxygen(O2) at about λ=0.76 µm,– ozone(O3)

• below 0.3 µm almost completely, • in the range 0.3–0.4 µm considerably,• some in the visible range,

– water vapor(H2O) and carbon dioxide(CO2) in the infrared region,

– dust particles and other pollutants in the atmosphere at various wavelengths.


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• The solar energy reaching the earth’s surface is weakened considerably by the atmosphere and to about 950 W/m2 on a clear day and much less on cloudy or smoggy days.

• Practically all of the solar radiation reaching the earth’s surface falls in the wavelength band from 0.3 to 2.5 µm.

• Another mechanism that attenuates solar radiation as it passes through the atmosphere is scatteringor reflectionby air molecules and other particles such as dust, smog, and water droplets suspended in the atmosphere.

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• The solar energy incident on a surface on earth is considered to consist of directand diffuseparts.

• Direct solar radiation GD: the part of solar radiation that reaches the earth’s surface without being scattered or absorbed by the atmosphere.

• Diffuse solar radiation Gd:

the scattered radiation is

assumed to reach the earth’s

surface uniformly from all

directions.

• Then the total solar energy incident on the unit area of a horizontal surface on the ground is:

(12-49)( )2cos W/msolar D dG G Gθ= +

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Fundamentals of Thermal Radiationmazlan/?download=Heat Transfer... · • The dual nature of radiation: – In some cases, the physical manifestations of radiation may be explained