MEL 804

Radiation and Conduction (3-0-0)

Dr. Prabal Talukdar

Assistant Professor

Department of Mechanical Engineering

IIT Delhi

Radiation Heat Transfer

Contents

• Basic definitions

• Laws with radiation

Thermal Radiation

• Radiation heat transfer can take place in a vacuum. It does not need a medium unlike conduction/convection

• Thermal radiation is the stream of electromagnetic radiation emitted by a material entity on account of its finite absolute temperature

• Infrared radiation from a common household radiator or electric heater is an example of thermal radiation, as is the light emitted by a glowing incandescent light bulb.

• Thermal radiation is generated when heat from the movement of electrons within atoms is converted to electromagnetic radiation

• Dominant in high temperature applications

Spectrum of Electro-magnetic Radiation

Thermal radiation falls in the range of 10-1-102 µm of the

Electro-magnetic spectrum.

Emission Process

Emission by a surface

Gray Diffuse

Solid angle

Solid angle

• dω= dAn/r2 = (r2 sinθ dθ dΦ)/r2 =sinθ dθ dΦ

Solid Angle for a Hemisphere

sr 2dsin2ddsindw2/

0

2/

0h

2

0

Spectral Intensity

• Iλ,e(λ,θ,)=dq/(dA1cos θ.dω.dλ) • Iλ,e is the rate at which radiant energy is emitted at the wave length λ

in the (θ, ) direction, per unit area of emitting surface normal to this direction, per unit solid angle about this direction and per unit wavelength interval dλ about λ.

Heat Flux

• dqλ=dq/dλ—rate at which radiation of wavelength λ leaves dA1 and passes through dAn (unit: W/µm)

• dqλ= Iλ,e(λ,θ, ) dA1cos θ dω

• Spectral radiation flux associated with dA1is

• Spectral heat flux associated with emission into hypothetical hemisphere above dA1 is

• Total heat flux associated with emissions in all directions and at all wavelengths is then

ddsincos),,(Idq e,"

2/

0

e,

2

0

" ddsincos),,(I)(q

0

"" d)(qq

Emissive Power

• Emissive power is the amount of radiation emitted per unit surface area

• Spectral , hemispherical emissive power

• Eλ(λ)(W/m2.µm)=

– Eλ →based on actual surface area

– Iλ,e →based on projected surface area

• Total hemispherical Emissive power:

2/

0

e,

2

0

ddsincos),,(I

d)(EE0

Relation between Emissive Power and Intensity

• Eλ=

• For a diffuse surface, Iλ(λ,θ,)= Iλ(λ)

Eλ =

Eλ= π Iλ,e(λ) Spectral basis

E=πIe Total basis

2/

0

e,

2

0

ddsincos),,(I

2/

0

2

0

e, ddsincos)(I

Irradiation

• Intensity of incident radiation: It can be defined as the rate which radiant energy of wavelength λ is incident from the (θ,) direction, per unit area of the intercepting surface normal to the direction, per unit solid angle about this direction, and per unit wavelength interval dλ about λ

• Radiation incident from all directions gives the irradiation

• Spectral irradiation Gλ(λ) =

• Total irradiation

2/

0

i,

2

0

ddsincos),,(I

2

0

m/W d)(GG

Radiosity

• Radiosity accounts for all the radiant energy leaving a surface– Emitted and reflected part

re

2/

0

re,

2

00

I

dddsincos),,(IJ

For a surface which is diffuse emitter and diffuse reflector

Blackbody Radiation

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

• For a prescribed temperature and wavelength, no surface can emit more energy than a black body

• Although the radiation emitted by a blackbody is a function of wavelength and temperature, it is independent of direction. That is blackbody is a diffuse emitter

Planck Distribution

• The spectral distribution of blackbody emission is given by Planck as

where, Planck constant h = 6.6256x10-34J.s and

Boltzmann constants k = 1.3805x10-23 J/K

speed of light in vacuum c0=2.998x108 m/s

]1)kT/hc[exp(

hc2)T,(I

05

20

b,

]1)T/C[exp(

C)T,(I)T,(E

25

1b,b,

Planck Distribution

The emitted radiation varies continuously with wavelength•At any wavelength the magnitude of the emitted radiation increases with increasing temperature

The spectral radiation in which the radiation is concentrated depends on temperature, with comparatively more radiation appearing at shorter wavelengths as the temperature increases

A significant fraction of the radiation emitted by the sun, which may be approximated as a blackbody at 5800K, is in the visible region of the spectrum. In contrast, for T<800K, emission is predominantly in the infrared region of the spectrum and is not visible to the eye

Wien’s Displacement Law

• Differentiating the above equation with respect to λ and setting the result equal to zero, we get

λmaxT = 2897.8 µm.K

• According to this law, the maximum spectral emissive power is displaced to shorter wavelengths with increasing temperature

• The emission is in the middle of the visible spectrum (λ = 0.5 µm) for solar radiation, since the sun emits approximately as a blackbody as 5800K

]1)T/C[exp(

C)T,(I)T,(E

25

1b,b,

Stefan-Boltzmann Law

• Total Emissive power

= 5.67x10-8 W/m2K4

Since this emission is diffuse, the total intensity associated with blackbody emission Ib=Eb/π

]1)T/C[exp(

C)T,(E

25

1b,

4b

0 25

1b

TE

d]1)T/C[exp(

CE

Surface Emission

• Emissivity is the ratio of radiation emitted by the surface to the radiation emitted by a blackbody at the same temperature

• Spectral directional emissivity λ,θ(λ,θ,,T) of a surface at the temperature T is the ratio of the intensity of the radiation emitted at the wavelength λ and in the direction of θ and to the intensity of the radiation emitted by a blackbody at the same values of T and λ.

Hence)T,(I

)T,,,(I)T,,,(

b,

e,,

Blackbody and Real Emission

Emissivity

• Total directional emissivity

• Spectral hemispherical

emissivity

)T(I

)T,,(I)T,,(

b

e

dsincos)T,,(2

ddsincos)T,(I

ddsincos)T,,,(I

)T,(E

)T,(E)T,(

2/

0

,

2

0

2/

0

b,

2

0

2/

0

e,

b,

Total Hemispherical Emissivity

• Total hemispherical emissivity

• Directional distributions of

total diretctional

Emisivity

)T(E

)T(E)T(

b

• The emissivity of metallic surfaces is generally small, as low as 0.02 for higly polished gold and silver

•The presence of oxide layers may significantly increase the emissivity of metallic surfaces.

•The emissivity of non-conductors is comparatively large, generally exceeding 0.6

The emissivity of conductors increases with increasing temperature; However For non-conductors it may be both way.

Absorption, Reflection and Transmission

• Gλ = Gλ,ref+ G λ,abs+ Gλ,tr

• When a surface is opaque, Gλ,tr = 0

• There is no net effect of the reflection process on the medium, while absorption has the effect of increasing the internal energy of the medium

• Surface absorption and reflection are responsible for our perception of color

Absorptivity

• The absorptivity is a property that determines the fraction of the irradiation absorbed by a surface

• Surface exhibits selective absorption with respect to the wavelength and direction of the incident radiation

• Does not depend much on surface temperature

G

Gabs

Reflectivity

• It is a property that determines the fraction of the incident radiation reflected by a surface

• This property is inherently bi-directional• In addition to depending on the direction of the

incident radiation, it also depends on the direction of the reflected radiation

• Surface may be idealized as diffuse or specular

G

Gabs

Transmissivity

• Total hemispherical transmissivity

• For a semitransparent medium, ++ = 1G

G tr

Kirchoff’s law

• Consider a large isothermal surface of surface temperature Ts within which several small bodies are cofined

A1

A2

A3

Ts

G

E1

E3

E2

Kirchoff’s Law (cont’d)

• Regardless of its radiative properties, such a surface forms a blackbody cavity

• Accordingly, regardless of its orientation, the irradiation experienced by any body in the cavity is diffuse and equal to emission from a blackbody at Ts i.e. G = Eb(Ts)

• Under steady-state conditions,

T1 = T2 = T3 =---- = Ts

and net energy transfer to each surface is zero

Kirchoff’s Law (cont’d)

• Applying an energy balance to a control surface about body 1,

1GA1 – E1(Ts)A1 = 0

E1(Ts)/ 1= Eb(Ts)

Applying to all bodies,

E1(Ts)/ 1 = E2(Ts)/ 2 = ------- = Eb(Ts)

12

2

1

1