1. Radiation Heat Transfer
MEL 804
Radiation and Conduction (3-0-0)
Dr. Prabal Talukdar
Assistant Professor
Department of Mechanical Engineering
IIT Delhi

2. Contents
Basic definitions
Laws with radiation

3. 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

4. Spectrum of Electro-magnetic Radiation
Thermal radiation falls in the range of µm of the
Electro-magnetic spectrum.

5. Emission Process

6. Emission by a surface
Gray
Diffuse

7. Solid angle

8. Solid angle
dω= dAn/r2 = (r2 sinθ dθ dΦ)/r2 =sinθ dθ dΦ

9. Solid Angle for a Hemisphere

10. 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.

11. 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

12. 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:

13. Relation between Emissive Power and Intensity
For a diffuse surface, Iλ(λ,θ,)= Iλ(λ)
Eλ =
Eλ= π Iλ,e(λ) Spectral basis
E=πIe Total basis

14. 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

15. Radiosity
Radiosity accounts for all the radiant energy leaving a surface
Emitted and reflected part
For a surface which is diffuse emitter
and diffuse reflector

16. 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

17. Planck Distribution
The spectral distribution of blackbody emission is given by Planck as
where, Planck constant h = x10-34J.s and
Boltzmann constants k = x10-23 J/K
speed of light in vacuum c0=2.998x108 m/s

18. Planck Distribution The emitted radiation varies continuously
with wavelength
At any wavelength the magnitude of the
emitted radiation increases
with increasing temperature
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
The spectral radiation in which the radiation
is concentrated depends on temperature,
with comparatively more radiation appearing
at shorter wavelengths as the temperature
increases

19. Wien’s Displacement Law
Differentiating the above equation with respect to λ and setting the result equal to zero, we get
λmaxT = 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

20. 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

22. 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

23. Blackbody and Real Emission

24. Emissivity Total directional emissivity Spectral hemispherical

25. Total Hemispherical Emissivity
Directional distributions of
total diretctional
Emisivity

27. The presence of oxide layers may significantly increase the emissivity of metallic
surfaces.
The emissivity of metallic surfaces is generally small, as low as 0.02 for higly polished gold and silver
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.

28. 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

29. 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

30. 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

31. Transmissivity Total hemispherical transmissivity
For a semitransparent medium, ++ = 1

32. Kirchoff’s law
Consider a large isothermal surface of surface temperature Ts within which several small bodies are cofined Ts G A1 A2 E1 A3 E2 E3

33. 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

34. 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)