Thermal radiation basics - Emissivity, Black body, Gray body etc

Thermal Radiation is the third mode of heat transfer. 

All solids and liquids emit thermal radiation at all temperatures above absolute zero.

Thermal radiation is emitted in the form of electromagnetic waves ( EMW ) which is continuous spectrum of all the wavelengths.

Thermal radiation ( EMW ) doesn't require material medium for its propagation that means it can travel in vacuum as well.

Most of the thermal radiation lie in the range of 0.1 to 10 microns which is clear from the figure given below.

All the surfaces has capacity to absorb all or a part of the radiation emitted by surrounding surfaces and falling on it.

Black surface - It is an ideal surface which absorbs all the radiations falling on it regardless of its wavelength or direction. It is obvious that it is a hypothetical surface.

Note that for a given temperature and wavelength a black surface emits the maximum amount of energy.

Emissive power (E) - It is the radiant flux emitted from the surface of the body ( W/m² ).

                           

Emissivity - It is the ratio of emissive power of a surface to the emissive power of a black surface. Since emissive power of a black surface is maximum so emissivity always lies between 0 and 1.

It is denoted by ε.

                       So, ε = E/E_b   

                               _And  0 ≤ ε ≤ 1

Emissivity of a body or surface depends upon following

1. The nature of surface

2. The temperature of surface and

3. The wavelength or frequency of radiation falling on it.

Emissivity of a polished metal surface is of order less than 0.1 , oxidised metal surface of order 0.6, non-metal it is of order 0.8-0.9 and for liquids it is order 0.9-0.95 .

Monochromatic emissive power ( E_λ ) - It is the radiant flux emitted per unit wavelength ( W/m²-μm ).

             

E_λ = dE/dλ         or        dE = E_λdλ

Note that E_λ is the quantity which when integrated over all wavelengths yields E.

Monochromatic emissivity ( ε_λ ) = E_λ/E_bλ

Note that the word monochromatic and spectral are same and they are used according to ease.

Gray Surface - A Surface the same value of ε_λ for all the wavelengths.

Gray surface is an idealization used in engineering to simplify the task.

Radiation falling on a surface:

Whenever radiation fall on any surface it may be either reflected by or transmitted through or absorbed by the surface or any combination of these takes place. This is clear from following figure.

Irradiation ( H ) - Radiant flux incident on the surface of the body.

Reflectivity ( ρ )- Fraction of irradiation reflected by the body.

Transmissivity ( τ ) - Fraction of irradiation transmitted through the body.

Absorptivity ( α )- Fraction of irradiation absorbed by the body ( or surface ).

If H_a , H_r  and H_t  be the amount of radiation absorbed, reflected and transmitted respectively the we can write,

              H = H_a + H_r +  H_t

       Also,

                 α  =  H_a/ H

                  τ  =  H_t / H

   and          ρ  =  H_r/ H

Clearly,      α  + τ + ρ  = 1 .

For a black surface       α = 1  ,   τ = 0  ,   ρ = 0

For opaque surface        τ = 0      α + ρ = 1    

For a white body            ρ = 1    α = 0  ,   τ = 0.