Notes on Thermal Radiation


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What is Radiation?

  • Radiation is the energy emitted by matter in the form of electromagnetic waves.
  • Here we will look into thermal radiation (10-7 m to 10-4 m) since we are dealing with heat transfer.
  • In radiation, the internal energy of an object decreases.

Rate of emission of radiation by a body depends on-

  • Surface temperature
  • Surface Nature
  • Wavelength or frequency of radiation

Read More- Convection Heat Transfer Process

Important Definitions

Total Emissive Power (E)

  • The total amount of radiation (all wavelength range) emitted by a body per unit area and time.
  • A/C to Stefan-Boltzman, for a black body emissive power, is proportional to absolute temperature to the fourth power.

Eb = σAT4 W/m2

σ = Stefan-Boltzman Constant (5.67*10-8 W/m2K4)

Monochromatic Emissive Power (Eλ)

  • Rate of energy radiated per unit area of the surface per unit wavelength.
  • At any given temperature the amount of radiation emitted per unit wavelength varies at different wavelengths. So, Monochromatic Emissive Power (Eλ) of the surface is used.

Emissivity (ε)

  • The ability of the body surface to radiate heat.
  • It is also defined as the ratio of emissive power of a body to the emissive power of a black body of equal temperature.
  • Its value varies for different substances ranging from 0 (white body) to 1 (black body).
  • Emissivity may vary with temperature and wavelength.

Irradiation (G)

  • Total incident radiation on a surface from all directions per unit time per unit area of the surface.

Radiosity (J)

  • It refers to all of the radiant energy leaving a surface per unit area of the surface.

J = ε + ρG

ρ = reflectivity

Reflectivity (ρ)

  • Fraction of incident radiation reflected.
  • For white body :- ρ = 1, α = 0, τ = 0

Absorptivity (α)

  • Fraction of incident radiation absorbed.
  • For Black Body α = 1, ρ = 1, τ = 0

Transmittivity (τ)

  • τ = 0 for black, white and opaque body (α + ρ = 1).
  • The fraction of incident radiation transmitted.

Read Also- Modes of Heat Transfer, Convection

Different Laws in Thermal Radiation

These are the important laws we should know in order to understand and solve the problems of the Thermal Radiation Chapter in Heat and Mass Transfer.

  • Stefan-Boltzmann Law

According to this law, the total emissive power of a black body is directly proportional to the fourth power of its absolute temperature.

Eb = σT4

σ is Stefan-Boltzmann Constant (5.67 × 10-8 W/m²K4)

  • Kirchhoff’s Law

This law states that at any temperature the ratio of total emissive power (E) to the total absorptivity (α) is constant for all substances which are in thermal equilibrium with the surroundings.

E/ α = constant


The emissivity (ε) of a body is equal to its absorptivity (α) when the body remains in thermal equilibrium with its surroundings.

ε = α

  • Planck’s Law

The total emissive power of a Gray body varies with the wavelength at a given temperature and varies with the temperature too.

So, it’s a function of wavelength and temperature, i.e. E = f(λ, T)

Now According to Max Planck, the spectral distribution of the radiation intensity of a black body is given by –

(Eλ)b = p/q

Where p = 2πc2-5

q = exp(ch / λkT) – 1

(Eλ)b = monochromatic emissive power

  • Wien’s Displacement Law

It gives a relationship between the temperature of a black body and the wavelength at which the maximum value of monochromatic emissive power occurs.

The product of wavelength (λ) and temperature (T) is constant.

λmaxT = constant = 2898 or 2900 µmK (Unit)

λmax unit is micrometer

  • Combining Planck’s Law and Wien’s Displacement Law results in the condition for maximum monochromatic emissive power for a black body.

(Eλb)max = 1.285 × 10-5 T5W/m2 per meter length

  • Lambert’s Cosine Law

This law states that the total emissive power Eθ from a radiating plane surface in any direction is directly proportional to the cosine of the angle of emission.

Eθ = Encosθ

Where En = total emissive power in the normal direction (of the radiating surface).

  • The law is true for diffuse radiation surfaces.
  • The diffuse radiation surface means the radiation intensity is constant.

Note- Symbols have usual meanings.

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