Heat Transfer of Radiation

Heat transfer through radiation takes place in form of electromagnetic waves mainly in the infrared region. Radiation emitted by a body is a consequence of thermal agitation of its composing molecules. Radiation heat transfer can be described by a reference to the so-called 'black body'.

The Black Body

A black body is defined as a body that absorbs all radiation that falls on its surface. Actual black bodies don't exist in nature - though its characteristics are approximated by a hole in a box filled with highly absorptive material. The emission spectrum of such a black body was first fully described by Max Planck.
A black body is a hypothetic body that completely absorbs all wavelengths of thermal radiation incident on it. Such bodies do not reflect light, and therefore appear black if their temperatures are low enough so as not to be self-luminous. All blackbodies heated to a given temperature emit thermal radiation.
The radiation energy per unit time from a blackbody is proportional to the fourth power of the absolute temperature and can be expressed with Stefan-Boltzmann Law as

q = σ T⁴ A         (1)
where
q = heat transfer per unit time (W)
σ = 5.6703 10^-8 (W/m²K⁴) - The Stefan-Boltzmann Constant
T = absolute temperature Kelvin (K)
A = area of the emitting body (m²)

The Stefan-Boltzmann Constant in Imperial Units

σ = 5.6703 10^-8 (W/m²K⁴)
    = 0.1714 10^-8 ( Btu/(h ft^{2 o}R⁴) )

    =  0.119 10^-10 ( Btu/(h in^{2 o}R⁴) )

 

Example - Radiation from the surface of the Sun
If the surface temperature of the sun is 5800 K and if we assume that the sun can be regarded as a black body the radiation energy per unit time can be expressed by modifying (1) like

 q / A = σ T⁴
    = (5.6703 10^-8 W/m²K⁴) (5800 K)⁴
    = 6.42 10⁷ W/m² 

Gray Bodies and Emissivity Coefficients

 

For objects other than ideal blackbodies ('gray bodies') the Stefan-Boltzmann Law can be expressed as

q = ε σ T⁴ A         (2)
where
ε = emissivity of the object (one for a black body)

For the gray body the incident radiation (also called irradiation) is partly reflected, absorbed or transmitted.

 

The emissivity coefficient lies in the range 0 < tyle: italic;">ε < 1 depending on the type of material and the temperature of the surface. The emissivity of some common materials

• oxidized Iron at 390 ^oF (199 ^oC) > ε = 0.64
• polished Copper at 100 ^oF (38 ^oC) > ε = 0.03
• emissivity coefficient for some common materials
  

Net Radiation Loss Rate

If an hot object is radiating energy to its cooler surroundings the net radiation heat loss rate can be expressed as

q = ε σ (T_h⁴ - T_c⁴) A_c         (3)
where
T_h = hot body absolute temperature (K)
T_c = cold surroundings absolute temperature (K)
A_c = area of the object  (m²)

• Radiation Constants for some common Building Materials

Heat loss from a heated surface to unheated surroundings with mean radiant temperatures are indicated in the chart below.