Radiation Heat Transfer
Heat transfer due to emission of electromagnetic waves is known as thermal radiation
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Heat transfer through radiation takes place in the form of electromagnetic waves mainly in the infrared region. The radiation emitted by a body is the consequence of thermal agitation of its composing molecules. The radiation of heat can be described by the 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
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 ft2 oR4) )
= 0.119 10-10 ( Btu/(h in2 oR4) )
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 (1)
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 < 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 coefficients for some common materials
The Net Radiation Loss Rate
If an hot object is radiating energy to its cooler surroundings the net radiation heat loss rate can be expressed like
q = ε σ (Th4 - Tc4) Ac (3)
where
Th = hot body absolute temperature (K)
Tc = cold surroundings absolute temperature (K)
Ac = area of the object (m2)
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 (W/m2 K4)
= 5.6703 10-8 (5800 (K))4
= 6.42 107 W/m2
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