Heat transfer via radiation

In the context of heat transfer, radiation is the transfer of energy through electromagnetic waves (or photons). Radiation occurs when the electronic configuration of atoms or molecules change. Unlike convection or conduction, radiation doesn't need a medium to transfer heat, and can transfer heat through vacuums, which is how the thermal energy from the Sun reaches the Earth. All objects above absolute zero emit thermal radiation.

The maximum rate of radiation that can be emitted from the surface of an object is given by the Stefan-Boltzmann equation:

Q•=σATs4\overset{•}{Q}=σA{T}_{s}^{4} (W)

Where Q•\overset{•}{Q}    is the rate of heat transfer, A is the surface area, Ts{T}_{s} is the absolute temperature of the surface, and σσ is the Stefan-Boltzmann constant (5.67×10−8Wm−2K−45.67×{10}^{-8} W {m}^{-2} {K}^{-4}). This equation gives an idealized maximum rate of radiation. Ideal surfaces that emit radiation at this maximum rate are called blackbodies, and the radiation that blackbodies emit is called blackbody radiation. The actual radiation emitted by surfaces is less than their blackbody radiation at the same temperature, and is given by:

Q•=εσATs4\overset{•}{Q}=εσA{T}_{s}^{4}       (W)

Where εε is the emissivity of the surface. Emissivity measures how well a surface approximates a blackbody, and ranges in value between 0 and 1, where a value of 1 is a blackbody.

Common emissivity values table

Table of some emissivities of some materials (Çengel 2010)

Emissivity isn't the only important radiation related property of a surface. Another important property is absorption, which gives the fraction of radiation energy that intercepts a surface that is absorbed by the surface. Absorptivity (αα) has a value between 0 and 1, where a value of 1 is a perfect absorber and a blackbody. So, a black body is a perfect emitter with a emissivity of 1, and a perfect absorber with an absorptivity of 1.

Emissivity and absorptivity are related by Kirchhoff's Law, which states that for a body in thermodynamic equilibrium, the emissivity is equal to the absorptivity.

The other ways that electromagnetic radiation can interact with a material is through reflection and transmission. Reflection occurs when radiation bounces off of a surface and is redirected, and transmission occurs when radiation passes through a target. Radiation from a source can be reflected, absorbed, or transmitted when it intercepts a surface, and the energy related to these is related with:

Eincident=Ereflected+Eabsorbed+Etransmitted{E}_{incident}={E}_{reflected}+{E}_{absorbed}+{E}_{transmitted}

It can be difficult to determine what the rate of heat transfer is between two objects because of all of the variables that are involved, such as the properties of the surfaces of the objects, the object's orientation relative to each other, and the properties of the medium that radiation passes through. However, the math to solve the rate of heat transfer between two objects can be simplified if: the emissivity and surface area are relatively low at a temperature Ts{T}_{s} and is completely enclosed by a much larger surface at Tsurroundings{T}_{surroundings} and the medium through which the radiation passes through has a negligible effect on the radiation, which will lead to the equation:

Q•=εσA(Ts4−Tsurr4)\overset{•}{Q}=εσA({T}_{s}^{4}-{T}_{surr}^{4})    (W)



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