Quick
All surfaces of finite temperature emit energy in the form of electromagnetic waves. Hence, in the absence of an intervening medium, there is net heat transfer by radiation between two surfaces at different temperatures.
Equation
| q"rad = | | = εEb(Ts) – αG = εσ(Ts4 – T4sur) |
Nomenclature
| E | emissive power |
| Ts | absolute temperature of the surface |
| σ | Stefan-Boltzmann constant |
| ε | emissivity |
| G | irradiation |
| α | absorptivity |
Visualization
 |
T1 and T2 are temperatures at the surface
q"1 and q"2 are the heat transfers from the solid surfaces. |
Details
Thermal radiation is energy emitted by matter that is at a nonzero temperature. Emission may occur from gases, liquids, and solids. Regardless of the form of matter, the emission may be attributed to changes in the electron configurations of the constituent atoms or molecules. The energy of the radiation field is transported by electromagnetic waves (or alternatively, photons). While the transfer of energy by conduction or convection requires the presence of a material medium, radiation does not. In fact, radiation transfer occurs most efficiently in a vacuum.
Consider radiation transfer processes for the surface in the following figure. Radiation that is emitted by the surface originates from the thermal energy of matter bounded by the surface, and the rate at which energy is released per unit area (W/m2) is termed the surface emissive power E. There is an upper limit to the emissive power, which is prescribed by the Stefan-Boltzmann law:
where Ts is the absolute temperature (K) of the surface and σ is the Stefan-Boltzmann constant (σ = 5.67 x 10-8 W/m2K4). Such a surface is called an ideal radiator or blackbody.
The heat flux emitted by a real surface is less than that of a blackbody at the same temperature and is given by:
where ε is a radiative property of the surface termed the emissivity. With values in the range 0 ≤ ε ≤ 1, this property provides a measure of how efficiently a surface emits energy relative to a blackbody. It depends strongly on the surface material and finish.
Radiation may also be incident on a surface from its surroundings. The radiation may originate from a special source, such as the sun, or from other surfaces to which the surface of interest is exposed. Irrespective of the source(s), we designate the rate at which all such radiation is incident on a unit area of the surface as the irradiation G.
A portion, or all, of the irradiation may be absorbed by the surface, thereby increasing the thermal energy of the material. The rate at which radiant energy is absorbed per unit surface area may be evaluated from knowledge of a surface radiative property termed the absorptivity α.
For this equation, 0 ≤ α ≤ 1. If α < 1 and the surface is opaque, portions of the irradiation are reflected. If the surface is semitransparent, portions of the irradiation may also be transmitted. However, while absorbed and emitted radiation increase and reduce, respectively, the thermal energy of matter, reflected and transmitted radiation have no effect on this energy. Note that the value of α depends on the nature of the irradiation, as well as on the surface itself. For example, the absorptivity of a surface to solar radiation may differ from its absorptivity to radiation emitted by the walls of a furnace.
In many engineering problems (a notable exception being problems involving solar radiation or radiation from other very high temperature sources), liquids can be considered opaque, and gases can be considered transparent, to radiation heat transfer. Solids can be opaque (as is the case for metals) or semitransparent (as is the case for thin sheets of some polymers and some semiconducting materials).
A special case that occurs frequently involves radiation exchange between a small surface at Ts and a much larger, isothermal surface that completely surrounds the smaller one. The surroundings could, for example, be the walls of a room or a furnace whose temperature Tsur differs from that of an enclosed surface (Tsur ≠ Ts). For such a condition, the irradiation may be approximated by emission from a blackbody at Tsur, in which case G = σTsur4. If the surface is assumed to be one for which α = ε (a gray surface), the net rate of radiation heat transfer from the surface, expressed per unit area of the surface, is:
| (Eq4) | | q"rad = | | = εEb(Ts) – αG = εσ(Ts4 – T4sur) |
|
This expression provides the difference between thermal energy that is released due to radiation emission and that which is gained due to radiation absorption.
There are many applications for which it is convenient to express the net radiation heat exchange in the form:
| (Eq5) | qrad = hrA(Ts – Tsur) |
where, from Eq1, the radiation heat transfer coefficient hr is:
| (Eq6) | hr = εσ(Ts + Tsur)(Ts2 + T2sur) |
Here the radiation mode has been modeled in a manner similar to convection. In this sense the radiation rate equation has been linearized, making the heat rate proportional to a temperature difference rather than to the difference between two temperatures to the fourth power. Note, however, that hr depends strongly on temperature, while the temperature dependence of the convection heat transfer coefficient h is generally weak.
The surfaces of the following figure may also simultaneously transfer heat by convection to an adjoining gas. For the conditions of the following figure, the total rate of heat transfer from the surface is then:
| (Eq7) | q = qconv + qrad = hA(Ts – T∞) + εAσ(Ts4 – T4sur) |
Radiation transmits energy as electromagnetic waves in space. The transfer can happen in empty space and does not require any matter, but the emission (generation) of the radiation and the absorption does require a substance to be present. Surface emission is usually written as a fraction, emissivity ε, of a perfect black body emission as:
qx = εσATs4
with the surface temperature, Ts, and the Stefan-Boltzmann constant, σ. Typical values of the emissivity range from 0.92 for nonmetallic surfaces to 0.6 to 0.9 for nonpolished metallic surfaces, to less than 0.1 for highly polished metal surfaces. Radiation is distributed over a range of wavelengths and it is emitted and absorbed differently for different surfaces. Note that in thermodynamics qx may be written as a capital Q with a dot over it.