Thermal radiation

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"Heat radiation" redirects here. It is not to be confused with Heat-Ray (disambiguation).
The peak wavelength and total radiated amount vary with temperature according to Wien's displacement law. Although this shows relatively high temperatures, the same relationships hold true for any temperature down to absolute zero. Visible light is between 380 and 750 nm.





Thermal radiation is one of the fundamental mechanisms of heat transfer.




Absorptivity, reflectivity, and emissivity of all bodies are dependent on the wavelength of the radiation. The temperature determines the wavelength distribution of the electromagnetic radiation. For example, fresh snow, which is highly reflective to visible light (reflectivity about 0.90), appears white due to reflecting sunlight with a peak wavelength of about 0.5 micrometers. Its emissivity at a temperature of about −5 °C (23 °F), peak wavelength of about 12 micrometers, is 0.99.


The incandescent light bulb has a spectrum overlapping the black body spectra of the sun and the earth. Some of the photons emitted by a tungsten light bulb filament at 3000 K are in the visible spectrum. Most of the energy is associated with photons of longer wavelengths; these do not help a person see, but still transfer heat to the environment, as can be deduced empirically by observing an incandescent light bulb. Whenever EM radiation is emitted and then absorbed, heat is transferred. This principle is used in microwave ovens, laser cutting, and RF hair removal.


Surface effects[edit]




Nanostructures with spectrally selective thermal emittance properties offer numerous technological applications for energy generation and efficiency, e.g., for cooling photovoltaic cells and buildings. These applications require high emittance in the frequency range corresponding to the atmospheric transparency window in 8 to 13 micron wavelength range. A selective emitter radiating strongly in this range is thus exposed to the clear sky, enabling the use of the outer space as a very low temperature heat sink.

Personalized cooling technology is another example of an application where optical spectral selectivity can be beneficial. Conventional personal cooling is typically achieved through heat conduction and convection. However, the human body is a very efficient emitter of IR radiation, which provides additional cooling mechanism. Most conventional fabrics are opaque to IR radiation and block thermal emission from the body to the environment. Fabrics for personalized cooling applications have been proposed that enable IR transmission to directly pass through clothing, while being opaque at visible wavelengths. Fabrics that are transparent in the infrared can radiate body heat at rates that will significantly reduce the burden on power-hungry air-conditioning systems.




Near-field and far-field[edit]

The general properties of thermal radiation as described by the Planck’s law apply if the linear dimension of all parts considered, as well as radii of curvature of all surfaces are large compared with the wavelength of the ray considered’ (typically from 8-25 micrometres for the emitter at 300 K). Indeed, thermal radiation as discussed above takes only radiating waves (far-field, or electromagnetic radiation) into account. A more sophisticated framework involving electromagnetic theory must be used for smaller distances from the thermal source or surface (near-field thermal radiation). For example, although far-field thermal radiation at distances from surfaces of more than one wavelength is generally not coherent to any extent, near-field thermal radiation (i.e., radiation at distances of a fraction of various radiation wavelengths) may exhibit a degree of both temporal and spatial coherence.[4]

Planck’s law of thermal radiation has been challenged in recent decades by predictions and successful demonstrations of the radiative heat transfer between objects separated by nanoscale gaps that deviate significantly from the law predictions. This deviation is especially strong (up to several orders in magnitude) when the emitter and absorber support surface polariton modes that can couple through the gap separating cold and hot objects. However, to take advantage of the surface-polariton-mediated near-field radiative heat transfer, the two objects need to be separated by ultra-narrow gaps on the order of microns or even nanometers. This limitation significantly complicates practical device designs.

Another way to modify the object thermal emission spectrum is by reducing the dimensionality of the emitter itself. This approach builds upon the concept of confining electrons in quantum wells, wires and dots, and tailors thermal emission by engineering confined photon states in two- and three-dimensional potential traps, including wells, wires, and dots. Such spatial confinement concentrates photon states and enhances thermal emission at select frequencies. To achieve the required level of photon confinement, the dimensions of the radiating objects should be on the order of or below the thermal wavelength predicted by Planck’s law. Most importantly, the emission spectrum of thermal wells, wires and dots deviates from Planck’s law predictions not only in the near field, but also in the far field, which significantly expands the range of their applications.


°C (°F) Subjective color[5]
480 °C (896 °F) faint red glow
580 °C (1,076 °F) dark red
930 °C (1,710 °F) bright orange
1,100 °C (2,010 °F) pale yellowish orange
1,300 °C (2,370 °F) yellowish white

Selected radiant heat fluxes[edit]


kW/m2 Effect
170 Maximum flux measured in a post-flashover compartment
80 Thermal Protective Performance test for personal protective equipment
52 Fiberboard ignites at 5 seconds
29 Wood ignites, given time
20 Typical beginning of flashover at floor level of a residential room
12.5 Wood produces ignitable volatiles by pyrolysis
6.4 Human skin: second-degree burn blisters after 18 seconds
4.5 Human skin: second-degree burn blisters after 30 seconds
1.4 Sunlight, sunburns potentially within 30 minutes

Interchange of energy[edit]



Here, represents the spectral absorption component, spectral reflection component and the spectral transmission component. These elements are a function of the wavelength () of the electromagnetic radiation. The spectral absorption is equal to the emissivity ; this relation is known as Kirchhoff's law of thermal radiation. An object is called a black body if, for all frequencies, the following formula applies:







Radiative power[edit]

Power emitted by a black body plotted against the temperature according to the Stefan–Boltzmann law.

Thermal radiation power of a black body per unit area of radiating surface per unit of solid angle and per unit frequency is given by Planck's law as:

or in terms of wavelength

where is a constant.

This formula mathematically follows from calculation of spectral distribution of energy in quantized electromagnetic field which is in complete thermal equilibrium with the radiating object. The equation is derived as an infinite sum over all possible frequencies. The energy, , of each photon is multiplied by the number of states available at that frequency, and the probability that each of those states will be occupied.

Integrating the above equation over the power output given by the Stefan–Boltzmann law is obtained, as:

where the constant of proportionality is the Stefan–Boltzmann constant and is the radiating surface area.

The wavelength , for which the emission intensity is highest, is given by Wien's displacement law as:

For surfaces which are not black bodies, one has to consider the (generally frequency dependent) emissivity factor . This factor has to be multiplied with the radiation spectrum formula before integration. If it is taken as a constant, the resulting formula for the power output can be written in a way that contains as a factor:



Definitions of constants used in the above equations:

Planck's constant 6.626 069 3(11)×10−34 J·s = 4.135 667 43(35)×10−15 eV·s
Wien's displacement constant 2.897 768 5(51)×10−3 m·K
Boltzmann constant 1.380 650 5(24)×10−23 J·K−1 = 8.617 343 (15)×10−5 eV·K−1
Speed of light 299 792 458 m·s−1


Definitions of variables, with example values:

Surface area Acuboid = 2ab + 2bc + 2ac;
Acylinder = 2π·r(h + r);
Asphere = 4π·r2

Radiative heat transfer[edit]

The net radiative heat transfer from one surface to another is the radiation leaving the first surface for the other minus that arriving from the second surface.

  • For black bodies, the rate of energy transfer from surface 1 to surface 2 is:

where is surface area, is energy flux (the rate of emission per unit surface area) and is the view factor from surface 1 to surface 2. Applying both the reciprocity rule for view factors, , and the Stefan–Boltzmann law, , yields:

where is the Stefan–Boltzmann constant and is temperature.[10] A negative value for indicates that net radiation heat transfer is from surface 2 to surface 1.

  • For two grey-body surfaces forming an enclosure, the heat transfer rate is:

where and are the emissivities of the surfaces.[10]

Formulas for radiative heat transfer can be derived for more particular or more elaborate physical arrangements, such as between parallel plates, concentric spheres and the internal surfaces of a cylinder.[10]

See also[edit]


  3. ^ a b S. Blundell, K. Blundell (2006). Concepts in Thermal Physics. Oxford University Press. p. 247. ISBN 978-0-19-856769-1. 
  4. ^ [1] Review of coherrent thermal radiation
  5. ^ The Physics of Coloured Fireworks
  8. ^ R. Bowling Barnes (24 May 1963). "Thermography of the Human Body Infrared-radiant energy provides new concepts and instrumentation for medical diagnosis". Science. 140 (3569): 870–877. Bibcode:1963Sci...140..870B. doi:10.1126/science.140.3569.870. PMID 13969373. 
  10. ^ a b c d Heat and Mass Transfer, Yunus A. Cengel and Afshin J. Ghajar, 4th Edition
  11. ^ Infrared#Different regions in the infrared Short-wavelength infrared is 1.4-3µm, mid-wavelength infrared is 3-8µm
  12. ^ The Efficient Windows Collaborative: Window Technologies

Further reading[edit]

External links[edit]