Thermal radiation

From Wikipedia, the free encyclopedia
  (Redirected from Radiant heat)
Jump to: navigation, search
This article is about any type of electromagnetic radiation from an object related to its temperature. For infrared light, see Infrared.
This diagram shows how the peak wavelength and total radiated amount vary with temperature according to Wien's displacement law. Although this plot 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 in visible light can be seen on this hot metalwork. Its emission in the infrared is invisible to the human eye and the camera the image was taken with, but an infrared camera could show it (See Thermography).

Thermal radiation is electromagnetic radiation generated by the thermal motion of charged particles in matter. All matter with a temperature greater than absolute zero emits thermal radiation. When the temperature of the body is greater than absolute zero, interatomic collisions cause the kinetic energy of the atoms or molecules to change. This results in charge-acceleration and/or dipole oscillation which produces electromagnetic radiation, and the wide spectrum of radiation reflects the wide spectrum of energies and accelerations that occur even at a single temperature.

Examples of thermal radiation include the visible light and infrared light emitted by an incandescent light bulb, the infrared radiation emitted by animals and detectable with an infrared camera, and the cosmic microwave background radiation. Thermal radiation is different from thermal convection and thermal conduction—a person near a raging bonfire feels radiant heating from the fire, even if the surrounding air is very cold.

Sunlight is part of thermal radiation generated by the hot plasma of the Sun. The Earth also emits thermal radiation, but at a much lower intensity and different spectral distribution (infrared rather than visible) because it is cooler. The Earth's absorption of solar radiation, followed by its outgoing thermal radiation are the two most important processes that determine the temperature and climate of the Earth.

If a radiation-emitting object meets the physical characteristics of a black body in thermodynamic equilibrium, the radiation is called blackbody radiation.[1] Planck's law describes the spectrum of blackbody radiation, which depends only on the object's temperature. Wien's displacement law determines the most likely frequency of the emitted radiation, and the Stefan–Boltzmann law gives the radiant intensity.[2]

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


Thermal radiation is the emission of electromagnetic waves from all matter that has a temperature greater than absolute zero.[3] It represents a conversion of thermal energy into electromagnetic energy. Thermal energy results in kinetic energy in the random movements of atoms and molecules in matter. All matter with a temperature by definition is composed of particles which have kinetic energy, and which interact with each other. These atoms and molecules are composed of charged particles, i.e., protons and electrons, and kinetic interactions among matter particles result in charge-acceleration and dipole-oscillation. This results in the electrodynamic generation of coupled electric and magnetic fields, resulting in the emission of photons, radiating energy away from the body through its surface boundary. Electromagnetic radiation, including light, does not require the presence of matter to propagate and travels in the vacuum of space infinitely far if unobstructed.

The characteristics of thermal radiation depend on various properties of the surface it is emanating from, including its temperature, its spectral absorptivity and spectral emissive power, as expressed by Kirchhoff's law.Cite error: A <ref> tag is missing the closing </ref> (see the help page).

Subjective color to the eye of a black body thermal radiator[edit]

°C (°F) Subjective color[4]
480 °C (896 °F) faint red glow
580 °C (1,076 °F) dark red
730 °C (1,350 °F) bright red, slightly orange
930 °C (1,710 °F) bright orange
1,100 °C (2,010 °F) pale yellowish orange
1,300 °C (2,370 °F) yellowish white
> 1,400 °C (2,550 °F) white (yellowish if seen from a distance through atmosphere)

Selected radiant heat fluxes[edit]

(1 W/cm2 = 10 kW/m2)

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
16 Human skin: Sudden pain and second-degree burn blisters after 5 seconds
12.5 Wood produces ignitable volatiles by pyrolysis
10.4 Human skin: Pain after 3 seconds, second-degree burn blisters after 9 seconds
6.4 Human skin: Second-degree burn blisters after 18 seconds
4.5 Human skin: Second-degree burn blisters after 30 seconds
2.5 Human skin: Burns after prolonged exposure, radiant flux exposure typically encountered during firefighting
1.4 Sunlight, sunburns potentially within 30 minutes


Interchange of energy[edit]

Radiant heat panel for testing precisely quantified energy exposures at National Research Council, near Ottawa, Ontario, Canada.

Thermal radiation is one of the principal mechanisms of heat transfer. It entails the emission of a spectrum of electromagnetic radiation due to an object's temperature. Other mechanisms are convection and conduction. The interplay of energy exchange by thermal radiation is characterized by the following equation:

\alpha+\rho+\tau=1. \,

Here, \alpha \, represents the spectral absorption component, \rho \, spectral reflection component and \tau \, the spectral transmission component. These elements are a function of the wavelength (\lambda\,) of the electromagnetic radiation. The spectral absorption is equal to the emissivity \epsilon \,; 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:

\alpha = \epsilon =1.\,

In a practical situation and room-temperature setting, humans lose considerable energy due to thermal radiation. However, the energy lost by emitting infrared light is partially regained by absorbing the heat flow due to conduction from surrounding objects, and the remainder resulting from generated heat through metabolism. Human skin has an emissivity of very close to 1.0 .[6] Using the formulas below shows a human, having roughly 2 square meter in surface area, and a temperature of about 307 K, continuously radiates approximately 1000 watts. However, if people are indoors, surrounded by surfaces at 296 K, they receive back about 900 watts from the wall, ceiling, and other surroundings, so the net loss is only about 100 watts. These heat transfer estimates are highly dependent on extrinsic variables, such as wearing clothes, i.e. decreasing total thermal circuit conductivity, therefore reducing total output heat flux. Only truly gray systems (relative equivalent emissivity/absorptivity and no directional transmissivity dependence in all control volume bodies considered) can achieve reasonable steady-state heat flux estimates through the Stefan-Boltzmann law. Encountering this "ideally calculable" situation is virtually impossible (although common engineering procedures surrender the dependency of these unknown variables and "assume" this to be the case). Optimistically, these "gray" approximations will get you close to real solutions, as most divergence from Stefan-Boltzmann solutions is very small (especially in most STP lab controlled environments).

If objects appear white (reflective in the visual spectrum), they are not necessarily equally reflective (and thus non-emissive) in the thermal infrared. Most household radiators are painted white but this is sensible given that they are not hot enough to radiate any significant amount of heat, and are not designed as thermal radiators at all - they are actually convectors, and painting them matt black would make virtually no difference to their efficacy. Acrylic and urethane based white paints have 93% blackbody radiation efficiency at room temperature[7] (meaning the term "black body" does not always correspond to the visually perceived color of an object). These materials that do not follow the "black color = high emissivity/absorptivity" caveat will most likely have functional spectral emissivity/absorptivity dependence.

Calculation of radiative heat transfer between groups of object, including a 'cavity' or 'surroundings' requires solution of a set of simultaneous equations using the Radiosity method. In these calculations, the geometrical configuration of the problem is distilled to a set of numbers called view factors, which give the proportion of radiation leaving any given surface that hits another specific surface. These calculations are important in the fields of solar thermal energy, boiler and furnace design and raytraced computer graphics.

A selective surface can be used when energy is being extracted from the sun. For instance, when a green house is made, most of the roof and walls are made out of glass. Glass is transparent in the visible (approximately 0.4 µm<λ<0.8 µm) and near-infrared wavelengths, but opaque to mid- to far-wavelength infrared (approximately λ>3 µm).[8][9] Therefore glass lets in radiation in the visible range, allowing us to be able to see through it, but doesn’t let out radiation that is emitted from objects at or close to room temperature. This traps what we feel as heat. This is known as the greenhouse effect and can be observed by getting into a car that has been sitting in the sun. Selective surfaces can also be used on solar collectors. We can find out how much help a selective surface coating is by looking at the equilibrium temperature of a plate that is being heated through solar radiation. If the plate is receiving a solar irradiation of 1350 W/m² (minimum is 1325 W/m² on July 4 and maximum is 1418 W/m² on January 3) from the sun the temperature of the plate where the radiation leaving is equal to the radiation being received by the plate is 393 K (248 °F). If the plate has a selective surface with an emissivity of 0.9 and a cut off wavelength of 2.0 µm, the equilibrium temperature is approximately 1250 K (1790 °F). Note that the calculations were made neglecting convective heat transfer and neglecting the solar irradiation absorbed in the clouds/atmosphere for simplicity, however, the theory is still the same for an actual problem. If we have a surface, such as a glass window, with which we would like to reduce the heat transfer from, a clear reflective film with a low emissivity coating can be placed on the interior of the wall. “Low-emittance (low-E) coatings are microscopically thin, virtually invisible, metal or metallic oxide layers deposited on a window or skylight glazing surface primarily to reduce the U-factor by suppressing radiative heat flow”.[10] By adding this coating we are limiting the amount of radiation that leaves the window thus increasing the amount of heat that is retained inside the window.

Radiative heat transfer[edit]

The radiative heat transfer from one surface to another is equal to the radiation entering the first surface from the other, minus the radiation leaving the first surface.

  • For a black body
 \dot{Q}_{1 \rightarrow 2} = A_{1}E_{b1}F_{1 \rightarrow 2} - A_{2}E_{b2}F_{2 \rightarrow 1}[8]

Using the reciprocity rule, A_{1}F_{1 \rightarrow 2} = A_{2}F_{2 \rightarrow 1} , this simplifies to:

 \dot{Q}_{1 \rightarrow 2} = \sigma A_{1}F_{1 \rightarrow 2}(T_1^4-T_2^4) \![8]

where \sigma is the Stefan–Boltzmann constant and F_{1 \rightarrow 2} is the view factor from surface 1 to surface 2.

  • For a grey body with only two surfaces the heat transfer is equal to:
 \dot{Q}= \dfrac{\sigma(T_1^4-T_2^4)}{\dfrac{1-\epsilon_1}{A_1\epsilon_1}+ \dfrac{1}{A_1F_{1 \rightarrow 2}}+ \dfrac{1-\epsilon_2}{A_2\epsilon_2}}

where \epsilon are the respective emissivities of each surface. However, this value can easily change for different circumstances and different equations should be used on a case per case basis.

Radiative power[edit]

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

u(\nu,T)=\frac{2 h\nu^3}{c^2}\cdot\frac1{e^{h\nu/k_BT}-1}

or in terms of wavelength


where \beta 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, E=h \nu, 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 \nu the power output given by the Stefan–Boltzmann law is obtained, as:

P = \sigma \cdot A \cdot T^4

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

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

\lambda_{max} = \frac{b}{T}

For surfaces which are not black bodies, one has to consider the (generally frequency dependent) emissivity factor \epsilon(\nu). 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 \epsilon as a factor:

P = \epsilon \cdot \sigma \cdot A \cdot T^4

This type of theoretical model, with frequency-independent emissivity lower than that of a perfect black body, is often known as a grey body. For frequency-dependent emissivity, the solution for the integrated power depends on the functional form of the dependence, though in general there is no simple expression for it. Practically speaking, if the emissivity of the body is roughly constant around the peak emission wavelength, the gray body model tends to work fairly well since the weight of the curve around the peak emission tends to dominate the integral.

The figure below shows Power emitted by a black body plotted against the temperature based on the Stefan–Boltzmann law.

Liquid nitrogen


Definitions of constants used in the above equations:

h \, Planck's constant 6.626 0693(11)×10−34 J·s = 4.135 667 43(35)×10−15 eV·s
b \, Wien's displacement constant 2.897 7685(51)×10−3 m·K
k_B \, Boltzmann constant 1.380 6505(24)×10−23 J·K−1 = 8.617 343(15)×10−5 eV·K−1
\sigma \, Stefan–Boltzmann constant 5.670 373(21)×10−8 W·m−2·K−4
c \, Speed of light 299,792,458 m·s−1


Definitions of variables, with example values:

T \, Absolute temperature For units used above, must be in kelvin (e.g. Average surface temperature on Earth = 288 K)
A \, Surface area Acuboid = 2ab + 2bc + 2ac;
Acylinder = 2π·r(h + r);
Asphere = 4π·r2

See also[edit]


  1. ^ K. Huang, Statistical Mechanics (2003), p.278
  2. ^ K. Huang, Statistical Mechanics (2003), p.280
  3. ^ S. Blundell, K. Blundell (2006). Concepts in Modern Physics. Oxford University Press. p. 247. ISBN 978-0-19-856769-1. 
  4. ^ The Physics of Coloured Fireworks
  5. ^ John J. Lentini - Scientific Protocols for Fire Investigation, CRC 2006, ISBN 0849320828, table from NFPA 921, Guide for Fire and Explosion Investigations
  6. ^ 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. 
  7. ^ S. Tanemura, M. Tazawa, P. Jing, T. Miki, K. Yoshimura, K. Igarashi, M. Ohishi, K. Shimono, M. Adachi, Optical Properties and Radiative Cooling Power of White Paints,[1] ISES 1999 Solar World Congress
  8. ^ a b c Heat and Mass Transfer, Yunus A. Cengel and Afshin J. Ghajar, 4th Edition
  9. ^ Infrared#Different regions in the infrared Short-wavelength infrared is 1.4-3µm, Mid-wavelength infrared is 3-8µm
  10. ^ The Efficient Windows Collaborative: Window Technologies

Further reading[edit]

External links[edit]