Thermal radiation

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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. Wiens law.svg
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.
Thermal radiation in visible light can be seen on this hot metalwork. Its emission in the infrared is invisible to the human eye. Infrared cameras are capable of capturing this infrared emission (see Thermography). Hot metalwork.jpg
Thermal radiation in visible light can be seen on this hot metalwork. Its emission in the infrared is invisible to the human eye. Infrared cameras are capable of capturing this infrared emission (see Thermography).

Thermal radiation is electromagnetic radiation generated by the thermal motion of particles in matter. All matter with a temperature greater than absolute zero emits thermal radiation. Particle motion results in charge-acceleration or dipole oscillation which produces electromagnetic radiation.

Electromagnetic radiation form of energy emitted and absorbed by charged particles, which exhibits wave-like behavior as it travels through space

In physics, electromagnetic radiation refers to the waves of the electromagnetic field, propagating (radiating) through space, carrying electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) light, ultraviolet, X-rays, and gamma rays.

Matter substance that has rest mass and volume, or several other definitions

In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic particles, and in everyday as well as scientific usage, "matter" generally includes atoms and anything made up of them, and any particles that act as if they have both rest mass and volume. However it does not include massless particles such as photons, or other energy phenomena or waves such as light or sound. Matter exists in various states. These include classical everyday phases such as solid, liquid, and gas – for example water exists as ice, liquid water, and gaseous steam – but other states are possible, including plasma, Bose–Einstein condensates, fermionic condensates, and quark–gluon plasma.

Temperature physical property of matter that quantitatively expresses the common notions of hot and cold

Temperature is a physical quantity expressing hot and cold. It is measured with a thermometer calibrated in one or more temperature scales. The most commonly used scales are the Celsius scale, Fahrenheit scale, and Kelvin scale. The kelvin is the unit of temperature in the International System of Units (SI), in which temperature is one of the seven fundamental base quantities. The Kelvin scale is widely used in science and technology.

Contents

The infrared radiation emitted by animals that is detectable with an infrared camera, and the cosmic microwave background radiation, are all examples of thermal radiation.

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 solely 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]

Black body idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence; in thermal equilibrium has an emissivity of ε = 1.0

A black body or blackbody is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. A white body is one with a "rough surface [that] reflects all incident rays completely and uniformly in all directions."

Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems. In a system in its own state of internal thermodynamic equilibrium, no macroscopic change occurs. Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, almost or perfectly exactly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium.

Black-body radiation thermal electromagnetic radiation

Black-body radiation is the thermal electromagnetic radiation within or surrounding a body in thermodynamic equilibrium with its environment, emitted by a black body. It has a specific spectrum and intensity that depends only on the body's temperature, which is assumed for the sake of calculations and theory to be uniform and constant.

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

Heat transfer transport of thermal energy in physical systems

Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes. Engineers also consider the transfer of mass of differing chemical species, either cold or hot, to achieve heat transfer. While these mechanisms have distinct characteristics, they often occur simultaneously in the same system.

Overview

Thermal radiation, also known as heat, is the emission of electromagnetic waves from all matter that has a temperature greater than absolute zero. [3] It represents the conversion of thermal energy into electromagnetic energy. Thermal energy consists of the kinetic energy of 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.

Absolute zero coldest possible temperature

Absolute zero is the lowest limit of the thermodynamic temperature scale, a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as 0. The fundamental particles of nature have minimum vibrational motion, retaining only quantum mechanical, zero-point energy-induced particle motion. The theoretical temperature is determined by extrapolating the ideal gas law; by international agreement, absolute zero is taken as −273.15° on the Celsius scale, which equals −459.67° on the Fahrenheit scale. The corresponding Kelvin and Rankine temperature scales set their zero points at absolute zero by definition.

Thermal energy internal energy present in a system due to its temperature; is not a state function

Thermal energy can refer to several distinct thermodynamic quantities, such as the internal energy of a system; heat or sensible heat, which are defined as types of transfer of energy ; or for the characteristic energy of a degree of freedom in a thermal system , where is temperature and is the Boltzmann constant.

Proton nucleon (constituent of the nucleus of the atom) that has positive electric charge; symbol p

A proton is a subatomic particle, symbol
p
or
p+
, with a positive electric charge of +1e elementary charge and a mass slightly less than that of a neutron. Protons and neutrons, each with masses of approximately one atomic mass unit, are collectively referred to as "nucleons".

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. [3] The radiation is not monochromatic, i.e., it does not consist of just a single frequency, but comprises a continuous dispersion of photon energies, its characteristic spectrum. If the radiating body and its surface are in thermodynamic equilibrium and the surface has perfect absorptivity at all wavelengths, it is characterized as a black body. A black body is also a perfect emitter. The radiation of such perfect emitters is called black-body radiation. The ratio of any body's emission relative to that of a black body is the body's emissivity, so that a black body has an emissivity of unity.

Absorptance of the surface of a material is its effectiveness in absorbing radiant energy. It is the ratio of the absorbed to the incident radiant power. This should not be confused with absorbance and absorption coefficient.

Kirchhoffs law of thermal radiation Law of wavelength-specific emission and absorption

In heat transfer, Kirchhoff's law of thermal radiation refers to wavelength-specific radiative emission and absorption by a material body in thermodynamic equilibrium, including radiative exchange equilibrium.

Emissivity

The emissivity of the surface of a material is its effectiveness in emitting energy as thermal radiation. Thermal radiation is electromagnetic radiation and it may include both visible radiation (light) and infrared radiation, which is not visible to human eyes. The thermal radiation from very hot objects is easily visible to the eye. Quantitatively, emissivity is the ratio of the thermal radiation from a surface to the radiation from an ideal black surface at the same temperature as given by the Stefan–Boltzmann law. The ratio varies from 0 to 1. The surface of a perfect black body emits thermal radiation at the rate of approximately 448 watts per square metre at room temperature ; all real objects have emissivities less than 1.0, and emit radiation at correspondingly lower rates.

Spectral response of two paints and a mirrored surface, in the visible and the infrared. From NASA. ThermalPaint.png
Spectral response of two paints and a mirrored surface, in the visible and the infrared. From NASA.

Absorptivity, reflectivity, and emissivity of all bodies are dependent on the wavelength of the radiation. Due to reciprocity, absorptivity and emissivity for any particular wavelength are equal – a good absorber is necessarily a good emitter, and a poor absorber a poor emitter. The temperature determines the wavelength distribution of the electromagnetic radiation. For example, the white paint in the diagram to the right is highly reflective to visible light (reflectivity about 0.80), and so appears white to the human eye due to reflecting sunlight, which has a peak wavelength of about 0.5 micrometers. However, its emissivity at a temperature of about −5 °C (23 °F), peak wavelength of about 12 micrometers, is 0.95. Thus, to thermal radiation it appears black.

The distribution of power that a black body emits with varying frequency is described by Planck's law. At any given temperature, there is a frequency fmax at which the power emitted is a maximum. Wien's displacement law, and the fact that the frequency is inversely proportional to the wavelength, indicates that the peak frequency fmax is proportional to the absolute temperature T of the black body. The photosphere of the sun, at a temperature of approximately 6000 K, emits radiation principally in the (humanly) visible portion of the electromagnetic spectrum. Earth's atmosphere is partly transparent to visible light, and the light reaching the surface is absorbed or reflected. Earth's surface emits the absorbed radiation, approximating the behavior of a black body at 300 K with spectral peak at fmax. At these lower frequencies, the atmosphere is largely opaque and radiation from Earth's surface is absorbed or scattered by the atmosphere. Though about 10% of this radiation escapes into space, most is absorbed and then re-emitted by atmospheric gases. It is this spectral selectivity of the atmosphere that is responsible for the planetary greenhouse effect, contributing to global warming and climate change in general (but also critically contributing to climate stability when the composition and properties of the atmosphere are not changing).

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.

Unlike conductive and convective forms of heat transfer, thermal radiation can be concentrated in a tiny spot by using reflecting mirrors. Concentrating solar power takes advantage of this fact. In many such systems, mirrors are employed to concentrate sunlight into a smaller area. Instead of mirrors, Fresnel lenses can also be used to concentrate heat flux. (In principle, any kind of lens can be used, but only the Fresnel lens design is practical for very large lenses.) Either method can be used to quickly vaporize water into steam using sunlight. For example, the sunlight reflected from mirrors heats the PS10 Solar Power Plant, and during the day it can heat water to 285 °C (558.15 K) or 545 °F.

Surface effects

Lighter colors and also whites and metallic substances absorb less illuminating light, and thus heat up less; but otherwise color makes small difference as regards heat transfer between an object at everyday temperatures and its surroundings, since the dominant emitted wavelengths are nowhere near the visible spectrum, but rather in the far infrared. Emissivities at those wavelengths have little to do with visual emissivities (visible colors); in the far infra-red, most objects have high emissivities. Thus, except in sunlight, the color of clothing makes little difference as regards warmth; likewise, paint color of houses makes little difference to warmth except when the painted part is sunlit.

The main exception to this is shiny metal surfaces, which have low emissivities both in the visible wavelengths and in the far infrared. Such surfaces can be used to reduce heat transfer in both directions; an example of this is the multi-layer insulation used to insulate spacecraft.

Low-emissivity windows in houses are a more complicated technology, since they must have low emissivity at thermal wavelengths while remaining transparent to visible light.

Nanostructures with spectrally selective thermal emittance properties offer numerous technological applications for energy generation and efficiency, [4] 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. [5]

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 infrared radiation, which provides an additional cooling mechanism. Most conventional fabrics are opaque to infrared radiation and block thermal emission from the body to the environment. Fabrics for personalized cooling applications have been proposed that enable infrared 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.[ citation needed ]

Properties

There are four main properties that characterize thermal radiation (in the limit of the far field):

Near-field and far-field

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. [6]

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. [4] 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. [7] 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.

Subjective color to the eye of a black body thermal radiator

°C (°F)Subjective color [8]
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

The time to a damage from exposure to radiative heat is a function of the rate of delivery of the heat. [9] Radiative heat flux and effects: [10] (1 W/cm2 = 10 kW/m2)

kW/m2Effect
170Maximum flux measured in a post-flashover compartment
80Thermal Protective Performance test for personal protective equipment
52 Fiberboard ignites at 5 seconds
29 Wood ignites, given time
20Typical 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
10.4Human skin: Pain after 3 seconds, second-degree burn blisters after 9 seconds
6.4Human skin: second-degree burn blisters after 18 seconds
4.5Human skin: second-degree burn blisters after 30 seconds
2.5Human skin: burns after prolonged exposure, radiant flux exposure typically encountered during firefighting
1.4 Sunlight, sunburns potentially within 30 minutes. Note sunburn is NOT a thermal burn, it is caused by DNA damage due to ultraviolet radiation.

Interchange of energy

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

Thermal radiation is one of the three 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:

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:

In a practical situation and room-temperature setting, humans lose considerable energy due to thermal radiation in infra-red in addition to that lost by conduction to air (aided by concurrent convection, or other air movement like drafts). The heat energy lost is partially regained by absorbing heat radiation from walls or other surroundings. (Heat gained by conduction would occur for air temperature higher than body temperature.) Otherwise, body temperature is maintained from generated heat through internal metabolism. Human skin has an emissivity of very close to 1.0. [11] 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. 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 almost 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 close to real solutions, as most divergence from Stefan-Boltzmann solutions is very small (especially in most STP lab controlled environments).

Spectral response of two paints and a mirrored surface, in the visible and the infrared. From NASA. ThermalPaint.png
Spectral response of two paints and a mirrored surface, in the visible and the infrared. From NASA.

If objects appear white (reflective in the visual spectrum), they are not necessarily equally reflective (and thus non-emissive) in the thermal infrared – see the diagram at the left. Most household radiators are painted white, which 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 – instead, they are actually convectors, and painting them matt black would make little difference to their efficacy. Acrylic and urethane based white paints have 93% blackbody radiation efficiency at room temperature [12] (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.

Human-Infrared.jpg
Human-Visible.jpg
A comparison of a thermal image (top) and an ordinary photograph (bottom) shows that a trash bag is transparent, but glass (the man's spectacles) is opaque in long-wavelength infrared.

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). [13] [14] Therefore, glass lets in radiation in the visible range, allowing us to be able to see through it, but does not 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.[ citation needed ] 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). The calculations were made neglecting convective heat transfer and neglecting the solar irradiation absorbed in the clouds/atmosphere for simplicity, the theory is still the same for an actual problem.

To reduce the heat transfer from a surface, such as a glass window, a clear reflective film with a low emissivity coating can be placed on the interior of the surface. “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”. [15] 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.

Since any electromagnetic radiation, including thermal radiation, conveys momentum as well as energy, thermal radiation also induces very small forces on the radiating or absorbing objects. Normally these forces are negligible, but they must be taken into account when considering spacecraft navigation. The Pioneer anomaly, where the motion of the craft slightly deviated from that expected from gravity alone, was eventually tracked down to asymmetric thermal radiation from the spacecraft. Similarly, the orbits of asteroids are perturbed since the asteroid absorbs solar radiation on the side facing the sun, but then re-emits the energy at a different angle as the rotation of the asteroid carries the warm surface out of the sun's view (the YORP effect).

Radiative power

Power emitted by a black body plotted against the temperature according to the Stefan-Boltzmann law. Emissive Power.svg
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 instead of per unit frequency, per unit wavelength as

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. Plancks law shows that radiative energy increases with temperature, and explains why the peak of an emission spectrum shifts to shorter wavelengths at higher temperatures. It can also be found that energy emitted at shorter wavelengths increases more rapidly with temperature relative to longer wavelengths. [16] The equation is derived as an infinite sum over all possible frequencies in a semi-sphere region. 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:

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.

Constants

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
Stefan–Boltzmann constant 5.670 373 (21)×10−8 W·m−2·K−4
Speed of light 299 792 458 m·s−1

Variables

Definitions of variables, with example values:

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

Radiative heat transfer

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.

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. [13] A negative value for indicates that net radiation heat transfer is from surface 2 to surface 1.

where and are the emissivities of the surfaces. [13]

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. [13]

See also

Related Research Articles

Infrared electromagnetic radiation with longer wavelengths than those of visible light

Infrared radiation (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with longer wavelengths than those of visible light, and is therefore generally invisible to the human eye, although IR at wavelengths up to 1050 nanometers (nm)s from specially pulsed lasers can be seen by humans under certain conditions. IR wavelengths extend from the nominal red edge of the visible spectrum at 700 nanometers, to 1 millimeter (300 GHz). Most of the thermal radiation emitted by objects near room temperature is infrared. As with all EMR, IR carries radiant energy and behaves both like a wave and like its quantum particle, the photon.

Radiation Waves or particles propagating through space or through a medium, carrying energy

In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or through a material medium. This includes:

Wiens displacement law

Wien's displacement law states that the black-body radiation curve for different temperatures will peak at different wavelengths that are inversely proportional to the temperature. The shift of that peak is a direct consequence of the Planck radiation law, which describes the spectral brightness of black-body radiation as a function of wavelength at any given temperature. However, it had been discovered by Wilhelm Wien several years before Max Planck developed that more general equation, and describes the entire shift of the spectrum of black-body radiation toward shorter wavelengths as temperature increases.

Brightness temperature or radiance temperature is the temperature a black body in thermal equilibrium with its surroundings would have to be to duplicate the observed intensity of a grey body object at a frequency . This concept is used in radio astronomy, planetary science and materials science.

Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T, when there is no net flow of matter or energy between the body and its environment.

Thermography infrared imaging

Infrared thermography (IRT), thermal imaging, and thermal video are examples of infrared imaging science. Thermographic cameras usually detect radiation in the long-infrared range of the electromagnetic spectrum and produce images of that radiation, called thermograms. Since infrared radiation is emitted by all objects with a temperature above absolute zero according to the black body radiation law, thermography makes it possible to see one's environment with or without visible illumination. The amount of radiation emitted by an object increases with temperature; therefore, thermography allows one to see variations in temperature. When viewed through a thermal imaging camera, warm objects stand out well against cooler backgrounds; humans and other warm-blooded animals become easily visible against the environment, day or night. As a result, thermography is particularly useful to the military and other users of surveillance cameras.

In radiometry, radiant exitance or radiant emittance is the radiant flux emitted by a surface per unit area, whereas spectral exitance or spectral emittance is the radiant exitance of a surface per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. This is the emitted component of radiosity. The SI unit of radiant exitance is the watt per square metre, while that of spectral exitance in frequency is the watt per square metre per hertz (W·m−2·Hz−1) and that of spectral exitance in wavelength is the watt per square metre per metre (W·m−3)—commonly the watt per square metre per nanometre. The CGS unit erg per square centimeter per second is often used in astronomy. Radiant exitance is often called "intensity" in branches of physics other than radiometry, but in radiometry this usage leads to confusion with radiant intensity.

Wien approximation

Wien's approximation is a law of physics used to describe the spectrum of thermal radiation. This law was first derived by Wilhelm Wien in 1896. The equation does accurately describe the short wavelength spectrum of thermal emission from objects, but it fails to accurately fit the experimental data for long wavelengths emission.

In radiometry, radiosity is the radiant flux leaving a surface per unit area, and spectral radiosity is the radiosity of a surface per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. The SI unit of radiosity is the watt per square metre, while that of spectral radiosity in frequency is the watt per square metre per hertz (W·m−2·Hz−1) and that of spectral radiosity in wavelength is the watt per square metre per metre (W·m−3)—commonly the watt per square metre per nanometre. The CGS unit erg per square centimeter per second is often used in astronomy. Radiosity is often called intensity in branches of physics other than radiometry, but in radiometry this usage leads to confusion with radiant intensity.

The surface of the Sun radiates light and heat at approximately 5,500 °C. The Earth is much cooler and so radiates heat back away from itself at much longer wavelengths, mostly in the infrared range. The idealized greenhouse model is based on the fact that certain gases in the Earth's atmosphere, including carbon dioxide and water vapour, are transparent to the high-frequency, high-energy solar radiation, but are much more opaque to the lower frequency infrared radiation leaving the surface of the earth. Thus heat is easily let in, but is partially trapped by these gases as it tries to leave. Rather than get hotter and hotter, Kirchhoff's law of thermal radiation says that the gases of the atmosphere also have to re-emit the infrared energy that they absorb, and they do so, also at long infrared wavelengths, both upwards into space as well as downwards back towards the Earth's surface. In the long-term, thermal equilibrium is reached when all the heat energy arriving on the planet is leaving again at the same rate. In this idealized model, the greenhouse gases cause the surface of the planet to be warmer than it would be without them, in order for the required amount of heat energy finally to be radiated out into space from the top of the atmosphere.

Radiation properties

Conduction and convection are heat transfer processes that require the presence of a medium. Radiation heat transfer is characteristically different from the other two in that it does not require a medium and, in fact it reaches maximum efficiency in a vacuum. Electromagnetic radiation has some proper characteristics depending on the frequency and wavelengths of the radiation. The phenomenon of radiation is not yet fully understood. Two theories have been used to explain radiation; however neither of them is perfectly satisfactory.

The Gebhart factors are used in radiative heat transfer, it is a means to describe the ratio of radiation absorbed by any other surface versus the total emitted radiation from given surface. As such, it becomes the radiation exchange factor between a number of surfaces. The Gebhart factors calculation method is supported in several radiation heat transfer tools, such as TMG and TRNSYS.

Non-ionizing radiation electromagnetic radiation that does not carry enough energy per quantum to ionize atoms or molecules

Non-ionizingradiation refers to any type of electromagnetic radiation that does not carry enough energy per quantum to ionize atoms or molecules—that is, to completely remove an electron from an atom or molecule. Instead of producing charged ions when passing through matter, non-ionizing electromagnetic radiation has sufficient energy only for excitation, the movement of an electron to a higher energy state. Ionizing radiation which has a higher frequency and shorter wavelength than nonionizing radiation, has many uses but can be a health hazard; exposure to it can cause burns, radiation sickness, cancer, and genetic damage. Using ionizing radiation requires elaborate radiological protection measures which in general are not required with nonionizing radiation.

The planetary equilibrium temperature is a theoretical temperature that a planet would be at when considered simply as if it were a black body being heated only by its parent star. In this model, the presence or absence of an atmosphere is not considered, and one treats the theoretical black body temperature as if it came from an idealized surface of the planet.

The “radiation effect” results from radiation heat exchange between human bodies and surrounding surfaces, such as walls and ceilings. It may lead to phenomena such as houses feeling cooler in the winter and warmer in the summer at the same temperature. For example, in a room in which air temperature is maintained at 22° Celsius at all times, but in which the inner surfaces of the house is estimated to be an average temperature of 10° Celsius in the winter or 25° Celsius in the summer, heat transfer from the surfaces to the individual will occur, resulting in a difference in the perceived temperature.

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Further reading

Thermal Infrared Remote Sensing: