Directional emissive power

Fig. 5.10 Intensity L = Ia(T) and directional emissive power I = In(T) cos (3 of a diffuse radiating surface...

If the emissive power E of a radiation source-that is the energy emitted per unit area per unit time-is expressed in terms of the radiation of a single wavelength X, then this is known as the monochromatic or spectral emissive power E, defined as that rate at which radiation of a particular wavelength X is emitted per unit surface area, per unit wavelength in all directions. For a black body at temperature T, the spectral emissive power of a wavelength X is given by Planck s Distribution Law ... 

Gmachl, C., Cappasso, F., Narimanov, E.E., Nockel, J.U., Stone, A.D., Faist, J., Sivco, D.L., and Cho, A.Y., 1998, High-power directional emission from microlasers with chaotic resonances. Science 280 1556-1564. 

Companies in the United States are increasingly concerned with the environmental effects of their energy consumption. In particular, more and more corporations are taking action to reduce their co2 emissions, both direct emissions from their on-site combustion of fossil fuels and indirect emissions from purchased electricity (that is, the co2 emitted by the power plants they buy power... 

Related Calculations. If the six surfaces are not black but gray (in the radiation sense), it is nominally necessary to set up and solve six simultaneous equations in six unknowns. In practice, however, the network can be simplified by combining two or more surfaces (the two smaller end walls, for instance) into one node. Once this is done and the configuration factors are calculated, the next step is to construct a radiosity network (since each surface is assumed diffuse, all energy leaving it is equally distributed directionally and can therefore be taken as the radiosity of the surface rather than its emissive power). Then, using standard mathematical network-solution techniques, create and solve an equivalent network with direct connections between nodes representing the surfaces. For details, see Oppenheim [8],... 

Heat capacity per unit mass, J kg 1-K 1 Shorthand notation for direct exchange area Area of enclosure or zone t, m2 Speed of light in vacuum, m/s Planck s first and second constants, W-m2 and m-K Particle diameter and radius, Jim Monochromatic, blackbody emissive power, W/(m2 lm)... 

Exponential integral of order n, where n = 1, 2,3,.. . Hemispherical emissive power, W/m2 Hemispherical blackbody emissive power, W/m2 Volumetric fraction of soot Blackbody fractional energy distribution Direct view factor from surface zone i to surface zonej Refractory augmented black view factor F-bar Total view factor from surface zone i to surface zonej Planck s constant, J s Heat-transfer coefficient, W/(m2 K)... 

An adiabatic refractory surface of area Ar and emissivity er, for which Qr = 0, proves quite important in practice. A nearly radiatively adiabatic refractory surface occurs when differences between internal conduction and convection and external heat losses through the refractory wall are small compared with the magnitude of the incident and leaving radiation fluxes. For any surface zone, the radiant flux is given by Q = A(W - H) = tA(E - H) and Q = eA/p( - W) (if p 0). These equations then lead to the result that if Qr = 0,Er = Hr = Wrfor all 0 < er< 1. Sufficient conditions for modeling an adiabatic refractory zone are thus either to put , = 0 or to specify directly that Q, = 0 with , 0. If er = 0, SrSj = 0 for all 1 < j < M which leads directly by definition to Qr = 0. For er = 0, the refractory emissive power Er never enters the zoning calculations. For the special case of 0 and Mr = 1, a sin-... 

Radiation is emitted by every point on a plane surface in all directions into the hemisphere above the surface, ITie quantity that describes the magnitude of radiation emitted or incident in a. specified direction in space is the radiation intensity. Various radiation flu.xes such as emissive power, irradiation, and ra-diosity are expressed in terms of intensity. This is followed by a discussion of radiative propertie.s of materials such as emissivity, absoiptivity, reflectivity, and transmissivity and their dependence on wavelength, direction, and lemperatiire. The greenlioiijie effect is presented as an example- of the con.sequenccs of the wavelength dependence of radiation properties. We end tliis chapter with a dis cussion of attno.spheric and solar radiation. 

If all surfaces emitted radiation uniformly in all directions, the emissive power would be sufficient to quantify radiation, and we would not need to deal with intensity. The radiation emitted by a blackbody pet unit nonnal area is the same in all directions, and thus there is no directional dependence. But this is not the case for real surfaces. Before we define intensity, wc need to quantify the size of an opening in space. 

In practice, it is usually more convenient to work with radiation properties averaged over all directions, called hemispherical properties. Noting that the integral of the rate of radiation energy emitted at a specified wavelength per unit surface area over the entire hemisphere is spectral emissive power, the spectral hemispherical emissivity can be expressed as... 

The magnitude of a viewing angle in space is de.scrlbed by solid angle expressed as do dAJr. The radiation intensity for emitted radiation (f>) is defined as the rate at which ra dialion energy is emitted in the (, tf>) direction per unit area normal to this direction and per unit solid angle about this direction. The radiation flux for emilted radiation is the emissive power E, and is expressed as... 

The direction of the net radiation heat transfer depends on the relative magnitudes of 7, (the radiosity) and (, (the emissive power of a blackbody at the teinpeiature of the surface). It is from the surface if > 7,- and to the surface if 7f > ft),-. A negative value for ft indicates that heat transfer is to the surface. All of this radiation energy gained must be removed from the other side of the surface through some mechanism if the surface temperature is to remain constant. 

Consider radiative interchange between two finite black surface area elements Ai and A2 separated by a transparent medium. Since they are black, the surfaces emit isotropically and totally absorb all incident radiant energy. It is desired to compute the fraction of radiant energy, per unit emissive power 1, leaving Ai in all directions which is intercepted and absorbed by A2. The required quantity is defined as the direct view factor and is assigned the notation F12. Since the net radiant energy interchange Q12 = AiFi jEi between surfaces... 

The spectral intensity Lx(X,f3,p,T) characterises in a detailed way the dependence of the energy emitted on the wavelength and direction. An important task of both theoretical and experimental investigations is to determine this distribution function for as many materials as possible. This is a difficult task to carry out, and it is normally satisfactory to just determine the radiation quantities that either combine the emissions into all directions of the hemisphere or the radiation over all wavelengths. The quantities, the hemispherical spectral emissive power Mx and the total intensity L, characterise the distribution of the radiative flux over the wavelengths or the directions in the hemisphere. 

Here d2radiation flow emitted by the surface element into the solid angle element dee in the direction of the angle /3 and total intensity L has units W/m2sr it belongs to the directional total quantities and represents the part of the emissive power falling into a certain solid angle element. 

No radiator exists that has a spectral intensity Lx independent of the wave length. However, the assumption that Lx does not depend on j3 and ip applies in many cases as a useful approximation. Bodies with spectral intensities independent of direction, Lx = Lx(X,T), are known as diffuse radiators or as bodies with diffuse radiating surfaces. According to (5.9), for their hemispherical spectral emissive power it follows that... 

A black body is defined as a body where all the incident radiation penetrates it and is completely absorbed within it. No radiation is reflected or allowed to pass through it. This holds for radiation of all wavelengths falling onto the body from all angles. In addition to this the black body is a diffuse radiator. Its spectral intensity LXs does not depend on direction, but is a universal function iAs(A,T) of the wavelength and the thermodynamic temperature. The hemispherical spectral emissive power MXs(X,T) is linked to Kirchhoff s function LXs(X,T) by the simple relationship... 

A smooth, polished platinum surface emits radiation with an emissive power of M = 1.64 kW/m2. Using the simplified electromagnetic theory determine its temperature T, the hemispherical total emissivity s and the total emissivity s n in the direction of the surface normal. The specific electrical resistance of platinum may be calculated according... 

The concept of emissive power is used to quantify the amount of radiation emitted per unit surface area. The hemispherical spectral emissive power E is defined as the rate at which radiation of wavelength A is emitted in all directions from a surface per unit wavelength dX about A and per unit surface area. It is thus related to the spectral intensity of the emitted radiation by ... 

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