Spectral emissivity hemispherical

Integrating the energy emitted over all directions at a particular wavelength gives hemispherical-spectral emissivity. Hemispherical-Spectral Emissivity... 

Hemispherical spectral emissive power and total intensity... 

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. 

The hemispherical spectral emissive power MX, T) is obtained by integrating (5.4) over all the solid angles in the hemisphere. This yields... 

Fig. 5.6 Hemispherical spectral emissive power M (X,T) as a function of wavelength A at constant temperature T (schematic). The hatched area under the curve represents the emissive power M(T)...

The hemispherical spectral emissive power Mx(X,T) covers the wavelength dependency of the radiated energy in the entire hemisphere (hemispherical spectral quantity). 

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... 

The wavelength and temperature dependency given by (5.37) correspond to a relationship found by W. Wien [5.3] in 1896 to be approximately valid for the hemispherical spectral emissive power M S(X,T ) of an ideal radiator, a black body, with a temperature T. We will come back to the properties of black bodies in section 5.1.6 and more extensively in 5.2.2. In our example a spectral irradiance E M s has been assumed, so that its indirect dependence on T appears explicitly in (5.37). 

Hollow enclosure radiation and radiation of a black body (a x = 1) have identical properties. The black body radiates diffusely from (5.18) it holds for its hemispherical spectral emissive power 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... 

We refrain from deriving the equations for the spectral intensity and the hemispherical spectral emissive power of a black body, found by M. Planck [5.6], for... 

Fig. 5.23 Hemispherical spectral emissive power MXs(X,T) of a black body according to Planck s radiation law (5.50)...

Table 5.3 Hemispherical spectral emissive power of a black body divided by the fifth power of the temperature, according to (5.54) and fraction function F(0, AT) according to (5.60) as a function of the product AT...

The definitions of the four emissivities are brought together in Table 5.4. It additionally contains the relationships which are used in the calculation of the other three emissivities from the directional spectral emissivity a(A, / , f, T). This emissivity describes the directional and wavelength distributions of the emitted radiation flow, whilst the hemispherical spectral emissivity sx(X,T) only gives the spectral energy distribution. The directional total emissivity s (/3,f,T) only describes the distribution over the solid angles in the hemisphere. In contrast,... 

Fig. 5.30 Hemispherical spectral emissive power M (A, T) of a real body compared to the hemispherical spectral emissive power M g(A, T) of a black body at the same temperature. The hatched area represents the emissive power M(T) of the real body 0...

It holds for the hemispherical spectral emissive power of a real body that... 

If the hemispherical spectral absorptivity and emissivity shall agree, ax X,T) = sx(X,T), then according to Table 5.1 and 5.4 the equation... 

Fig. 5.31 Hemispherical spectral emissive power Mx(, T) = e(T) MXs(, T) of a grey Lambert radiator at a certain temperature...

Fig. 5.32 Approximately constant spectral emissivity for A > Ai as well as the pattern of the hemispherical spectral emissive power M and the spectral irradiance E, such that a grey radiator can be assumed...

Table 5.5 Hemispherical (spectral) emissivity ratio / n and refractive index n as...

Analogous to the hemispherical spectral emissivity of a solid, cf. Table 5.4, through... 

A radiator emits its maximum hemispherical spectral emissive power at Amax = 2.07 /im. Estimate its temperature T and its emissive power M(T), under the assumption that it radiates like a black body. 

The oven wall is exposed to radiation from glowing coal the spectral irradiance E can be assumed to be proportional to the hemispherical spectral emissive power M s(Tk) of a black body at Tk = 2000 K. 

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 ... 

A hemispherical spectral emissivity is a directional average of e e defined by ... 

This relation is known as Kirchhoff s law. Equation 7.27 may be substituted into the various relationships for the integrated emissivity or absorptivity. However, it does not follow that such quantities as directional total, hemispherical-spectral, or hemispherical total emissivity and absorptivity are necessarily equal. In fact, the integrated properties are only equal if certain restrictions are met. These are given in Table 7.1. 

The electric permeability given in Farads per metre (F/m) Net surface energy associated with surface tension (J/m s) Spectral, directional emissivity of a surface (—) Hemispherical, spectral emissivity of a surface (—)... 

FIG. 5-13 Hemispherical and normal emissivities of metals and their ratio. Dashed lines monochromatic (spectral) values versus r/X. Solid lines total values versus rT To convert ohm-centimeter-kelvins to ohm-meter-kelvins, multiply hy 10"l... 

Whilst the calculation of the radiant heat flux from a gas to an adjoining surface embraces inherent spectral and directional effects, a simplified approach has been developed by Hottel and Manglesdorf 54, which involves the determination of radiation emission from a hemispherical mass of gas of radius L, at temperature 7, ... 

The hemispherical emissive power E is defined as the radiant flux density (W/m2) associated with emission from an element of surface area dA into a surrounding unit hemisphere whose base is copla-nar with dA. If the monochromatic intensity ( 2, X) of emission from the surface is isotropic (independent of the angle of emission, 2), Eq. (5-101) may be integrated over the 2k sr of the surrounding unit hemisphere to yield the simple relation Ex = nix, where >, = Ex(X) is defined as the monochromatic or spectral hemispherical emissive power. 

FIG. 5-9 Spectral dependence of monochromatic blackbody hemispherical emissive power. 

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